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.
