The ratio of the differrence between the first and second Bohr orbit energies to that between second and third Bohr orbit energies is

Options

A. `1/2`
B. `1/3`
C. `27/5`
D. `4/9`

Answer

C

Explanation

`E_n = -(1.316 xx 10^6)/(n^2)`
`:.` Difference between first and second orbit
`DeltaE_1 = -1.316 xx 10^6 (1/1 - 1/(2^2)) = -1.316 xx 10^6 xx 3/4`
Difference between second and third orbit
`DeltaE_2 = -1.316 xx 10^6 (1/(2^2) - 1/(3^2)) = -1.316 xx 10^6 xx 5/36`
Ratio, `(DeltaE_1)/(DeltaE_2) = 3/4 xx 36/5 = 27/5`