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• Atomic Mass Of Hydrogen 3
• Atomic Mass Of Hydrogen 1 2 And 3

Atomic Spectra

Isotopes of Hydrogen: Natural Abundance Protium (hydrogen-1) has an atomic mass of 1.00782504, and is a stable isotope. It has one proton and no neutrons. Protium is also known as ordinary hydrogen. Atomic Mass of Hydrogen Atomic mass of Hydrogen is 1.0079 u. The atomic mass of hydrogen is 1 g/mole. To make up 1 kilogram or 1000 g of hydrogen element, 1000 moles of hydrogen is required. Each mole has a Avogadro's number of atoms or atoms. Thus, 1 kg hydrogen element or 1000 moles of hydrogen have atoms (or 1000 times the Avogadro's number).

When gaseous hydrogen in a glass tube is excited by a (5000)-volt electrical discharge, four lines are observed in the visible part of the emission spectrum: red at (656.3) nm, blue-green at (486.1) nm, blue violet at (434.1) nm and violet at (410.2) nm:

Other series of lines have been observed in the ultraviolet and infrared regions. Rydberg (1890) found that all the lines of the atomic hydrogen spectrum could be fitted to a single formula

[ dfrac{1}{lambda} = mathcal{R} left( dfrac{1}{n_1^{2}} - dfrac{1}{n_2^{2}} right), quad n_1 = 1, : 2, : 3..., : n_2 > n_1 label{1}]

where (mathcal{R}), known as the Rydberg constant, has the value (109,677) cm^-1 for hydrogen. The reciprocal of wavelength, in units of cm^-1, is in general use by spectroscopists. This unit is also designated wavenumbers, since it represents the number of wavelengths per cm. The Balmer series of spectral lines in the visible region, shown in Figure (PageIndex{1}) , correspond to the values (n_1 = 2, : n_2 = 3, : 4, : 5) and (6). The lines with (n_1 = 1) in the ultraviolet make up the Lyman series. The line with (n_2 = 2), designated the Lyman alpha, has the longest wavelength (lowest wavenumber) in this series, with (1/ lambda = 82.258) cm^-1 or (lambda = 121.57) nm.

Other atomic species have line spectra, which can be used as a 'fingerprint' to identify the element. However, no atom other than hydrogen has a simple relation analogous to Equation (ref{1}) for its spectral frequencies. Bohr in 1913 proposed that all atomic spectral lines arise from transitions between discrete energy levels, giving a photon such that

[ Delta E = h nu = dfrac{hc}{lambda} label{2}]

This is called the Bohr frequency condition. We now understand that the atomic transition energy (Delta E) is equal to the energy of a photon, as proposed earlier by Planck and Einstein.

The Bohr Atom

The nuclear model proposed by Rutherford in 1911 pictures the atom as a heavy, positively-charged nucleus, around which much lighter, negatively-charged electrons circulate, much like planets in the Solar system. This model is however completely untenable from the standpoint of classical electromagnetic theory, for an accelerating electron (circular motion represents an acceleration) should radiate away its energy. In fact, a hydrogen atom should exist for no longer than (5 times 10^{-11}) sec, time enough for the electron's death spiral into the nucleus. This is one of the worst quantitative predictions in the history of physics. It has been called the Hindenberg disaster on an atomic level. (Recall that the Hindenberg, a hydrogen-filled dirigible, crashed and burned in a famous disaster in 1937.)

Bohr sought to avoid an atomic catastrophe by proposing that certain orbits of the electron around the nucleus could be exempted from classical electrodynamics and remain stable. The Bohr model was quantitatively successful for the hydrogen atom, as we shall now show.

We recall that the attraction between two opposite charges, such as the electron and proton, is given by Coulomb's law

[F = begin{cases} -dfrac{e^{2}}{r^{2}} quad mathsf{(gaussian : units)} -dfrac{e^{2}}{4 pi epsilon_0 r^{2}} quad mathsf{(SI : units)} end{cases} label{3}]

We prefer to use the Gaussian system in applications to atomic phenomena. Since the Coulomb attraction is a central force (dependent only on r), the potential energy is related by

[F = -dfrac{dV(r)}{dr} label{4}]

We find therefore, for the mutual potential energy of a proton and electron,

[V(r) = -dfrac{e^2}{r} label{5}]

Bohr considered an electron in a circular orbit of radius (r) around the proton. To remain in this orbit, the electron must be experiencing a centripetal acceleration

[a = -dfrac{v^{2}}{r} label{6}]

where (v) is the speed of the electron. Using Equations (ref{4}) and (ref{6}) in Newton's second law, we find

[dfrac{e^{2}}{r^{2}} = dfrac{mv^{2}}{r} label{7}]

where (m) is the mass of the electron. For simplicity, we assume that the proton mass is infinite (actually (m_p approx 1836 m_e)) so that the proton's position remains fixed. We will later correct for this approximation by introducing reduced mass. The energy of the hydrogen atom is the sum of the kinetic and potential energies:

[E = T + V = dfrac{1}{2} mv^{2} - dfrac{e^{2}}{r} label{8}]

Using Equation (ref{7}) , we see that

[T = -dfrac{1}{2} V qquad mathsf{and} qquad E = dfrac{1}{2} V = -T label{9}]

This is the form of the virial theorem for a force law varying as (r^{-2}). Note that the energy of a bound atom is negative, since it is lower than the energy of the separated electron and proton, which is taken to be zero.

For further progress, we need some restriction on the possible values of (r) or (v). This is where we can introduce the quantization of angular momentum (mathbf{L} = mathbf{r} times mathbf{p}). Since (mathbf{p}) is perpendicular to (mathbf{r}), we can write simply

[L = rp = mvr label{10}]

Using Equation (ref{9}), we find also that

[r = dfrac{L^{2}}{me^{2}} label{11}]

We introduce angular momentum quantization, writing

[L = nhbar, qquad n = 1, : 2... label{12}]

excluding (n = 0), since the electron would then not be in a circular orbit. The allowed orbital radii are then given by

[r_n = n^{2} a_0 label{13}]

where

[a_0 equiv dfrac{hbar^{2}}{me^{2}} = 5.29 times 10^{-11} : mathsf{m} = 0.529Å label{14}]

which is known as the Bohr radius. The corresponding energy is

[E_n = -dfrac{e^{2}}{2a_0n^{2}} = -dfrac{me^{4}}{2hbar^{2}n^{2}}, qquad n = 1, : 2... label{15}]

Rydberg's formula (Equation (ref{1})) can now be deduced from the Bohr model. We have

[ dfrac{hc}{lambda} = E_{n_2} - E_{n_1} = dfrac{2pi^{2}me^{4}}{h^{2}} left( dfrac{1}{n_1^{2}} - dfrac{1}{n_2^{2}} right) label{16}]

and the Rydbeg constant can be identified as

[mathcal{R} = dfrac{2pi^{2}me^{4}}{h^{3}c} approx 109,737 : mathsf{cm}^{-1} label{17}]

The slight discrepency with the experimental value for hydrogen ( (109,677) ) is due to the finite proton mass. This will be corrected later.

