Nuclear Physics And Radioactivity Question 96
Question: The electric potential between a proton and an electron is given by $ V=V_{0},In,\frac{r}{r_{0}} $ , where $ r_{0} $ is a constant. Assuming Bohr’s model to he-applicable, write variation of $ r_{n} $ with n, n being the principal quantum number
Options:
A) $ r_{n}\propto n $
B) $ r_{n}\propto 1/n $
C) $ r_{n}\propto n^{2} $
D) $ r_{n}\propto 1/n^{2} $
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Answer:
Correct Answer: A
Solution:
[a] Potential energy $ U=eV=eV_{0}In\frac{r}{r_{0}} $
$ \therefore ForceF=-| \frac{dU}{dr} |=\frac{eV_{0}}{r} $
$ \therefore $ The force will provide the necessary centripetal Force. Hence $ \frac{mv^{2}}{r}=\frac{eV_{0}}{r}\Rightarrow v=\sqrt{\frac{eV_{0}}{m}} $ ?(i) And $ mvr=\frac{nh}{2\pi } $ …(ii) From equations (i) and (ii), $ mr=( \frac{nh}{2\pi } )\sqrt{\frac{m}{eV_{0}}} $ Or $ r\propto n $
BETA
