Q. 28

# The inverse squar

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 p2 and prb 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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