The Bohr model can be readily extended to hydrogenlike ions, systems in which a single electron orbits a nucleus of arbitrary atomic number (Z). Thus (Z = 1) for hydrogen, (Z = 2) for (mathsf{He}^{+}), (Z = 3) for (mathsf{Li}^{++}), and so on. The Coulomb potential (ref{5}) generalizes to

[V(r) = -dfrac{Ze^{2}}{r}, label{18}]

the radius of the orbit (Equation (ref{13})) becomes

[r_n = dfrac{n^{2}a_0}{Z} label{19}]

and the energy Equation (ref{15}) becomes

[E_n = -dfrac{Z^{2}e^{2}}{2a_0n^{2}} label{20}]

De Broglie's proposal that electrons can have wavelike properties was actually inspired by the Bohr atomic model. Since

[L = rp = nhbar = dfrac{nh}{2pi} label{21}]

we find

[2pi r = dfrac{nh}{p} = nlambda label{22}]

Therefore, each allowed orbit traces out an integral number of de Broglie wavelengths.

Wilson (1915) and Sommerfeld (1916) generalized Bohr's formula for the allowed orbits to

[oint p , dr = nh, qquad n =1, : 2... label{23}]

The Sommerfeld-Wilson quantum conditions Equation (ref{23}) reduce to Bohr's results for circular orbits, but allow, in addition, elliptical orbits along which the momentum (p) is variable. According to Kepler's first law of planetary motion, the orbits of planets are ellipses with the Sun at one focus. Figure (PageIndex{2}) shows the generalization of the Bohr theory for hydrogen, including the elliptical orbits. The lowest energy state (n = 1) is still a circular orbit. But (n = 2) allows an elliptical orbit in addition to the circular one; (n = 3) has three possible orbits, and so on. The energy still depends on (n) alone, so that the elliptical orbits represent degenerate states. Atomic spectroscopy shows in fact that energy levels with (n > 1) consist of multiple states, as implied by the splitting of atomic lines by an electric field (Stark effect) or a magnetic field (Zeeman effect). Some of these generalized orbits are drawn schematically in Figure (PageIndex{2}).

The Bohr model was an important first step in the historical development of quantum mechanics. It introduced the quantization of atomic energy levels and gave quantitative agreement with the atomic hydrogen spectrum. With the Sommerfeld-Wilson generalization, it accounted as well for the degeneracy of hydrogen energy levels. Although the Bohr model was able to sidestep the atomic 'Hindenberg disaster,' it cannot avoid what we might call the 'Heisenberg disaster.' By this we mean that the assumption of well-defined electronic orbits around a nucleus is completely contrary to the basic premises of quantum mechanics. Another flaw in the Bohr picture is that the angular momenta are all too large by one unit, for example, the ground state actually has zero orbital angular momentum (rather than (hbar)).

The assumption of well-defined electronic orbits around a nucleus in the Bohr atom is completely contrary to the basic premises of quantum mechanics.

Quantum Mechanics of Hydrogenlike Atoms

In contrast to the particle in a box and the harmonic oscillator, the hydrogen atom is a real physical system that can be treated exactly by quantum mechanics. In addition to their inherent significance, these solutions suggest prototypes for atomic orbitals used in approximate treatments of complex atoms and molecules.

For an electron in the field of a nucleus of charge (+Ze), the Schrӧdinger equation can be written

[left{ -dfrac{hbar^{2}}{2m} nabla^{2} - dfrac{Ze^{2}}{r} right} psi(r) = Epsi(r) label{24}]

It is convenient to introduce atomic units in which length is measured in bohrs:

[a_0 = dfrac{hbar^{2}}{me^{2}} = 5.29 times 10^{-11} : mathsf{m} equiv 1 : mathsf{bohr} ]

and energy in hartrees:

[dfrac{e^2}{a_0} = 4.358 times 10^{-18} : mathsf{J} = 27.211 : mathsf{eV} equiv 1 : mathsf{hartree} ]

Electron volts ((mathsf{eV})) are a convenient unit for atomic energies. One (mathsf{eV}) is defined as the energy an electron gains when accelerated across a potential difference of (1 : mathsf{volt}). The ground state of the hydrogen atom has an energy of (-1/2 : mathsf{hartree}) or (-13.6 : mathsf{eV}). Conversion to atomic units is equivalent to setting

[hbar = e = m = 1]

in all formulas containing these constants. Rewriting the Schrӧdinger equation in atomic units, we have

[left{ -dfrac{1}{2} nabla^{2} - dfrac{Z}{r} right} psi(r) = Epsi(r) label{25}]

Since the potential energy is spherically symmetrical (a function of (r) alone), it is obviously advantageous to treat this problem in spherical polar coordinates (r, : theta, : phi). Expressing the Laplacian operator in these coordinates [cf. Eq (6-20)],

[ -dfrac{1}{2} left{ dfrac{1}{r^{2}} dfrac{partial}{partial r} r^{2} dfrac{partial}{partial r} + dfrac{1}{r^{2}sintheta} dfrac{partial}{partial theta} sintheta dfrac{partial}{partial theta} + dfrac{1}{r^{2}sin^{2}theta} dfrac{partial^{2}}{partialphi^{2}} right} times psi(r, : theta, : phi) - dfrac{Z}{r} psi(r, : theta, : phi) = Epsi(r, : theta, : phi) label{26}]

Equation (ref{26}) shows that the second and third terms in the Laplacian represent the angular momentum operator (hat{L}^{2}). Clearly, Equation (ref{26}) will have separable solutions of the form

[psi(r, : theta, : phi) = R(r)Y_{ell m}(theta, : phi) label{27}]

Substituting Equation (ref{27}) into Equation (ref{26}) and using the angular momentum eigenvalue Equation Equation (ref{6-34}), we obtain an ordinary differential equation for the radial function (R(r)):

[left{ -dfrac{1}{2r^{2}} dfrac{d}{dr} r^{2} dfrac{d}{dr} + dfrac{ell(ell + 1)}{2r^{2}} - dfrac{Z}{r} right} R(r) = ER(r) label{28}]

