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 1

The correct option is B

$4$

Step - 1: Given

The last line of the Balmer series means transition will from $n_2=\infty to{n}_1=2$

The last line of the Lyman series means transition will from $n_2=\infty to{n}_1=1$

Step - 2: Formula

Wavelength is given by $\frac{1}{\lambda }=R\left(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2}\right)$

Step - 3: Solution

Wavelength of Balmer series, $$\begin{gathered} \frac{1}{{\lambda }_B}=R\left(\frac{1}{2^2}-\frac{1}{{\infty }^2}\right) \\ \frac{1}{{\lambda }_B}=\frac{R}{4} \end{gathered}$$

Wavelength of Lyman series, $$\begin{gathered} \frac{1}{{\lambda }_L}=R\left(\frac{1}{1^2}-\frac{1}{{\infty }^2}\right) \\ \frac{1}{{\lambda }_L}=\frac{R}{1} \end{gathered}$$

Ratio of wavelengths of Balmer to Lyman, $\frac{{\lambda }_B}{{\lambda }_L}=\frac{4}{1}$

Hence option B is correct.