Taking into account the motion of the nucleus of a hydrogen atom, find the expressions for the electron’s binding energy in the ground state and for the Rydberg constant. How much (in percent) do the binding energy and the Rydberg constant, obtained without taking into account the motion of the nucleus, differ from the more accurate corresponding value of these quantities ?
Text Solution
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Sol. If mass of nucleus is considered (not infinity) then the reduced mass of nucleus electron system can be taken as
µ = 
Here m is mass of electron and M is that of nucleus.
he binding energy in ground state of hydrogen atom can
now be given as
E = + 
or = 13.6 × 
eV
or = 
eV
We’ve hydrogen atom Rydberg constant is given as
R = 
If effect of mass of nucleus is
considered the new value of Rydberg constant can be given as R µ = 
R µ = 
Percentage difference in the values of R and R µ is given as 
= 
= 
× 100 
0.055%
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