Note that in the domain of the variable (r), the angular momentum contribution (ell (ell + 1) / 2r^{2}) acts as an effective addition to the potential energy. It can be identified with centrifugal force, which pulls the electron outward, in opposition to the Coulomb attraction. Carrying out the successive differentiations in Equation (ref{29}) and simplifying, we obtain

[dfrac{1}{2}R'(r) + dfrac{1}{r}R'(r) + left[dfrac{Z}{r} - dfrac{ell(ell + 1)}{2r^{2}} + Eright]R(r) = 0 label{29}]

another second-order linear differential equation with non-constant coefficients. It is again useful to explore the asymptotic solutions to Equation (ref{29}), as (r rightarrow infty). In the asymptotic approximation,

[R'(r) - 2rlvert E rvert R(r) approx 0 label{30}]

having noted that the energy (E) is negative for bound states. Solutions to Equation (ref{30}) are

[R(r) approx mathsf{const} , e^{pmsqrt{2lvert E rvert}r} label{31}]

We reject the positive exponential on physical grounds, since (R(r) rightarrow infty) as (r rightarrow infty), in violation of the requirement that the wavefunction must be finite everywhere. Choosing the negative exponential and setting (E = -Z^{2}/2) the ground state energy in the Bohr theory (in atomic units), we obtain

[R(r) approx mathsf{const} , e^{-Zr} label{32}]

It turns out, very fortunately, that this asymptotic approximation is also an exact solution of the Schrӧdinger equation (Equation (ref{29})) with (ell = 0), just what happened for the harmonic-oscillator problem in Chap. 5. The solutions to Equation (ref{29}), designated (R_{nell}(r)), are labeled by (n), known as the principal quantum number, as well as by the angular momentum (ell), which is a parameter in the radial equation. The solution in Equation (ref{32}) corresponds to (R_{10}(r)). This should be normalized according to the condition

[int_{0}^{infty} [R_{10}(r)]^{2} , r^{2} , dr = 1 label{33}]

A useful definite integral is

[int_{0}^{infty} r^{n} , e^{-alpha r} , dr = dfrac{n!}{alpha^{n + 1}} label{34}]

The normalized radial function is thereby given by

[R_{10}(r) = 2Z^{3/2} e^{-Zr} label{35}]

Since this function is nodeless, we identify it with the ground state of the hydrogenlike atom. Multipyling Equation (ref{35}) by the spherical harmonic (Y_{00} = 1/ sqrt{4pi} ), we obtain the total wavefunction (Equation (ref{27}))

[psi_{100}(r, theta, phi) = left( dfrac{Z^{3}}{pi} right)^{1/2} e^{-Zr} label{36}]

This is conventionally designated as the 1s function (psi_{1s}(r)).

Integrals in spherical-polar coordinates over a spherically-symmetrical integrand (like the 1s orbital) can be significantly simplified. We can do the reduction

[int_{0}^{infty} int_{0}^{pi} int_{0}^{2pi} f(r) , r^{2} , sintheta , dr , dtheta , dphi = int_{0}^{infty} f(r) , 4pi r^{2} , dr label{37}]

since integration over (theta) and (phi) gives (4pi), the total solid angle of a sphere. The normalization of the 1s wavefunction can thus be written as

[int_{0}^{infty} [psi_{1s}(r)]^{2} , 4pi r^{2} , dr = 1 label{38}]

Hydrogen Atom Ground State

There are a number of different ways of representing hydrogen-atom wavefunctions graphically. We will illustrate some of these for the 1s ground state. In atomic units,

[psi_{1s}(r) = dfrac{1}{sqrt{pi}}e^{-r} label{39}]

is a decreasing exponential function of a single variable (r), and is simply plotted in Figure 3.

Figure (PageIndex{3}) gives a somewhat more pictorial representation, a three-dimensional contour plot of (psi_{1s}(r)) as a function of (x) and (y) in the (x), (y)-plane.

According to Born's interpretation of the wavefunction, the probability per unit volume of finding the electron at the point ((r, : theta, : phi) ) is equal to the square of the normalized wavefunction

[rho_{1s}(r) = [psi_{1s}(r)]^{2} = dfrac{1}{pi}e^{-2r} label{40}]

This is represented in Figure 5 by a scatter plot describing a possible sequence of observations of the electron position. Although results of individual measurements are not predictable, a statistical pattern does emerge after a sufficiently large number of measurements.

The probability density is normalized such that

[int_{0}^{infty} rho_{1s}(r) , 4pi r^{2} , dr = 1 label{41}]

In some ways (rho (r)) does not provide the best description of the electron distribution, since the region around (r = 0), where the wavefunction has its largest values, is a relatively small fraction of the volume accessible to the electron. Larger radii (r) represent larger physical regions since, in spherical polar coordinates, a value of (r) is associated with a shell of volume (4pi r^{2} , dr). A more significant measure is therefore the radial distribution function

[D_{1s}(r) = 4pi r^{2} [psi_{1s}(r)]^{2} label{42}]

which represents the probability density within the entire shell of radius (r), normalized such that

[int_{0}^{infty} D_{1s}(r) , dr = 1 label{43}]

The functions (rho_{1s}(r) ) and (D_{1s}(r) ) are both shown in Figure (PageIndex{6}). Remarkably, the 1s RDF has its maximum at (r = a_0), equal to the radius of the first Bohr orbit

Atomic Orbitals

The general solution for (R_{nell}(r)) has a rather complicated form which we give without proof:

[R_{nell}(r) = N_{nell} , rho^{ell} , L_{n + ell}^{2ell + 1} , (rho) e^{-rho /2} qquad rho equiv dfrac{2Zr}{n} label{44}]

Here (L_{beta}^{alpha}) is an associated Laguerre polynomial and (N_{nell}), a normalizing constant. The angular momentum quantum number (ell) is by convention designated by a code: s for (ell = 0), p for (ell = 1), d for (ell = 2), f for (ell = 3), g for (ell = 4), and so on. The first four letters come from an old classification scheme for atomic spectral lines: sharp, principal, diffuse and fundamental. Although these designations have long since outlived their original significance, they remain in general use. The solutions of the hydrogenic Schrӧdinger equation
in spherical polar coordinates can now be written in full

[psi_{nell m}(r, : theta, : phi) = R_{nell}(r)Y_{ell m}(theta, : phi) n = 1, : 2... qquad ell = 0, : 1... : n - 1 qquad m = 0, : pm 1, : pm 2... : pm ell label{45}]

where (Y_{ell m}) are the spherical harmonics tabulated in Chap. 6. Table 1 below enumerates all the hydrogenic functions we will actually need. These are called hydrogenic atomic orbitals, in anticipation of their later applications to the structure of atoms and molecules.

