Question:
If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1Å, and (ii) R = 10 Å.
Solution:
The kinetic energy of the H atom is 13.6 eV
Potential energy of an electron and proton is -27.2 eV
Total energy of the electron = -13.6 eV
When R = 0.1Å, the ground state energy is same as the earlier = -13.6 eV
When R = 10 Å,
The kinetic energy = 0.16 eV
The potential energy of electron and proton = -3.83 eV
Total energy of the electron = -3.67 eV.
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