Answer :

Wavelength

∴ --------(1)

Now equating the new force equation with centripetal force,

------(2)

Where r is the new radius.

But we know that, ,putting this in equation 1

----------(3)

For , we get Bohr radius of the electron, ------(4)

Now, let the change in the orbital radius be p which is a small change.

∴ , ------(5)

∵ eq. 3 and 2 are the same, we equate them,

Now p^{2} and pr_{b} are ≪1

∴ neglecting them, --------(6)

Now kinetic energy

K.E. =

**Now putting value of p** and **,K.E for hydrogen atom ground state**

**∴** **K.E**

Now P.E. ----------(7)

Let

Differentiating w.r.t r

Substituting above in the integral (7) we get,

P.E.

Using equation (5) and putting , we get,

Using equation (6) ()

Now putting the values, we get,

(using )

∴ change in ground state energy

=

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