Atoms - Result Question 32

34. An electron changes its position from orbit $n=2$ to the orbit $n=4$ of an atom. The wavelength of the emitted radiations is $(R=$ Rydberg’s constant)

[2001]

(a) $\frac{16}{R}$

(b) $\frac{16}{3 R}$

(c) $\frac{16}{5 R}$

(d) $\frac{16}{7 R}$

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Answer:

Correct Answer: 34. (b)

Solution:

  1. (b) $\bar{{}v}=R(\frac{1}{n_1^{2}}-\frac{1}{n_2^{2}})$, where $n_1=2, n_2=4$

$\bar{{}v}=R(\frac{1}{4}-\frac{1}{16})$

$\frac{1}{\lambda}=R(\frac{12}{4 \times 16}) \quad \Rightarrow \quad \lambda=\frac{16}{3 R}$