# The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from: Option 1) 3 2 Option 2) 4 2 Option 3) 4 3 Option 4) 2 1

Energy diffference for infrared radiation will be smaller than those ultraviolet region.

Transition corresponding to Infra red region is:

$2\rightarrow 1;\frac{1}{\lambda }=R(1-\frac{1}{4})\:or\:\lambda =\frac{4}{3R}=12003mm(UV)\\ 3\rightarrow 2;\frac{1}{\lambda }=R\left ( \frac{1}{4} -\frac{1}{9}\right )\:or \lambda =\frac{36}{5R}$

$\lambda =\frac{36}{5}\times 91nm=648nm(visible\:region)\\ 4\rightarrow 2\:\frac{1}{\lambda }=R\left ( \frac{1}{4} -\frac{1}{16}\right )=R\frac{3}{16}\\ \lambda =\frac{16}{3R}=\frac{16}{3R}\times 91nm=480nm(visible)$

$4\rightarrow 3;\frac{1}{\lambda }=R\left ( \frac{1}{9}-\frac{1}{16}\right )=R(\frac{7}{144})\\ \lambda =\frac{144}{7R}=\frac{144}{7}\times 91nm=1872nm\:IR$

Option 1)

3 2

This solution is incorrect

Option 2)

4 2

This solution is incorrect

Option 3)

4 3

This solution is correct

Option 4)

2 1

This solution is incorrect

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