A) Equal to one fourth the circumference of the first orbit
B) Equal to half the circumference of the first orbit
C) Equal to twice the circumference of the first orbit
D) Equal to the circumference of the first orbit
Correct Answer: D
Solution :
\[mv{{r}_{n}}=\frac{nh}{2\pi }\Rightarrow p{{r}_{n}}=\frac{nh}{2\pi }\Rightarrow \frac{h}{\lambda }\times {{r}_{n}}=\frac{nh}{2\pi }\] \[\Rightarrow \lambda =\frac{2\pi {{r}_{n}}}{n},\]for first orbit \[n=1\]so \[\lambda =2\pi {{r}_{1}}\] = circumference of first orbit
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