A) \[{{K}_{n}}\] independent of n, \[{{r}_{n}}\propto n\]
B) \[{{K}_{n}}\propto \frac{1}{n},{{r}_{n}}\propto n\]
C) \[{{K}_{n}}\propto \frac{1}{n},{{r}_{n}}\propto {{n}^{2}}\]
D) \[{{K}_{n}}\propto \frac{1}{{{n}^{2}}},{{r}_{n}}\propto {{n}^{2}}\]
Correct Answer: A
Solution :
[a] \[\frac{m{{v}^{2}}}{r}=\frac{K}{r}\text{ or }v=\sqrt{\frac{K}{m}}=cr{}^\circ \] Now \[mvr=\frac{nh}{2\pi }\text{ or }r=\frac{nh}{2\pi mv}\] \[\therefore r\propto n.\] Also kinetic energy \[K=\frac{m{{v}^{2}}}{2}=\frac{m}{2}\times \frac{K}{m}=\frac{K}{2}.\]You need to login to perform this action.
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