When n = 3, the quantum number of an element is

Analyze the question: The question is worded poorly. It most likely means: when the principal quantum number n = 3, what is the maximum number of electrons that can occupy that shell? The options (3, 9, 18, 21) suggest this.

Concept: The maximum number of electrons in a shell is given by the formula:

Maximum electrons = 2n²

Solution:

For n = 3:

• 2n² = 2 × 3² = 2 × 9 = 18

Check by subshells:

• 3s holds 2 electrons
• 3p holds 6 electrons
• 3d holds 10 electrons
• Total = 2 + 6 + 10 = 18

Checking the other options:

• A (3) is just the value of n itself.
• B (9) is n², which is the number of orbitals in the shell (1 + 3 + 5 = 9), not the number of electrons.
• D (21) does not match any rule.

Each orbital holds 2 electrons, so 9 orbitals × 2 = 18 electrons.

Tip: Remember the pattern 2n²: shell 1 holds 2, shell 2 holds 8, shell 3 holds 18, shell 4 holds 32. If you see "n = something" and options that look like electron counts, apply 2n² right away. Also remember n² gives orbitals and 2n² gives electrons, so you won't mix them up.