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  • The energy level of an atom for Ist , IInd & IIIrd level are <img alt="\mathrm{E, \frac{4 E}{3}, 2 E}" src="/latex-image/?%5Cmathrm%7BE%2C%20%5Cf

The energy level of an atom for Ist , IInd & IIIrd level are \mathrm{E, \frac{4 E}{3}, 2 E} respectively. A photon of wavelength \mathrm{\lambda } is emitted for a transition 3 to 1 . What will be the wavelength of emission from 2 to 1 in terms of \mathrm{\lambda }.

Option: 1

5\lambda


Option: 2

\mathrm{\left ( \frac{5}{4} \right )\lambda}


Option: 3

\mathrm{\left ( \frac{3}{2} \right )\lambda}


Option: 4

\mathrm{3\lambda}


Answers (1)

best_answer

\begin{aligned} \Delta E_{3 \rightarrow 1} & =E-2 E \\ & =E=\frac{h c}{\lambda}..........(1) \\ \Delta E_{2 \rightarrow 1} & =E-\frac{4 E}{3}=\frac{E}{3}=\frac{h c}{\lambda^{\prime}}-.....(2) \end{aligned}

Dividing equation :- 

\frac{E}{\frac{E}{3}}=\frac{\lambda^{\prime}}{\lambda}

\lambda^{\prime}=3 \lambda

Note :- Not counclering signs.

\therefore Option (4) is the right answer.

Posted by

shivangi.bhatnagar

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