If a shell can hold a maximum of 32 electrons, what is the principal quantum number n for that shell?

• A. n = 4
• B. n = 2
• C. n = 3
• D. n = 5

Answer: (A)

Verified step by step guidance

1. Recall the formula for the maximum number of electrons that can occupy a shell with principal quantum number \( n \): \[ \text{Maximum electrons} = 2n^2 \]
2. Set the maximum number of electrons equal to 32, since the shell can hold up to 32 electrons: \[ 2n^2 = 32 \]
3. Solve for \( n^2 \) by dividing both sides of the equation by 2: \[ n^2 = \frac{32}{2} = 16 \]
4. Take the square root of both sides to find \( n \): \[ n = \sqrt{16} \]
5. Determine the positive value of \( n \) since the principal quantum number must be a positive integer, which gives \( n = 4 \).