When a vast population of hydrogen atoms completely de-excites from the excited energy level $n=7$ t

Question

When a vast population of hydrogen atoms completely de-excites from the excited energy level $n=7$ to the lower level $n=2$, the absolute maximum number of distinct observable emission spectral lines is

Professor PC Thomas Classes · Answer

(a) : The universal formula specifying the maximum number of physically possible spectral lines generated when electrons transition downward between two distinct energy levels $n_2$ and $n_1$ is $\frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2}$. For this specific cascade, the upper limit is $n_2 = 7$ and the lower boundary is $n_1 = 2$. Processing these figures: $\frac{(7 - 2)(7 - 2 + 1)}{2} = \frac{(5)(6)}{2} = \frac{30}{2} = 15$ unique lines.