Question

The frequency of the line in the emission spectrum of hydrogen when the atoms of the gas contain electrons in the third energy level are

• A. $1.268 \times 10^{14}Hz$and$2.864 \times 10^{16}Hz$
• B. $3.214 \times 10^{10}Hz$and$1.124 \times 10^{12}Hz$
• C. $1.806 \times 10^{12}Hz$and$6.204 \times 10^{15}Hz$
• D. $4.568 \times 10^{14}Hz$and$2.924 \times 10^{15}Hz$

Answer 1

Answer: (D)

$4.568 \times 10^{14}Hz$and$2.924 \times 10^{15}Hz$

Answer 2

If an electron is in 3^rd orbit, two spectral lines are possible

(1) When it falls from 3^rd orbit to 2^nd orbit.

In equation $\nu = 3.289 \times 10^{15}\left\lbrack \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack$

$\nu_{1} = 3.289 \times 10^{15}\left\lbrack \frac{1}{2^{2}} - \frac{1}{3^{2}} \right\rbrack = 3.289 \times 10^{15} \times \frac{5}{36} =$ $4.568 \times 14^{14}Hz$

(2) When it falls from 3^rd orbit to 1^st orbit :

}{= 2.924 \times 10^{15}Hz}$$