Question

The frequency of $1^{st}$ line of Balmer series in $H_2$ atom is ${\nu }_o$. The frequency of line emitted by singly ionised $He$ atom is,

• A. $2{\nu }_o$
  
• B. $4{\nu }_o$
  
• C. $\frac{{\nu }_o}{2}$
  
• D. $\frac{{\nu }_o}{4}$
  

Answer 1

The correct option is B $4{\nu }_o$


We know that
$\nu$ $\propto$ $Z^2$
Where $\nu \to$ frequency of atom
$Z\to$ atomic number

$\Rightarrow \frac{{\nu }_H}{{\nu }_{He}}={\left(\frac{Z_H}{Z_{He}}\right)}^2={\left(\frac{1}{2}\right)}^2$

$\begin{array}{c}{\nu }_{He}=4{\nu }_H=4{\nu }_0\end{array}$

Hence, $\left(B\right)$ is the correct answer.