Imagine an atom made up of a proton and a hypothetical particle of dounle the masss 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 `lambda` ( given in terms of the Rydberg constant R for hydrogen atom ) equal to

Options

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

Answer

C

Explanation

In hydrogen atom `E_(n)= - (Rhc)/n^(2)`. Also `E_(n) prop 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Here, the electron has been replaced by a particle whose mass is double of an electron.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 `n^(th)` orbit will be given by
`E_(n)= -(2Rhc)/n^(2)`
The longest wavelength `lambda_("max")` (or minimum energy) photon will correspond to the transition of particle from `n=3` to `n=2`.
`:. (hc)/lambda_("max")=E_(3)-E_(2)=Rhc(1/2^(2)-1/3^(2))`
`implies lambda_("max")=18/(5R)`