The radii of two of the first four Bohre's orbits of the hydrogen atom are in the ratio ` 1: 4`. The enrgy differnce betweeen them may be :

Options

A. Either ` 12. 09 eV or 3.4 eV`
B. Either ` 2. 55 eV or 1 0 . 2 Ev`
C. `Either 13 . 6 eV or 3.4 ev`
D. Either 3.4eV or 0. 85 eV`

Answer

B

Explanation

The two orbits are either I and II or II and IV
` because `(r_(n_(2)))/(r_(n_(1))) = 4/1 and ` r_m prop n^2`
Thus ` E_2 -E_1 = (-13.6)/5 + 13.6 = 10.2eV`
` e_4- E_2 =- ( 13.6 )/(16) + ( 13 .6)/5 = 2 . 55 eV` .