When an electron is transisted from 2E to E energy level, the wavelength of resultant photon produced is λ1. If electron transition involves 43E to E level, the wave length of resultant photon is λ2 . The correct relation between λ1&λ2 is λ2=Xλ1 . Then find the value of x ?

2E-E=hcλ1 ⇒E=hcλ1again, 4E3−E=hcλ2⇒E3=hcλ2 or E=3hcλ2=hcλ1 or λ2=3λ1

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When an electron is transisted from 2E to E energy level, the wavelength of resultant photon produced is $λ_{1}$ . If electron transition involves $\frac{4}{3}$ E to E level, the wave length of resultant photon is $λ_{2}$ . The correct relation between $λ_{1} & λ_{2}$ is $λ_{2} = X λ_{1}$ . Then find the value of x ?

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answer is 3.

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Detailed Solution

$\begin{array}{l} 2E-E= \frac{h c}{λ_{1}} \Rightarrow E= \frac{h c}{λ_{1}} \\ again, \frac{4 E}{3} - E= \frac{h c}{λ_{2}} \\ \Rightarrow \frac{E}{3} = \frac{h c}{λ_{2}} or E=3 \frac{h c}{λ_{2}} = \frac{h c}{λ_{1}} or λ_{2} = 3 λ_{1} \end{array}$