Question

A particular hydrogen-like ion emits radiation of frequency 2.92 × 10¹⁵ Hz when it makes the transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be ______.

पर्याय

• 0.44 × 10¹⁵

• 4.38 × 10¹⁵

• 6.57 × 10¹⁵

• 2.46 × 10¹⁵

Answer 1

A particular hydrogen-like ion emits radiation of frequency 2.92 × 10¹⁵ Hz when it makes the transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in the transition from n = 2 to n = 1 will be 2.46 × 10¹⁵.

Explanation:

Let z be the atomic number of a hydrogen-like atom, and the transition occurs from n₁ to n₂.

As a result, the wavelength in transition,

`1/lambda = Rz^2(1/(n_1^2) - 1/n_2^2)`

For first transition, n₁ = 3, n₂ = 1

`1/lambda = Rz^2(1/1 - 1/9)`

= `8/9Rz^2`

c = fλ

⇒ `f = 8/9 Rz^2.c` ......(i)

Similarly for n₁ = 2 to n = 1

`f^' = Rz^2c(1/1 - 1/4)`

= `Rz^2c xx 3/4` ........(ii)

We get, by dividing eqn (ii) by eqn (i)

`f^'/f = 27/32`

⇒ `f^' = (27/32)f`

`f^' = 27/32 xx 2.92 xx 10^15` Hz

= `2.46 xx 10^15` Hz