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

• A. 2
• B. 3
• C. 4
• D. 1

Answer: (C)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the shell number in an atom, and for each shell, the possible subshells are determined by the azimuthal quantum number \(l\).
2. The azimuthal quantum number \(l\) can take integer values from \$0\( up to \)n-1\(. So for \)n = 4\(, \)l\( can be \)0, 1, 2,\( or \)3$.
3. Each value of \(l\) corresponds to a different subshell: \(l=0\) is the \(s\) subshell, \(l=1\) is the \(p\) subshell, \(l=2\) is the \(d\) subshell, and \(l=3\) is the \(f\) subshell.
4. Count the number of possible \(l\) values for \(n=4\), which gives the total number of subshells in the \(n=4\) shell.
5. Conclude that the number of subshells in the \(n=4\) shell is equal to the number of allowed \(l\) values, which is \$4$.