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
Open in App
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.E∝n6
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.