The energy levels for a hydrogenic system are given by

[E_n = -dfrac{Z^{2}}{2n^{2}} : mathsf{hartrees} label{46}]

and depends on the principal quantum number alone. Considering all the allowed values of (ell) and (m), the level (E_n) has a degeneracy of (n^{2}). Figure 7 shows an energy level diagram for hydrogen ((Z = 1) ). For (E geq 0), the energy is a continuum, since the electron is in fact a free particle. The continuum represents states of an electron and proton in interaction, but not bound into a stable atom. Figure (PageIndex{7}) also shows some of the transitions which make up the Lyman series in the ultraviolet and the Balmer series in the visible region.

The (ns) orbitals are all spherically symmetrical, being associated with a constant angular factor, the spherical harmonic (Y_{00} = 1/ sqrt{4pi} ). They have (n - 1) radial nodes—spherical shells on which the wavefunction equals zero. The 1s ground state is nodeless and the number of nodes increases with energy, in a pattern now familiar from our study of the particle-in-a-box and harmonic oscillator. The 2s orbital, with its radial node at (r = 2) bohr, is also shown in Figure (PageIndex{3}).

p- and d-Orbitals

The lowest-energy solutions deviating from spherical symmetry are the 2p-orbitals. Using Equations (ref{44}), (ref{45}) and the (ell = 1) spherical harmonics, we find three degenerate eigenfunctions:

[psi_{210}(r, : theta, : phi) = dfrac{1}{4sqrt{2pi}}re^{-r/2} costheta label{47}]

and

[psi_{21 pm 1}(r, : theta, : phi) = mp dfrac{1}{4sqrt{2pi}}re^{-r/2} sintheta e^{pm i phi} label{48}]

The function (psi_{210}) is real and contains the factor (r costheta ), which is equal to the cartesian variable (z). In chemical applications, this is designated as a 2p_z orbital:

[psi_{2p_z} = dfrac{1}{4sqrt{2pi}}ze^{-r/2} label{49}]

A contour plot is shown in Figure (PageIndex{8}). Note that this function is cylindrically-symmetrical about the (z)-axis with a node in the (x), (y)-plane. The (psi_{21 pm 1}) are complex functions and not as easy to represent graphically. Their angular dependence is that of the spherical harmonics (Y_{1 pm 1}) , shown in Figure 6-4. As noted in Chap. 4, any linear combination of degenerate eigenfunctions is an equally-valid alternative eigenfunction. Making use of the Euler formulas for sine and cosine

[cosphi = dfrac{e^{iphi} + e^{-iphi}}{2} qquad mathsf{and} qquad sinphi = dfrac{e^{iphi} - e^{-iphi}}{2} label{50}]

and noting that the combinations (sinthetacosphi) and (sinthetasinphi) correspond to the cartesian variables (x) and (y), respectively, we can define the alternative 2p orbitals

[psi_{2p_x} = dfrac{1}{sqrt{2}}(psi_{21-1} - psi_{211}) = dfrac{1}{4sqrt{2pi}} xe^{-r/2} label{51}]

and

[psi_{2p_y} = -dfrac{i}{sqrt{2}}(psi_{21-1} + psi_{211}) = dfrac{1}{4sqrt{2pi}} ye^{-r/2} label{52}]

Clearly, these have the same shape as the 2p_z-orbital, but are oriented along the (x)- and (y)-axes, respectively. The threefold degeneracy of the p-orbitals is very clearly shown by the geometric equivalence the functions 2p_x, 2p_y and 2p_z, which is not obvious for the spherical harmonics. The functions listed in Table 1 are, in fact, the real forms for all atomic orbitals, which are more useful in chemical applications. All higher p-orbitals have analogous functional forms (x , f(r)), (y , f(r)) and (z , f(r)) and are likewise 3-fold degenerate.

The orbital (psi_{320}) is, like (psi_{210}), a real function. It is known in chemistry as the (d_{z^{2}})-orbital and can be expressed as a cartesian factor times a function of (r):

[psi_{3d_{z^{2}}} = psi_{320} = (3z^{2} - r^{2}) f(r) label{53}]

A contour plot is shown in Figure (PageIndex{9}). This function is also cylindrically symmetric about the (z)-axis with two angular nodes—the conical surfaces with (3z^{2} - r^{2} = 0). The remaining four 3d orbitals are complex functions containing the spherical harmonics (Y_{2 pm 1} ) and (Y_{2 pm 2}) pictured in Figure 6-4. We can again construct real functions from linear combinations, the result being four geometrically equivalent 'four-leaf clover' functions with two perpendicular planar nodes. These orbitals are designated (d_{x^{2} - y^{2}}, : d_{xy}, : d_{zx}) and (d_{yz}). Two of them are shown in Figure 9. The (d_{z^{2}}) orbital has a different shape. However, it can be expressed in terms of two non-standard d-orbitals, (d_{z^{2} - x^{2}}) and (d_{y^{2} - z^{2}}). The latter functions, along with (d_{x^{2} - y^{2}}) add to zero and thus constitute a linearly dependent set. Two combinations of these three functions can be chosen as independent eigenfunctions.

Summary

The atomic orbitals listed in Table 1 are illustrated in Figure (PageIndex{20}). Blue and red indicate, respectively, positive and negative regions of the wavefunctions (the radial nodes of the 2s and 3s orbitals are obscured). These pictures are intended as stylized representations of atomic orbitals and should not be interpreted as quantitatively accurate.

The electron charge distribution in an orbital (psi_{nell m}(mathbf{r})) is given by

[rho(mathbf{r}) = lvert psi_{nell m}(mathbf{r}) rvert ^{2} label{54} ]

which for the s-orbitals is a function of (r) alone. The radial distribution function can be defined, even for orbitals containing angular dependence, by

[D_{nell}(r) = r^{2} [R_{nell}(r)]^{2} label{55}]

This represents the electron density in a shell of radius (r), including all values of the angular variables (theta), (phi). Figure (PageIndex{11}) shows plots of the RDF for the first few hydrogen orbitals.

Contributors and Attributions

Seymour Blinder (Professor Emeritus of Chemistry and Physics at the University of Michigan, Ann Arbor)

• Integrated by Daniel SantaLucia (Chemistry student at Hope College, Holland MI)

Properties of Hydrogen

Hydrogen is the smallest element, with one proton and one electron. It is highly abundant and has unique and important chemical properties.

Learning Objectives

Indicate the different kinds of reactions hydrogen may participate in and discuss its basic properties

Key Takeaways

Key Points

• Hydrogen is the lightest element and will explode at concentrations ranging from 4-75 percent by volume in the presence of sunlight, a flame, or a spark.
• Despite its stability, hydrogen forms many bonds and is present in many different compounds.
• Three naturally occurring isotopes of hydrogen exist: protium, deuterium, and tritium, each with different properties due to the difference in the number of neutrons in the nucleus.

