In a set of experiment on a hydrogen on a hypothetical one-electron atom, the wavelength of the photons emitted from transition ending in the ground state `(n = 1)` are shown in the energy level diagram

`lambda_(5 to 1) = 73.86 nm`
`lambda_(4 to 1) = 75.63 nm`
`lambda_(3 to 1) = 79.76 nm`
`lambda_(2 to 1) = 94.54 nm`
If an electron made a transition from `n = 4 to n = 2 level, the wavelength of the light that it would emit is nearly

Options

A. `380 nm`
B. `190 nm`
C. `76 nm`
D. `510 nm`

Answer

A

Explanation

` Delta E_(4 to 2) = (E_(4) - E_(1)) - (E_(2) - E_(1))`
`= 16.42 eV - 13.14 eV = 3.28 eV`
`lambda_(4 to 2) = (hc)/(Delta E _(4 to 2)) = (1242 eV nm)/(3.28 eV)`
`= 378.65 nm = 380 nm`