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's atomic 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

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's atomic 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

Infinity Learn · Accepted Answer

In hydrogen atom $$En=$$−$$Rhcn2Also$$ En∝m, where m is the mass of the electron. Here the electron has been replaced by a particle whose mass is double of an electron. Therefore, for this hypothetical atom energy in nth orbit will be given by $$En=$$−$$2Rhcn2The$$ longest wavelength λmax (or$$ minimum $$energy) photon will correspond to the transition of particle from n $$=$$ $$3$$ to n $$=$$ $$2$$⇒hcλ$$max=E3$$−$$E2=2Rhc122$$−$$132$$ This gives λ$$max=185R$$

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