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Imagine an atom made up of a proton and a hypothetical particle of double the mass of the
electron but having the same charge as the electron. Apply the Bohr atomic model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength of photon in the Balmer series has wavelength $λ$ (given in terms of the Rydberg constant R for hydrogen atom) equal to

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$\frac{9}{5 R}$

$\frac{18}{5 R}$

$\frac{36}{5 R}$

$\frac{4}{5 R}$

answer is C.

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Detailed Solution

$E \propto m$

$∴ λ \propto \frac{1}{m}$

In case of hydrogen atom for longest wavelength of photon in the Balmer series,

$\frac{1}{λ} = R (\frac{1}{4} - \frac{1}{9}) or λ = \frac{36}{5 R}$

For this atom, $λ' = \frac{λ}{2} = \frac{18}{5 R}$ $(∵ m = 2 m)$

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