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

D

Explanation

We know that
`lambda prop (1)/(m)`
For ordinarry hydrogen atom ,
`(1)/(lambda) = R [1/(2)^(2) - (1)/(3)^(2)] = (5 R)/(36) or lambda = (36)/(5 R)`
`"With hypothetical particals, required wavelength"`
`lambda' = (1)/(2) xx (36)/(5 R) = (18)/(5 R)`