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

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