Question

In a $H$-like sample, electrons make transition from $4^{th}$ excited state to the $2^{nd}$ state, then:

• A. $6$ different spectral lines are observed.
• B. $3$ different spectral lines are observed.
• C. number of lines belonging to the Balmer series is $3$.
• D. number of lines belonging to the Lyman series is $2$.

Answer 1

Answer: (A), (C)

The correct options are
A $6$ different spectral lines are observed.
C number of lines belonging to the Balmer series is $3$.

For an electronic transition from $n_2$ to $n_1$ state, the number of lines in the spectrum are equal to $\frac{(n_2-n_1)(n_2-n_1+1)}{2}$
Here, $n_2=5$ and $n_1=2$

Hence, the number of lines are equal to $\frac{(5-2)(5-2+1)}{2}=6$

Hence, when in a $H$-like sample, electrons make transition from $4^{th}$ excited state to $2^{nd}$ state, then $6$ different spectral lines are observed.

Out of these, three lines, $5\to 2$, $4\to 2$ and $3\to 2$ belong to the Balmer series.

Hence, options A and C are correct.