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

• A. 1
• B. 3
• C. 2
• D. 4

Answer: (D)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the shell number and determines the number of subshells within that shell.
2. The number of subshells in a given 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\(, corresponding to the subshells \)4s\(, \)4p\(, \)4d\(, and \)4f$ respectively.
4. Therefore, the total number of subshells in the \(n = 4\) shell is the count of these \(l\) values, which is 4.
5. This means the \(n = 4\) shell contains 4 subshells.