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 atom model and consider all possible transitions of this hypothetical particle to the first excit

Question

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 atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength $λ$ (given in terms of the Rydberg constant $R$ for the hydrogen atom) equal to [2000]

Smart Achievers · Accepted Answer

(3)

For an ordinary hydrogen atom, the longest wavelength,

$\frac{1}{λ} = R [\frac{1}{2^{2}} - \frac{1}{3^{2}}] = \frac{5 R}{36}$ or $λ = \frac{36}{5 R}$

With the hypothetical particle, the required wavelength is

$λ' = \frac{1}{2} \times \frac{36}{5 R} = \frac{18}{5 R}$ $∵$ $λ \propto \frac{1}{m}$

Solution

1 9/(5R)

2 36/(5R)

3 18/(5R)

4 4/R

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