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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

  • Option 1)

    2\rightarrow 1

  • Option 2)

    3\rightarrow 2

  • Option 3)

    4\rightarrow 2

  • Option 4)

    5\rightarrow 4


Answers (1)


As we learnt in

Energy emitted due to transition of electron -

\Delta E= Rhcz^{2}\left ( \frac{1}{n_{f}\, ^{2}}-\frac{1}{n_{i}\, ^{2}} \right )

\frac{1}{\lambda }= Rz^{2}\left ( \frac{-1}{n_{i}\, ^{2}}+\frac{1}{n_{f}\, ^{2}} \right )

- wherein

R= R hydberg\: constant

n_{i}= initial state \\n_{f}= final \: state


 Since n = 4 \rightarrown = 3 results in ultraviolet so to obtain infrared the energy gap should be smaller. Only option with smaller energy gap is 5\rightarrow4.

Hence correct option is 4.

Option 1)

2\rightarrow 1

This is an incorrect option.

Option 2)

3\rightarrow 2

This is an incorrect option.

Option 3)

4\rightarrow 2

This is an incorrect option.

Option 4)

5\rightarrow 4

This is the correct option.

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