SATHEE: Atoms And Nuclei Question 283

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) $n_{1} = 3 n_{2}$

B) $n_{1} = 4 n_{2}$

C) $n_{1} = 2 n_{2}$

D) $n_{1} = 5 n_{2}$

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, $T_{n} = \frac{2 π r_{n}}{v_{n}} \propto \frac{r_{n}}{v_{n}}$ Now $r_{n} \propto n^{2}; v_{n} \propto \frac{1}{n} ∴ \frac{r_{n}}{v_{n}} \propto n^{3} o r T_{n} \propto n^{3}$

Here $8 = {(\frac{n_{1}}{n_{2}})}^{3} o r \frac{n_{1}}{n_{2}} = 2 i .e ., n_{1} = 2 n_{2}$

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Atoms And Nuclei Question 283

Question: An electron in a hydrogen atom makes a transition from n=n1 to n=n2 . 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:

Answer:

Solution:

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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?