An electron in a hydrogen atom is in the third excited state. It returns to the ground state by emitting photons. How many different photon wavelengths are possible?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6
The ground state is \( n = 1 \), the first excited state \( n = 2 \), and so on, so the third excited state is \( n = 4 \). On the way down the electron can jump between any two levels from \( n = 4 \) to \( n = 1 \), and each pair of levels gives one spectral line.
\( \displaystyle \text{number of lines} = \frac{n(n-1)}{2} = \frac{4\times3}{2} = 6 \)
\( 4\rightarrow3,\; 4\rightarrow2,\; 4\rightarrow1 \)
\( 3\rightarrow2,\; 3\rightarrow1 \)
\( 2\rightarrow1 \)