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Imagine an atom made up of proton and a hypothetical particle of double the mass of electron but having the same charge as the electron . Apply the Bohr's atomic model and consider all possible transitions of this hypothetical particle to the first excited level. The largest wavelength photon that will be emitted has wavelength $\lambda$ (given in terms of the Rydberg constant R for the hydrogen atom) equal to.


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Energy is related to mass
$E_n\propto m$
The longest wavelength $\lambda_{max}$ photon will correspond to the transition of particle from n=3 to n=2
$\large\frac{1}{\lambda_{max}} = 2R(\large\frac{1}{2^2}-\large\frac{1}{3^2})$
$\lambda_{max} = \large\frac{18}{5R}$
Hence answer is (c)
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