Imagine an atom made of a proton and a hypothetical particle of double the mass of the electron but having the same change as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle of the first excited level. the longest wavelength photon that will be emitted has wavelength [given in terms of the Rydberg constant `R` for the hydrogen atom] equal to

Options

A. `(9)/(5R)`
B. `(36)/(5R)`
C. `(18)/(5R)`
D. `(4)/(R)`

Answer

C

Explanation

Energy is related to mass:
`E_(n)propm`
The longest wavelength `lamda_(max)` photon will correspond to the transition of particle from =3 to n=2.
`(1)/(lamda_(max))=2R((1)/(2^(2))-(1)/(3^(2)))`
`lamda_(max)=(18)/(5R)`