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 \rightarrow 2

  • Option 2)

    4 \rightarrow 2

  • Option 3)

    4 \rightarrow 3

  • Option 4)

    2 \rightarrow 1

 

Answers (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 \rightarrow 2

This solution is incorrect 

Option 2)

4 \rightarrow 2

This solution is incorrect 

Option 3)

4 \rightarrow 3

This solution is correct 

Option 4)

2 \rightarrow 1

This solution is incorrect 

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