To determine how many electrons in an atom with 30 electrons have the quantum number \( n = 3 \), we can follow the electron filling order according to the Aufbau principle.
The electron configuration of an atom with 30 electrons (which corresponds to the element zinc, \( \text{Zn} \)) is as follows:
- \( 1s: 2 \)
- \( 2s: 2 \)
- \( 2p: 6 \)
- \( 3s: 2 \)
- \( 3p: 6 \)
- \( 4s: 2 \)
- \( 3d: 10 \)
- \( 4p: 2 \)
Now, let's analyze the relevant shells for \( n = 3 \):
- The \( 3s \) subshell has 2 electrons.
- The \( 3p \) subshell has 6 electrons.
- The \( 3d \) subshell has 10 electrons.
So, adding these up, we have:
- \( 3s: 2 \)
- \( 3p: 6 \)
- \( 3d: 10 \)
Now total the electrons in the \( n = 3 \) level: \[ 2 (from : 3s) + 6 (from : 3p) + 10 (from : 3d) = 18 \]
Thus, the total number of electrons in the atom with the quantum number \( n = 3 \) is \( 18 \).
The correct answer is 18.