How many subshells and electrons are associated with n = 4?

Options

A. (a) 32, 64
B. (b) 16, 32
C. (c) 4, 16
D. (d) 8, 16

Explanation

To determine how many subshells and electrons are associated with \( n = 4 \), we can follow these steps:

### Step 1: Identify the value of the principal quantum number (n)
We are given that \( n = 4 \).

### Step 2: Determine the number of subshells
The number of subshells associated with a principal quantum number \( n \) is equal to \( n \) itself. Therefore, for \( n = 4 \), there are 4 subshells:
- 4s
- 4p
- 4d
- 4f

### Step 3: Count the number of orbitals in each subshell
- The 4s subshell has 1 orbital.
- The 4p subshell has 3 orbitals.
- The 4d subshell has 5 orbitals.
- The 4f subshell has 7 orbitals.

### Step 4: Calculate the total number of orbitals
Now, we can sum the number of orbitals from each subshell:
\[ 1 \, (\text{from } 4s) + 3 \, (\text{from } 4p) + 5 \, (\text{from } 4d) + 7 \, (\text{from } 4f) = 16 \, \text{orbitals} \]

### Step 5: Calculate the total number of electrons
Each orbital can hold a maximum of 2 electrons (due to the Pauli exclusion principle). Therefore, the total number of electrons that can be accommodated in these orbitals is:
\[ 2 \times \text{(number of orbitals)} = 2 \times 16 = 32 \, \text{electrons} \]

### Final Answer
Thus, for \( n = 4 \):
- Number of subshells = 4
- Number of electrons = 32

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