The Bohr model for the H-atom relies on the Coulomb’s law of electrostatics. Coulomb’s law has not directly been verified for very short distances of the order of angstroms. Supposing Coulomb’s law between two opposite charge +q1, –q2 is modified to
Calculate in such a case, the ground state energy of an H-atom, if
Let the case consider the case when
Let
where
The electrostatic force of attraction between the positively charged nucleus and negatively charged electrons provides the necessary centripetal force.
Where rn is the radius of nth orbit of electron for n=1 and substituting the values of constant we get
This is the radius of orbit of electron in ground state of hydrogen atom again using Bohr second postulate the speed of the electron
For n=1 the speed of electron in ground state
The kinetic energy of electron in the ground state
Potential energy of electron in the ground state till R0
Potential energy from R0 to r,