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 atom model and consider all possible transitions of this hypothetical particle that will be emitted level . The longest wavelength photon that will be emitted has longest wavelength `lambda` (given in terms of the Rydberg constant `R` for the hydrogen atom) equal to

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)`