Key Terms

• diatomic: Consisting of two atoms

Physical Properties of Hydrogen

Hydrogen is the smallest chemical element because it consists of only one proton in its nucleus. Its symbol is H, and its atomic number is 1. It has an average atomic weight of 1.0079 amu, making it the lightest element. Hydrogen is the most abundant chemical substance in the universe, especially in stars and gas giant planets. However, monoatomic hydrogen is rare on Earth is rare due to its propensity to form covalent bonds with most elements. At standard temperature and pressure, hydrogen is a nontoxic, nonmetallic, odorless, tasteless, colorless, and highly combustible diatomic gas with the molecular formula H₂. Hydrogen is also prevalent on Earth in the form of chemical compounds such as hydrocarbons and water.

Hydrogen has one one proton and one electron; the most common isotope, protium (¹H), has no neutrons. Hydrogen has a melting point of -259.14 °C and a boiling point of -252.87 °C. Hydrogen has a density of 0.08988 g/L, making it less dense than air. It has two distinct oxidation states, (+1, -1), which make it able to act as both an oxidizing and a reducing agent. Its covalent radius is 31.5 pm.

Hydrogen exists in two different spin isomers of hydrogen diatomic molecules that differ by the relative spin of their nuclei. The orthohydrogen form has parallel spins; the parahydrogen form has antiparallel spins. At standard temperature and pressure, hydrogen gas consists of 75 percent orthohydrogen and 25 percent parahydrogen. Hydrogen is available in different forms, such as compressed gaseous hydrogen, liquid hydrogen, and slush hydrogen (composed of liquid and solid ), as well as solid and metallic forms.

The Hydrogen Atom: Many of the hydrogen atom’s chemical properties arise from its small size, such as its propensity to form covalent bonds, flammability, and spontaneous reaction with oxidizing elements.

Chemical Properties of Hydrogen

Hydrogen gas (H₂) is highly flammable and will burn in air at a very wide range of concentrations between 4 percent and 75 percent by volume. The enthalpy of combustion for hydrogen is -286 kJ/mol, and is described by the equation:

[latex]2 text{H}_2(text{g}) + text{O}_2(text{g}) rightarrow 2 text{H}_2text{O}(text{l}) + 572 text{kJ} (286 text{kJ}/text{mol H}_2)[/latex]

Hydrogen gas can also explode in a mixture of chlorine (from 5 to 95 percent). These mixtures can explode in response to a spark, heat, or even sunlight. The hydrogen autoignition temperature (the temperature at which spontaneous combustion will occur) is 500 °C. Pure hydrogen- oxygen flames emit ultraviolet light and are invisible to the naked eye. As such, the detection of a burning hydrogen leak is dangerous and requires a flame detector. Because hydrogen is buoyant in air, hydrogen flames ascend rapidly and cause less damage than hydrocarbon fires. H₂ reacts with oxidizing elements, which in turn react spontaneously and violently with chlorine and fluorine to form the corresponding hydrogen halides.

H₂ does form compounds with most elements despite its stability. When participating in reactions, hydrogen can have a partial positive charge when reacting with more electronegative elements such as the halogens or oxygen, but it can have a partial negative charge when reacting with more electropositive elements such as the alkali metals. When hydrogen bonds with fluorine, oxygen, or nitrogen, it can participate in a form of medium-strength noncovalent (intermolecular) bonding called hydrogen bonding, which is critical to the stability of many biological molecules. Compounds that have hydrogen bonding with metals and metalloids are known as hydrides.

Oxidation of hydrogen removes its electron and yields the H⁺ ion. Often, the H⁺ in aqueous solutions is referred to as the hydronium ion (H₃O⁺). This species is essential in acid-base chemistry.

Hydrogen Isotopes

Hydrogen naturally exists as three isotopes, denoted ¹H, ²H, and ³H. ¹H occurs at 99.98 percent abundance and has the formal name protium. ²H is known as deuterium and contains one electron, one proton, and one neutron (mass number = 2). Deuterium and its compounds are used as non-radioactive labels in chemical experiments and in solvents for ¹H-NMR spectroscopy. ³H is known as tritium and contains one proton, two neutrons, and one electron (mass number = 3). It is radioactive and decays into helium-3 through beta decay with a half life of 12.32 years.

Binary Hydrides

Hydrides are compounds in which one or more hydrogen anions have nucleophilic, reducing, or basic properties.

Learning Objectives

Discuss the properties of hydrides.

Key Takeaways

Key Points

• Binary hydrides are a class of compounds that consist of an element bonded to hydrogen, in which hydrogen acts as the more electronegative species.
• Free hydride anions exist only under extreme conditions. Instead, most hydride compounds have hydrogen centers with a hydridic character.
• Hydrides can be classified as ionic, covalent or interstitial, each of which possess different properties.

Key Terms

• hydride: A compound of hydrogen with a more electropositive element.

Compounds with Anionic Hydrogen

A hydride is the anion of hydrogen (H⁻), and it can form compounds in which one or more hydrogen centers have nucleophilic, reducing, or basic properties. In such hydrides, hydrogen is bonded to a more electropositive element or group.

Lithium Hydride, LiH: This is a space-filling model of a crystal of lithium hydride, LiH, a binary halide.

Hydride compounds often do not conform to classical electron -counting rules, but are described as multi-centered bonds with metallic bonding. Hydrides can be components of discrete molecules, oligomers, polymers, ionic solids, chemisorbed monolayers, bulk metals (interstitial), and other materials. While hydrides traditionally react as Lewis bases or reducing agents by donating electrons, some metal hydrides behave as both acids and hydrogen- atom donors.

Applications of Hydrides

Hydrides are commonly used as reducing agents, donating electrons in chemical reactions. Hydrides can be used as strong bases in organic syntheses, and their reaction with weak Bronsted acids releases dihydrogen (H₂).

Hydrides such as calcium hydride are used as dessicants, or drying agents, to remove trace water from organic solvents. In such cases, the hydride reacts with water, forming diatomic hydrogen and a hydroxide salt:

[latex]text{CaH}_2 + 2text{H}_2text{O} rightarrow 2text{H}_2 + text{Ca}(text{OH})_2[/latex]

The dry solvent can then be distilled or vac-transferred from the “solvent pot.”

