When an atom X absorbs radiation with a photon energy than the ionization energy of the atom, the atom is ionized to generate an ion `X^(+)` and the electron (called a photoelectron) is ejected at the same time. In this event, the energy is conserved as shown in Figure `1`, that is,
Photon energy (h)=ionization energy (IE) of `X+` kinetic energy of photoelectron.
When a molecule, for example, `H_(2)`, absorbs short-wavelength light, the photoelectron is ejected and an `H_(2)`, ion with a variety of vibrational states is produced. A photoelectron spectrum is a plot of the number of photoelectrons as a function of the kinetic energy of the photoelectrons. Figure-2 shows a typical photoelectron spectrum when `H_(2)` in the lowest vibrational level is irradiated by monochromatic light of `21.2 eV`. No photoelectrons are detected above `6.0 eV`. (eV is a unit of energy and `1.0 eV` is equal to `1.6xx10^(-19) J`)

Figure 1 Schematic diagram of photoelectron spectroscopy.
Figure 2 Photoelectron spectrum of `H_(2)`. The energy of the incident light is `21.2 eV`
`ul("Determine")` the bond energy `E_(C)(eV)` of `H_(2)` to the first decimal place.

Answer

`24.9 eV`= binding energy of a hydrogen molecule `+10.2 eV+10.2 eV`
Thus, the binding energy of a hydrogen molecule `E_(C)=4.5 eV`