Imagine an atom made up of proton and a hypothetical particle of double the mass of the electron but havign the same charge as the electron. Apply the Bhor atom 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 `lambda` (given in terms of the Rydberg constant R for the hydrogen atom) equal to (a) `9//5 R` (b) `36/5R` (c ) `18//5R` (d) `4//R`

Options

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

Answer

C

Explanation

`(1)/(lambda) = R [(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
For longest wavelength `n_(1) = 2, n_(2) = 3`
` :. (1)/(lambda) = R [(1)/(2^(2)) - (1)/(3^(2))] or (1)/(lambda) = R [(1)/(4) - (1)/(9)]`
`implies lambda = (1)/(m)`
So `lambda' = (1)/(2) xx (36)/(5 R) = (18)/(5 R)`