Hydride complexes are catalysts and catalytic intermediates in a variety of homogeneous and heterogeneous catalytic cycles. Important examples include hydrogenation, hydroformylation, hydrosilylation, and hydrodesulfurization catalysts. Even certain enzymes, like hydrogenase, operate via hydride intermediates. The energy carrier NADH reacts as a hydride donor or hydride equivalent.

Free hydride anions exist only under extreme conditions and are not invoked for homogeneous solutions. Instead, many compounds have a hydrogen center with a hydridic character. Hydrides can be characterized as ionic, covalent, or interstitial hydrides based on their bonding types.

Ionic Hydrides

Ionic, or saline, hydride is a hydrogen atom bound to an extremely electropositive metal, generally an alkali metal or an alkaline earth metal (for example, potassium hydride or KH). These types of hydrides are insoluble in conventional solvents, reflecting their non-molecular structures. Most ionic hydrides exist as “binary” materials that involve only two elements, one of which is hydrogen. Ionic hydrides are often used as heterogeneous bases and reducing reagents in organic synthesis.

Covalent Hydrides

Covalent hydrides refer to hydrogen centers that react as hydrides, or those that are nucleophilic. In these substances, the hydride bond, formally, is a covalent bond much like the bond that is made by a proton in a weak acid. This category includes hydrides that exist as discrete molecules, polymers, oligomers, or hydrogen that has been chem-adsorbed to a surface. A particularly important type of covalent hydride is the complex metal hydride, a powerful (reducing) soluble hydride that is commonly used in organic syntheses (for example, sodium borohydride or NaBH₄). Transition metal hydrides also include compounds that can be classified as covalent hydrides. Some are even classified as interstitial hydrides and other bridging hydrides. Classical transition metal hydrides feature a single bond between the hydrogen center and the transition metal.

Interstitial or Metallic Hydrides

Interstitial hydrides most commonly exist within metals or alloys. Their bonding is generally considered metallic. Such bulk transition metals form interstitial binary hydrides when exposed to hydrogen. These systems are usually non-stoichiometric, with variable amounts of hydrogen atoms in the lattice.

Isotopes of Hydrogen

Hydrogen has three naturally occurring isotopes: protium, deuterium and tritium. Each isotope has different chemical properties.

Learning Objectives

Discuss the chemical properties of hydrogen’s naturally occurring isotopes.

Key Takeaways

Key Points

• Protium is the most prevalent hydrogen isotope, with an abundance of 99.98%. It consists of one proton and one electron. It is typically not found in its monoatomic form, but bonded with itself (H₂) or other elements.
• Deuterium is a hydrogen isotope consisting of one proton, one neutron and one electron. It has major applications in nuclear magnetic resonance studies.
• Tritium is a hydrogen isotope consisting of one proton, two neutrons and one electron. It is radioactive, with a half-life of 12.32 years.

Key Terms

• diatomic: Consisting of two atoms.
• isotope: Forms of an element where the atoms have a different number of neutrons within their nuclei. As a consequence, atoms of the same isotope will have the same atomic number, but a different mass number.

Properties of Isotopes of Hydrogen

Hydrogen has three naturally occurring isotopes: ¹H (protium), ²H (deuterium), and ³H (tritium). Other highly unstable nuclei (⁴H to ⁷H) have been synthesized in the laboratory, but do not occur in nature. The most stable radioisotope of hydrogen is tritium, with a half-life of 12.32 years. All heavier isotopes are synthetic and have a half-life less than a zeptosecond (10^-21 sec). Of these, ⁵H is the most stable, and the least stable isotope is ⁷H.

Protium: Protium, the most common isotope of hydrogen, consists of one proton and one electron. Unique among all stable isotopes, it has no neutrons.

Protium

¹H is the most common hydrogen isotope with an abundance of more than 99.98%. The nucleus of this isotope consists of only a single proton (atomic number = mass number = 1) and its mass is 1.007825 amu. Hydrogen is generally found as diatomic hydrogen gas H₂, or it combines with other atoms in compounds —monoatomic hydrogen is rare. The H–H bond is one of the strongest bonds in nature, with a bond dissociation enthalpy of 435.88 kJ/mol at 298 K. As a consequence, H₂ dissociates to only a minor extent until higher temperatures are reached. At 3000K, the degree of dissociation is only 7.85%. Hydrogen atoms are so reactive that they combine with almost all elements.

Deuterium

²H, or deuterium (D), is the other stable isotope of hydrogen. It has a natural abundance of ~156.25 ppm in the oceans, and accounts for approximately 0.0156% of all hydrogen found on earth. The nucleus of deuterium, called a deuteron, contains one proton and one neutron (mass number = 2), whereas the far more common hydrogen isotope, protium, has no neutrons in the nucleus. Because of the extra neutron present in the nucleus, deuterium is roughly twice the mass of protium (deuterium has a mass of 2.014102 amu, compared to the mean hydrogen atomic mass of 1.007947 amu). Deuterium occurs in trace amounts naturally as deuterium gas, written ²H₂ or D₂, but is most commonly found in the universe bonded with a protium ¹H atom, forming a gas called hydrogen deuteride (HD or ¹H²H).

Chemically, deuterium behaves similarly to ordinary hydrogen (protium), but there are differences in bond energy and length for compounds of heavy hydrogen isotopes, which are larger than the isotopic differences in any other element. Bonds involving deuterium and tritium are somewhat stronger than the corresponding bonds in protium, and these differences are enough to make significant changes in biological reactions. Deuterium can replace the normal hydrogen in water molecules to form heavy water (D₂O), which is about 10.6% denser than normal water. Heavy water is slightly toxic in eukaryotic animals, with 25% substitution of the body water causing cell division problems and sterility, and 50% substitution causing death by cytotoxic syndrome (bone marrow failure and gastrointestinal lining failure). Consumption of heavy water does not pose a health threat to humans. It is estimated that a 70 kg person might drink 4.8 liters of heavy water without serious consequences.

The most common use for deuterium is in nuclear resonance spectroscopy. As nuclear magnetic resonance (NMR) requires compounds of interest to be dissolved in solution, the solution signal should not register in the analysis. As NMR analyzes the nuclear spins of hydrogen atoms, the different nuclear spin property of deuterium is not ‘seen’ by the NMR instrument, making deuterated solvents highly desirable due to the lack of solvent-signal interference.

Isotopes of Hydrogen: The three naturally occurring isotopes of hydrogen.

Tritium

³H is known as tritium and contains one proton and two neutrons in its nucleus (mass number = 3). It is radioactive, decaying into helium-3 through beta-decay accompanied by a release of 18.6 keV of energy. It has a half-life of 12.32 years. Naturally occurring tritium is extremely rare on Earth, where trace amounts are formed by the interaction of the atmosphere with cosmic rays.

