How many energy sublevels are present in each of the first three principal energy levels (n = 1, 2, and 3) of a hydrogen atom?

• A. 1 in n = 1, 1 in n = 2, and 1 in n = 3
• B. 3 in n = 1, 2 in n = 2, and 1 in n = 3
• C. 2 in n = 1, 3 in n = 2, and 4 in n = 3
• D. 1 in n = 1, 2 in n = 2, and 3 in n = 3

Answer: (D)

Verified step by step guidance

1. Recall that the number of energy sublevels within a principal energy level (n) is equal to the value of n itself. This means for each principal quantum number n, the number of sublevels is n.
2. For n = 1, the number of sublevels is 1. This corresponds to the 's' sublevel only.
3. For n = 2, the number of sublevels is 2. These are the 's' and 'p' sublevels.
4. For n = 3, the number of sublevels is 3. These include the 's', 'p', and 'd' sublevels.
5. Therefore, the pattern of sublevels for the first three principal energy levels is: 1 sublevel for n=1, 2 sublevels for n=2, and 3 sublevels for n=3.