A particular hydrogen - like ion emits the radiation of frequency 3 × 10 15 Hz when it makes transition from n = 2 to n = 1 . The frequency of radiation emitted in transition from n =3 to n = 1 is x 9 × 10 15 Hz , when x = _____.

Step-by-step solution

For Hydrogen like atom, energy emitted is E = - 13 . 6 Z 2 1 n i 2 - 1 n f 2 ⇒ E = C 1 n f 2 - 1 n i 2 ⇒ h ν = C 1 n f 2 - 1 n i 2 Therefore, the ratio v 1 v 2 = 1 n f 2 - 1 n i 2 2 - 1 1 n f 2 - 1 n i 2 3 - 1 = 1 1 - 1 4 1 1 - 1 9 = 3 4 8 9 = 3 4 × 9 8 ⇒ v 1 v 2 = 27 32 ⇒ v 2 = 32 27 v 1 = 32 27 × 3 × 10 15 Hz = 32 9 × 10 15 Hz Hence, x = 32 .