Question: Q. 2. What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state? $\square$ [O.D. Comptt. I, II, III 2013]
Show Answer
Solution:
Ans. If $n$ is the quantum number of highest energy level, then the total number of possible spectral lines emitted is
$$ N=\frac{n(n-1)}{2} $$
Here, third excited state means fourth energy level, i.e., $n=4$
$$ \begin{equation*} \therefore \quad N=\frac{4(4-1)}{2}=6 \tag{1} \end{equation*} $$