Heavier Synthetic Isotopes

⁴H contains one proton and three neutrons in its nucleus. It is a highly unstable isotope of hydrogen. It has been synthesized in the laboratory by bombarding tritium with fast-moving deuterium nuclei. In this experiment, the tritium nuclei captured neutrons from the fast-moving deuterium nucleus. The presence of the hydrogen-4 was deduced by detecting the emitted protons. Its atomic mass is 4.02781 ± 0.00011 amu. It decays through neutron emission with a half-life of 1.39 ×10⁻²² seconds.

⁵H is another highly unstable heavy isotope of hydrogen. The nucleus consists of a proton and four neutrons. It has been synthesized in a laboratory by bombarding tritium with fast-moving tritium nuclei. One tritium nucleus captures two neutrons from the other, becoming a nucleus with one proton and four neutrons. The remaining proton may be detected and the existence of hydrogen-5 deduced. It decays through double neutron emission and has a half-life of at least 9.1 × 10⁻²² seconds.

⁶H decays through triple neutron emission and has a half-life of 2.90×10⁻²² seconds. It consists of one proton and five neutrons.

⁷H consists of one proton and six neutrons. It was first synthesized in 2003 by a group of Russian, Japanese and French scientists at RIKEN’s RI Beam Science Laboratory, by bombarding hydrogen with helium-8 atoms. The helium-8’s neutrons were donated to the hydrogen’s nucleus. The two remaining protons were detected by the “RIKEN telescope”, a device composed of several layers of sensors, positioned behind the target of the RI Beam cyclotron.

Hydrogenation

Hydrogenation reactions, which involve the addition of hydrogen to substrates, have many important applications.

Learning Objectives

Discuss hydrogenation reactions.

Key Takeaways

Key Points

• Hydrogenation reactions typically have three components: hydrogen, the substrate, and catalysts, which are usually required to facilitate the reaction at lower temperatures and pressures.
• There are two classes of catalysts with different mechanisms of hydrogenation: heterogeneous and homogenous.
• Hydrogenation reactions are not limited to the conversion of alkenes to alkanes, but span a variety of reactions where substrates can effectively be reduced.
• Incomplete hydrogenation reactions have significant health implications and have been correlated with circulatory diseases.

Key Terms

• hydrogenation: The chemical reaction of hydrogen with another substance, especially with an unsaturated organic compound.
• substrate: The compound or material which is to be acted upon.

Hydrogenation Reactions

Hydrogenation refers to the treatment of substances with molecular hydrogen (H₂), adding pairs of hydrogen atoms to compounds (generally unsaturated compounds). These usually require a catalyst for the reaction to occur under normal conditions of temperature and pressure. Most hydrogenation reactions use gaseous hydrogen as the hydrogen source, but alternative sources have been developed. The reverse of hydrogenation, where hydrogen is removed from the compounds, is known as dehydrogenation. Hydrogenation differs from protonation or hydride addition because in hydrogenation the products have the same charge as the reactants.

Hydrogenation: Hydrogen can be added across a double bond—such as the olefin in maleic acid shown—by utilizing a catalyst, such as palladium.

Hydrogenation reactions generally require three components: the substrate, the hydrogen source, and a catalyst. The reaction is carried out at varying temperatures and pressures depending on the catalyst and substrate used. The hydrogenation of an alkene produces an alkane. The addition of hydrogen to compounds happens in a syn addition fashion, adding to the same face of the compound and entering from the least hindered side. Generally, alkenes will convert to alkanes, alkynes to alkenes, aldehydes and ketones to alcohols, esters to secondary alcohols, and amides to amines via hydrogenation reactions.

Catalysts of Hydrogenation

Generally, hydrogenation reactions will not occur between hydrogen and organic compounds below 480 degrees Celsius without metal catalysts. Catalysts are responsible for binding the H₂ molecule and facilitating the reaction between the hydrogen and the substrate. Platinum, palladium, rhodium, and ruthenium are known to be active catalysts which can operate at lower temperatures and pressures. Research is ongoing to procure non-precious metal catalysts which can produce similar activity at lower temperatures and pressures. Nickel-based catalysts, such as Raney nickel, have been developed, but still require high temperatures and pressures.

Heterogeneous Catalysis: The hydrogenation of ethylene (C₂H₄) on a solid support is an example of heterogeneous catalysis.

Catalysts can be divided into two categories: homogeneous or heterogeneous catalysts. Homogeneous catalysts are soluble in the solvent that contains the unsaturated substrate. Heterogeneous catalysts are found more commonly in industry, and are not soluble in the solvent containing the substrate. Often, heterogeneous catalysts are metal-based and are attached to supports based on carbon or oxide. The choice of support for these materials is important, as the supports can affect the activity of the catalysts. Hydrogen gas is the most common source of hydrogen used and is commercially available.

Hydrogenation is an exothermic reaction, releasing about 25 kcal/mol in the hydrogenation of vegetable oils and fatty acids. For heterogenous catalysts, the Horiuti-Polanyi mechanism explains how hydrogenation occurs. First, the unsaturated bond binds to the catalyst, followed by H₂ dissociation into atomic hydrogen onto the catalyst. Then one atom of hydrogen attaches to the substrate in a reversible step, followed by the addition of a second atom, rendering the hydrogenation process irreversible. For homogeneous catalysis, the metal binds to hydrogen to give a dihydride complex via oxidative addition. The metal binds the substrate and then transfers one of the hydrogen atoms from the metal to the substrate via migratory insertion. The second hydrogen atom from the metal is transferred to the substrate with simultaneous dissociation of the newly formed alkane via reductive elimination.

Industrial Uses of Hydrogenation Reactions

Heterogeneous catalytic hydrogenation is very important in industrial processes. In petrochemical processes, hydrogenation is used to saturate alkenes and aromatics, making them less toxic and reactive. Hydrogenation is also important in processing vegetable oils because most vegetable oils are derived from polyunsaturated fatty acids. Partial hydrogenation reduces most, but not all, of the carbon-carbon double bonds, making them better for sale and consumption. The degree of saturation of fats changes important physical properties such as the melting range of the oils; an example of this is how liquid vegetable oils become semi-solid at various temperatures.

Partial hydrogenation in margarine: Margarine is a semi-solid butter substitute created from vegetable oil, which is typically unsaturated and therefore liquid at room temperature. The process of partial hydrogenation adds hydrogen atoms and reduces the double bonds in the fatty acids, creating a semi-solid vegetable oil at room temperature.

Incomplete hydrogenation of the double bonds has health implications; some double bonds can isomerize from the cis to the trans state. This isomerization occurs because the trans configuration has lower energy than the cis configuration. The trans isomers have been implicated in contributing to pathological blood circulatory system conditions (i.e.,atherosclerosis and heart disease).

