The following diagram indicates the energy levels of a certain atom when the electron moves from 4E level to E. A photon of wavelength $λ_{1}$ is emitted. The wavelength of photon produced during its transition from $\frac{7}{3} E$ level to E is $λ_{2}$ . The ratio $\frac{λ_{1}}{λ_{2}}$ will be

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$\frac{9}{4}$

$\frac{4}{9}$

$\frac{3}{2}$

$\frac{7}{3}$

answer is B.

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Detailed Solution

$Transition from 4 E to E (4 E - E) = \frac{h c}{λ_{1}} \Rightarrow λ_{1} = \frac{h c}{3 E} . . . . . . . . . (i) Transition from \frac{7}{3} E to E (\frac{7}{3} E - E) = \frac{h c}{λ_{2}} \Rightarrow λ_{2} = \frac{3 h c}{4 E} . . . . . . . . . (i i) From equations (i) and (ii): \Rightarrow \frac{λ_{1}}{λ_{2}} = \frac{4}{9}$