Question

The frequency of the first line in Lyman series in the hydrogen spectrum is $\nu .$ What is the frequency of the corresponding line in the spectrum of body ionized Lithium?

• A. $\nu$
• B. $3\nu$
• C. $9\nu$
• D. $27\nu$

Answer 1

The correct option is C $9\nu$

The frequency of the radiation emitted will be,

$\Delta E=h\nu \Rightarrow \nu \propto \Delta E$

Also, $E_n=-13.6\left(\frac{Z^2}{n^2}\right)\text{eV}$

In Hydrogen atom, for the first Lyman series,

$n_f=1;n_i=2;Z=1$

$\Delta E=-(\Delta E_f-\Delta E_i)=(\Delta E_i-\Delta E_f)$

$\therefore \Delta E=13.6Z^2[\frac{1}{(n_f{)}^2}-\frac{1}{(n_i{)}^2}]$

$\Rightarrow \Delta E=13.6\times \frac{3}{4}\text{eV}.....\left(1\right)$

In Lithium atom, for the first Lyman series,

$n_f=1;n_i=2;Z=3$

$\Delta E=-(\Delta E_f-\Delta E_i)=(\Delta E_i-\Delta E_f)$

$\therefore \Delta E=13.6Z^2[\frac{1}{(n_f{)}^2}-\frac{1}{(n_i{)}^2}]$

$\Rightarrow \Delta E=13.6\times 9\times \frac{3}{4}\text{eV}.....\left(2\right)$

From (1) and (2) we get,

Frequency of the radiation emitted by Lithium atom will be $9$ times frequency of the radiation emitted by hydrogen atom.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.