What is the maximum number of electrons that can be contained within the n = 2 shell of an atom?

• A. 2
• B. 8
• C. 18
• D. 4

Answer: (B)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the shell or energy level of an electron in an atom. For \(n = 2\), we are looking at the second shell.
2. Determine the possible subshells within the \(n = 2\) shell. The azimuthal quantum number \(l\) can take values from \$0\( to \)n-1\(, so for \)n=2\(, \)l\( can be \)0\( (the 2s subshell) or \)1$ (the 2p subshell).
3. Calculate the number of orbitals in each subshell. The number of orbitals for a given \(l\) is \$2l + 1\(. For \)l=0\( (2s), there is \)1\( orbital; for \)l=1\( (2p), there are \)3$ orbitals.
4. Sum the total number of orbitals in the \(n=2\) shell: \$1\( (from 2s) \)+\( \)3\( (from 2p) \)= 4$ orbitals.
5. Since each orbital can hold a maximum of \$2\( electrons (due to the two possible spin states), multiply the total orbitals by \)2\( to find the maximum number of electrons: \)4 \times 2 = 8$ electrons.