Energy levels A, B and C of a certain atom correspond to increasing values of energy, i.e.

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12.Atoms

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Energy levels $A, B$ and $C$ of a certain atom correspond to increasing values of energy, i.e. $E_A < E_B < E_C$ . If $\lambda _1, \lambda _2$ and $\lambda _3$ are the wavelengths of radiations corresponding to transitions $C$ to $B, B$ to $A$ and $C$ to $A$ respectively , which of the following relations is correct ?

${\lambda _3} = {\lambda _1} + {\lambda _2}$

${\lambda _3} = \frac{{{\lambda _1}{\lambda _2}}}{{{\lambda _1} + {\lambda _2}}}$

${\lambda _1} + {\lambda _2} + {\lambda _3} = 0$

${\lambda _3}^2 = {\lambda _1}^2 + {\lambda _2}^2$

Solution

$\mathrm{E}_{\mathrm{c}}-\mathrm{E}_{\mathrm{A}}=\left(\mathrm{E}_{\mathrm{c}}-\mathrm{E}_{\mathrm{B}}\right)+\left(\mathrm{E}_{\mathrm{B}}-\mathrm{E}_{\mathrm{A}}\right)$

$\Rightarrow \frac{\mathrm{hc}}{\lambda_{3}}=\frac{\mathrm{hc}}{\lambda_{1}}+\frac{\mathrm{hc}}{\lambda_{2}}$

$\Rightarrow \lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}}$

Standard 12

Physics

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(NEET-2016)

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(IIT-2012)

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(AIPMT-2009)

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hard

Solution

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