Find the ratio of wavelengths of the emitted photons when an electron jumps from state n to ground state in hydrogen atom and in singly ionized helium atom.

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4 : 1

1 : 4

2 : 1

1 : 2

answer is A.

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Detailed Solution

From Bohrs theory we know that $λ \propto \frac{1}{Z^{2}} where λ$ is wavelength and Z is the atomic number

$\begin{array}{l} \Rightarrow \frac{λ_{H}}{λ_{He}} = \frac{Z_{He}^{2}}{Z_{H}^{2}} \\ \Rightarrow \frac{λ_{H}}{λ_{He}} = (\frac{2^{2}}{1^{2}}) \\ \Rightarrow \frac{λ_{H}}{λ_{He}} = \frac{4}{1} \end{array}$

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