Question

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is

• A. $2:1$
• B. $1:2$
• C. $4:1$
• D. $2:6$

Answer 1

The correct option is C $4:1$

Wavelength in Lyman series is given by $\frac{1}{\lambda }=R{Z}^2(1-\frac{1}{n^2})$
For last line, $n\to \infty$ so $\frac{1}{{\lambda }_L}=R{Z}^2$

Wavelength in Balmer series is given by $\frac{1}{\lambda }=R{Z}^2(\frac{1}{2^2}-\frac{1}{n^2})$
For last line $n\to \infty$ so $\frac{1}{{\lambda }_B}=\frac{R{Z}^2}{4}$
Therefore the required ratio is $\frac{{\lambda }_B}{{\lambda }_L}=\frac{4}{1}$