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

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Here, the electron has been replaced by a particle whose mass is double of an electron.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)`