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The figure shows the energy level of certain atom. When the electron de-excites from 3E to E, a electromagentic wave of wavelength $λ$ is emitted. What is the wavelength of the electromagnetic wave emitted when the electron de-excites from $\frac{5 E}{3}$ to E?
[Karnataka CET 2013, UP CPMT 2013]

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3 $λ$

2 $λ$

5 $λ$

$\frac{3 λ}{5}$

answer is A.

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Detailed Solution

As, electron de-excites from 3 $E \to E$

$∴ h ν = 3 E - E$

or $\frac{h c}{λ} = 2 E$ …(i)

When electron de-excites from $\frac{5 E}{3} \to E$

Substituting the value of E from Eq. (i) in above equation

$\frac{h c}{λ^{'}} = \frac{2}{3} (\frac{h c}{2 λ}) \Rightarrow λ^{'} = 3 λ$

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