An element undergoes a reaction as shown,

X+2e- --------> X2-

Energy released=30.87eV/atom.If the energy released is used to dissociate 4g of H2 molecules,equally into H+ and H*, where H* is the excited state of H atoms where the electron travels in orbit whose circumference equal to four times it's de Brogllie's wavelength.Determine the least moles of X that would be required:

Given I.E.of H=13.6eV/atom,bond energy of H2 =4.526eV/molecule.

Here, each molecule of H₂

1.)dissociates (this requires bond dissociation enthalpy) into

2)H⁺(for which we require ionization enthalpy) and

3)H^*(which is the excited H atom)
this atom is in the fourth state. Energy in this state = 13.6/n²= 13.6/16
therefore energy supplied = 13.6 – (13.6/16) = (15/16) 13.6

And we have a total of 4g H₂molecules means 2N_amolecules
Therefore energy required =
= 2 * 6.022*10²³(B.D.E + I.E. + energy for excitation)

=2 * 6.022*1023 (4.526 + 13.6 + (15/16) 13.6)

= (2 * 6.022*1023* 30.876) eV
This energy is supplies by atoms of X. Energy released per atom = 30.87eV /atom
so, atoms required = 2* 6.022*10²³= 2 moles