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Question

If in Bohr's atomic model, it is assumed that force between electron and proton varies inversely as r4, then the kinetic energy of the electron will be proportional to nγ, where γ is

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Solution

The force between electron and proton varies inversely as r4

F=Kr4

This force provides the necessary centripetal force,

mv2r=Kr4

v2=Kmr3

According to Bohr's postulate,

mvr=nh2π

Squaring both sides, we get,

m2v2r2=n2h24π2

Substituting the values of v2 in above equation, we get,

m2(Kmr3)r2=n2h24π2

r=Km4π2n2h2

So, K.E=12mv2=12m(Kmr3) ...(1)

Substituting the values of r in equation (1), we get,

K.E=12K(n2)3(h2)3K3m343π6

K.En6

Answer : 6
Why this Question?
This question will help in understanding the concept of centripetal force, angular momentum and energy of electron in nth orbit of Bohr model.

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