PYQ NEET- Atoms And Nuclei L-7

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

A) 1

B) 4

C) 0.5

D) 2

Answer: (B) 4#

Sol:#

In case of Balmer series : $$ \begin{aligned} & \mathrm{n}_1=\infty, \mathrm{n}_2=2 \ & \therefore \frac{1}{\lambda_B}=\operatorname{Rc}\left(\frac{1}{2^2}-\frac{1}{\infty^2}\right)=\frac{R c}{4} \end{aligned} $$

In case of Lyman series : $$ \begin{aligned} & \mathrm{n}_1=\infty, \mathrm{n}_2=1 \ & \therefore \frac{1}{\lambda_L}=R c\left(\frac{1}{1^2}-\frac{1}{\infty^2}\right)=\mathrm{Rc} \ & \therefore \frac{\lambda_B}{\lambda_L}=\frac{4}{1}=4 \end{aligned} $$