Atoms And Nuclei Question 283
Question: An electron in a hydrogen atom makes a transition from $ n=n_{1} $ to $ n=n_{2} $ . The time period of electron in the initial state is eight times that in the final state. Then which of the following statement is true?
Options:
A) $ n_{1}=3n_{2} $
B) $ n_{1}=4n_{2} $
C) $ n_{1}=2n_{2} $
D) $ n_{1}=5n_{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
- In the nth orbit, let $ r_{n} $ be the radius and $ v_{n} $ be the speed of electron. Time period, $ T_{n}=\frac{2\pi r_{n}}{v_{n}}\propto \frac{r_{n}}{v_{n}} $ Now $ r_{n}\propto n^{2};v_{n}\propto \frac{1}{n}\therefore \frac{r_{n}}{v_{n}}\propto n^{3}orT_{n}\propto n^{3} $
Here $ 8={{( \frac{n_{1}}{n_{2}} )}^{3}}or\frac{n_{1}}{n_{2}}=2\text{ i}\text{.e}\text{.,}n_{1}=2n_{2} $