The Hydrogen Economy

The hydrogen economy refers to using hydrogen as the next important source of fuel.

Key Takeaways

Key Points

• The current hydrocarbon economy is becoming impractical because of increasing demand and diminishing resources. The hydrogen economy could act as a replacement because of its higher energy density and its smaller negative impact on the environment.
• The hydrogen economy is limited because it is difficult to transport and store hydrogen. In addition, the dangers associated with hydrogen limit its practical application.
• Hydrogen can be generated via several processes, but is predominately accomplished by steam reforming fossil fuels. This process requires a large input of energy and releases carbon dioxide.

Key Terms

Atomic Mass Of Hydrogen 3

• hydrocarbon economy: Referring to the current global economy which is based on fossil fuels as the main energy source.
• hydrogen economy: A hypothetical future economy in which the primary form of stored energy for mobile applications and load balancing is hydrogen (H2). In particular, H2 replaces fossil fuels used to power automobiles.

Introduction: The Hydrogen Economy

The hydrogen economy refers to a hypothetical future system of delivering energy through the use of hydrogen (H₂). The term was first coined by John Bockris at a 1970 talk at the General Motors (GM) Technical Center. Advocates of this proposed system promote hydrogen as a potential fuel source. Free hydrogen does not occur naturally in quantities of use, like other energy sources, but it can be generated by various methods. As such, hydrogen is not a primary energy source, but an energy carrier. The feasibility of a hydrogen economy depends on issues including the use of fossil fuel, the generation of sustainable energy, and energy sourcing.

Comparing Hydrogen Energy to Other Sources

As a potential energy source, the hydrogen economy stands to eliminate or reduce the negative effects of using hydrocarbon fuels, the currently dominant energy source that releases high amounts of carbon into the atmosphere. In the current hydrocarbon economy, transportation is fueled by petroleum, the use of which ultimately results in the release of carbon dioxide (a greenhouse gas ) and many pollutants into the atmosphere. In addition, the supply of raw materials that are essential for a hydrocarbon economy is limited, and the demand for such fuels is increasing each year.

As a potential fuel, hydrogen is appealing because it has a high energy density by weight. This results in a 38% efficiency for a combustion engine, compared to 30% when gasoline was used as a fuel. In addition, it provides an environmentally clean source of energy that does not release pollutants. However, there are several obstacles for the use of hydrogen as a fuel, including the purity requirement of hydrogen and difficulties that arise with its storage.

Hydrogen production is a large and growing industry. Globally, 50 million metric tons of hydrogen (equivalent to 170 million tons of oil) were produced in 2004. There are two primary uses for hydrogen today. Half of the hydrogen produced is used to synthesize ammonia in the Haber process. The other half is used to convert heavy petroleum sources into lighter fractions which can be used as fuels. Currently, global hydrogen production is 48% from natural gas, 30% from oil, 18% from coal and 4% from water electrolysis.

Atomic Mass Of Hydrogen 1 2 And 3

The Hydrogen Economy: The hydrogen economy could possibly revolutionize the current energy infrastructure by transferring fuel demands from fossil fuels onto hydrogen.

Methods of Producing Hydrogen

Hydrogen production is mostly accomplished by steam reforming from hydrocarbons, but alternative methods are being developed. Steam reforming is conducted at high temperatures and possesses efficiencies up to 80%. The process involves methane and water and is highly exothermic:

[latex]text{CH}_4 + text{H}_2text{O} rightarrow text{CO} + 3text{H}_2 + 191.7 text{kJ}/text{mol}[/latex]

In a second stage, additional hydrogen is generated at a lower temperature:

[latex]text{CO}+text{H}_2text{O} rightarrow text{CO}_2 + text{H}_2 - 40.4text{kJ}/text{mol}[/latex]

Other ways of producing hydrogen from fossil fuels include partial oxidation and plasma reforming. Hydrogen can also be produced from water splitting. Fuel cells are electrochemical devices capable of transforming chemical energy into electrical energy. Fuel cells require less energy input than other alternatives and perform water electrolysis at lower temperatures, both of which have the potential of reducing the overall cost of hydrogen production. Water can also be split through thermolysis, but this requires high temperatures and catalysts. In addition, hydrogen can be produced via enzymes and bacteria fermentation, but this technology has not yet been prepared for main scale commercialization. Other methods include photoelectrocatalytic production, thermochemical production, and high temperature and pressure electrolysis.

Obstacles to Adoption of Hydrogen as a Fuel

One major obstacle in the hydrogen economy is its transport and storage. Although H₂ has high energy density based on mass, it has very low energy density based on volume. This is a problem because at ambient conditions molecular hydrogen exists as a gas. To be a suitable fuel, hydrogen gas must be either pressurized or liquified to provide enough energy. Increasing the gas pressure will ultimately improve the energy density by volume, but this requires a greater amount of energy be expended to pressurize the gas. Alternatively, liquid hydrogen or slush hydrogen (a combination of liquid and solid hydrogen) can be used. Liquid hydrogen, however, is cryogenic and boils at 20 K, therefore a lot of energy must be expended to liquify the hydrogen.

Storing hydrogen in tanks is ineffective because hydrogen tends to diffuse through any liner material intended to contain it, which ultimately leads to the weakening of the container. Hydrogen can be stored as a chemical hydride or in some other hydrogen-containing compound. These compounds can be transported relatively easily and then decomposed into hydrogen gas. Current barriers to practical storage stem from the fact that high temperatures and pressure are needed for the compound to form and for the hydrogen to be released. Hydrogen can be adsorbed onto the surface of a solid storage material and then be released upon necessity; this technology is still being investigated.

Hydrogen has one of the widest explosive/ignition mix ranges with air. This means that any leak of hydrogen from a hydrogen:air mixture will most likely lead to an explosion if it comes into contact with a spark or flame. This limits the use of hydrogen as a fuel, especially in enclosed areas such as tunnels or underground parking. Pure hydrogen-oxygen flames burn in the UV range and are invisible, so a flame detector is needed to detect if a hydrogen leak is burning. Hydrogen is also odorless, so leaks cannot be detected by smell.

Although the hydrogen economy is supposed to create a smaller carbon footprint, there are many concerns regarding the environmental effects of hydrogen manufacturing. The main source of hydrogen is fossil fuel reforming, but this method ultimately leads to higher emissions of carbon dioxide than using the fossil fuel in an internal combustion engine. Other issues include the fact that hydrogen generation via electrolysis requires a greater energy input than directly using renewable energy, and the possibility of other side products.