Atoms And Nuclei Question 301

Question: Suppose potential energy between electron and proton at separation r is given by U= K In (r), where K is a constant. For such a hypothetical hydrogen atom, the ratio of energy difference between energy levels (n=1 and n=2) and (n and n=4) is

Options:

A) 1

B) 2

C) 3

D) 4

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ -\frac{dU}{dr}=F $ (conservative force field)
    $ \Rightarrow F=\frac{-K}{r} $ provides the centrifugal force for circular motion of electron. $ \frac{mv^{2}}{r}=\frac{K}{r}\Rightarrow r=\frac{nh}{2\pi \sqrt{mK}} $ K.E. of electron $ =\frac{1}{2}mv^{2}=\frac{1}{2}K $ P.E. of electron = K In r E(n)=Total energy=K.E.+P.E.


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