Question

let $f_2$ be the frequency of second line of Lyman series and $f_1$ be the frequency of first line of Balmer series, then the frequency of first line of Lyman series is given by,

• A. $f_2-f_1$
• B. $f_2+f_1$
• C. $f_1-f_2$
• D. $\frac{f_1{f}_2}{f_1+f_2}$

Answer 1

The correct option is A $f_2-f_1$

For second line of Lyman series, $f_2=Rc(\frac{1}{1^2}-\frac{1}{3^2})$ ___(1)
For first line of Balmer series,
$f_1=Rc(\frac{1}{2^2}-\frac{1}{3^2})$ ___(2)
Subtracting (2) from (1) we get,
$\Rightarrow f=Rc(\frac{1}{1^2}-\frac{1}{2^2})$
The above equation gives the frequency of the first member of Lyman series.
$\Rightarrow f=f_2-f_1$

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

$$\begin{array}{c}\text{Why this question?}\\ \text{This question is based on the spectral line of hydrogen atom.}\end{array}$$