Atomic Physics Question 2
Question 2 - 2024 (01 Feb Shift 2)
A particular hydrogen - like ion emits the radiation of frequency $3 \times 10^{15} Hz$ when it makes transition from $n=2$ to $n=1$. The frequency of radiation emitted in transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} Hz$, when $x=$
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Answer: (32)
Solution:
$E=-13.6 z^{2}\left(\frac{1}{n _i^{2}}-\frac{1}{n _f^{2}}\right)$
$E=C\left(\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right)$
$h v=C\left[\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right]$
$\frac{v _1}{v _2}=\frac{\left[\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right] _{2-1}}{\left[\frac{1}{n _f^{2}}-\frac{1}{n _i^{2}}\right] _{3-1}}$
$=\frac{\left[\frac{1}{1}-\frac{1}{4}\right]}{\left[\frac{1}{1}-\frac{1}{9}\right]}=\frac{3 / 4}{8 / 9}$
$=\frac{3}{4} \times \frac{9}{8}$
$\frac{v _1}{v _2}=\frac{27}{32}$
$v _2=\frac{32}{27} v _1=\frac{32}{27} \times 3 \times 10^{15} Hz=\frac{32}{9} \times 10^{15} Hz$
