How many subshells are present in the principal quantum shell with n = 4?

• A. 2
• B. 1
• C. 3
• D. 4

Answer: (D)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the main energy level or shell of an electron in an atom.
2. Understand that the number of subshells within a principal shell is equal to the value of \(n\) because the azimuthal quantum number \(l\) can take integer values from \$0\( up to \)n-1$.
3. For \(n = 4\), the possible values of \(l\) are \$0, 1, 2,\( and \)3$, which correspond to the subshells labeled as s, p, d, and f respectively.
4. Count the number of possible \(l\) values to find the number of subshells: since \(l\) can be \$0, 1, 2,\( or \)3\(, there are 4 subshells in the \)n=4$ shell.
5. Therefore, the principal quantum shell with \(n=4\) contains 4 subshells.