Question

Value of ${n_1}$ and ${n_2}$ for ${H_\beta }$ spectral line for Balmer series in the hydrogen emission spectrum is:
$A.$ $1$ and $2$
$B.$ $2$ and $3$
$C.$ $3$ and $2$
$D.$ $2$ and $4$

Answer 1

As we know in the hydrogen spectrum, the number of spectral lines possible will be equal to the number of transitions possible between the highest orbital and first orbital for the specified series. For Balmer series $n = 2$

Complete solution
There are many lines in the Balmer series, the first line is called ${H_\alpha }$ , the second line is called ${H_\beta }$ and the third line is called ${H_\gamma }$ and so on.
We know for the Balmer series ${n_1}$ is fixed at $2$ and for the ${H_\beta }$ spectral line for the Balmer series ${n_2}$ is $4$ .
Therefore, the value of ${n_1}$ and ${n_2}$ are $2$ and $4$ respectively.

Thus, the correct option is $D$ .

Additional information
Balmer series: Balmer series is the series of visible lines in the hydrogen atom spectrum named as Balmer series. This series of spectral emission lines occur when the electron transitions from a high energy level to the lower energy level of $n = 2$ .
Balmer was able to relate the wavelength of emitted light using the Balmer formula,
$\lambda = C\left( {\dfrac{{{m^2}}}{{{m^2} - {n^2}}}} \right)$
Where, $\lambda$ is the observed wavelength, $C$ is a constant, $n$ is the lower energy with a value of $2$ and $m$ is the higher energy level, which has a value greater than $3$ .
The value of constant $\left( C \right)$ is $364.50682nm$ .
There are also other lines in the hydrogen spectrum such as Lyman series, Paschen series, Brackett series and Pfund series.

Note
It is to be noted that the Balmer series is particularly useful in astronomy because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the universe, and therefore are commonly seen and relatively strong compared to lines from other elements.