Question

A sample of the hydrogen atoms is excited to the n=4 state. In the spectrum of the emitted radiation, the number of lines in the ultraviolet and visible regions is respectively:

• A. $1:3$
• B. $2:1$
• C. $2:3$
• D. $3:1$

Answer 1

The correct option is B

$2:1$

The correct option is (B): $2:1$

Explanation for the correct answer:

Step 1: Given data:

$$\begin{gathered} \mathrm{Balmer}\mathrm{series}\to \mathrm{Visible}\to \mathrm{n}=2 \\ \mathrm{Lyman}\mathrm{series}\to \mathrm{Ultraviolet}\to \mathrm{n}=1 \end{gathered}$$

Step 2: Finding the number of lines in the visible region:

$$\begin{gathered} \frac{({\mathrm{n}}_2-{\mathrm{n}}_1)({\mathrm{n}}_2-{\mathrm{n}}_2+1)}{2} \\ \frac{(4-2)(4-2+1)}{2} \\ \frac{\left(2\right)\left(3\right)}{2} \\ =\frac{6}{2} \end{gathered}$$

= 3

Step 3: Finding the number of lines in the ultraviolet region:

$$\begin{gathered} \frac{({\mathrm{n}}_2-{\mathrm{n}}_1)({\mathrm{n}}_2-{\mathrm{n}}_1+1)}{2} \\ \frac{(4-1)(4-1+1)}{2} \\ \frac{\left(3\right)\left(4\right)}{2} \\ \frac{12}{2} \end{gathered}$$

= 6

So, the ratio of spectral lines in UV and visible is $6:3=2:1$

Therefore, the correct option is (B): $2:1$