With the following data:
- Length of the box : L = 2 a o Â
- a o is bohr radius -- 0.0529 nm -- Â Â
Allowed energy of a particle in one dimensional box is
             Â
E n = n 2 h 2 / 8 m L
2Â Â Â Â
Where  m is mass electron and h is plancks
constant
Ground state energy of the atom
is:
          E
=Â Â Â h 2 / 8 m L
2Â Â Â Â
             Â
= ( 6.635 *10 -34 Js ) 2 / (
8)(9.11*10-31 kg ) ( 2*0.0529 *10-9 )
2Â Â
               =  53.963*10-19
J
             Â
= 33.7273 eV
Actual ground state energy of hydrogen atom is: -13.6 eV
Diving:
            Â
33.7273 / 13.6Â Â = 2.4799 times
