Question

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number $Z$ of hydrogen like ion is :

• A. $3$
• B. $2$
• C. $1$
• D. $4$

Answer 1

The correct option is B $2$

For hydrogen
$\frac{hc}{\lambda }=Rhc(\frac{1}{1^2}-\frac{1}{2^2})$
for hydrogen like ion
$\frac{hc}{\lambda }=Z^{2}Rhc(\frac{1}{2^2}-\frac{1}{4^2})$
According to question,
$(\frac{1}{1}-\frac{1}{4})=Z^2(\frac{1}{4}-\frac{1}{16})$
Or $Z=2$.
Hence, option $\left(D\right)$ is correct.