Question

The frequency of the first line of Balmer series in hydrogen atom is $v_{0}Hz$. The frequency $v$ of this line emitted by a singly ionized He-atom is

• A. $2v_{0}Hz$
• B. $4v_{0}Hz$
• C. $\left(v_0/2\right)Hz$
• D. $\left(v_0/4\right)Hz$

Answer 1

Answer: (B)

$v=Z^{2}Rc\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
For hydrogen atom,
$v_0=(1{)}^{2}Rc\left[\frac{1}{2^2}-\frac{1}{3^2}\right]=\frac{5Rc}{36}$
For singly ionised He atom,
$v=(2{)}^{2}Rc\left[\frac{1}{2^2}-\frac{1}{3^2}\right]=\frac{20Rc}{36}$
$\therefore \frac{v}{v_0}=4\text{ or }v=4v_0$