First slide

Bohr Model of the Hydrogen atom.

Question

The transition from the state n = 4 to n =3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from :

Easy

A

3 → 2
B

4 → 2
C

5 → 4
D

2 → 1

Solution

$\frac{1}{λ} α (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}); ∴ \frac{1}{λ_{uv}} α (\frac{1}{3^{2}} - \frac{1}{4^{2}}) ∴ λ_{uv} \propto 20.5$
According to options :
$1 . \frac{1}{λ_{1}} \propto (\frac{1}{2^{2}} - \frac{1}{3^{2}}) ∴ λ_{1} \propto 7.2$
$2 . \frac{1}{λ_{2}} \propto (\frac{1}{2^{2}} - \frac{1}{4^{2}}) ∴ λ_{2} \propto 5.3$
$3 . \frac{1}{λ_{3}} \propto (\frac{1}{4^{2}} - \frac{1}{5^{2}}) ∴ λ_{3} \propto 44.4$
$4 . \frac{1}{λ_{4}} \propto (\frac{1}{1^{2}} - \frac{1}{2^{2}}) ∴ λ_{4} \propto 1.3$
For IR radiation :
$λ_{IR} > λ_{uv}; i . e ., λ_{3} > λ_{uv}$
So, transition should take place from 5 → 4

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