Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, $λ_{1}, λ_{2} and λ_{3}$ . Which one of the following equations correctly relates, $λ_{1}, λ_{2} and λ_{3}$ ?

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$λ_{1} = λ_{2} - λ_{3}$

$λ_{1} = λ_{3} - λ_{2}$

$\frac{1}{λ_{1}} = \frac{1}{λ_{2}} + \frac{1}{λ_{3}}$

$\frac{1}{λ_{1}} = \frac{1}{λ_{3}} + \frac{1}{λ_{2}}$

answer is C.

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Detailed Solution

As $λ_{1} < λ_{2} < λ_{3}$
${ΔE}_{1} = {ΔE}_{2} + {ΔE}_{3}$
$∴ \frac{hc}{λ_{1}} = \frac{hc}{λ_{2}} + \frac{hc}{λ_{3}}$
$∴ \frac{1}{λ_{1}} = \frac{1}{λ_{2}} + \frac{1}{λ_{3}}$

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