How many distinct emission lines are possible when an electron in the n = 4 energy level of a hydrogen atom transitions to the ground state (n = 1)?

• A. 3
• B. 6
• C. 5
• D. 4

Answer: (B)

Verified step by step guidance

1. Identify all possible energy levels involved in the transitions. Since the electron starts at n = 4 and ends at n = 1, the possible intermediate levels are n = 3, n = 2, and n = 1.
2. List all possible transitions the electron can make from higher to lower energy levels, remembering that each transition corresponds to an emission line. The electron can transition from n = 4 to n = 3, n = 4 to n = 2, n = 4 to n = 1, n = 3 to n = 2, n = 3 to n = 1, and n = 2 to n = 1.
3. Count the total number of distinct transitions by considering all pairs of energy levels where the initial level is higher than the final level. The formula to find the number of possible emission lines from level n is given by the combination formula: \(\frac{n(n-1)}{2}\).
4. Apply the formula for n = 4: calculate \(\frac{4 \times (4-1)}{2}\) to find the total number of distinct emission lines possible.
5. Interpret the result as the number of unique photon energies (or wavelengths) emitted when the electron transitions from n = 4 down to n = 1 through all possible intermediate steps.