The number of orbitals and subshells present in the shell with n = 4 is:

Options

A. 8, 2
B. 16, 4
C. 18, 3
D. 32, 5

Explanation

To determine the number of orbitals and subshells present in the shell with n = 4, we can follow these steps:

### Step 1: Identify the value of n
The principal quantum number \( n \) is given as 4. This indicates we are looking at the fourth shell.

### Step 2: Determine possible values of the azimuthal quantum number (l)
The azimuthal quantum number \( l \) can take values from 0 to \( n - 1 \). Therefore, for \( n = 4 \):
- Possible values of \( l \) are:
- \( l = 0 \) (s subshell)
- \( l = 1 \) (p subshell)
- \( l = 2 \) (d subshell)
- \( l = 3 \) (f subshell)

Thus, there are 4 subshells in total.

### Step 3: Calculate the number of orbitals for each subshell
The number of orbitals in each subshell can be determined using the formula \( 2l + 1 \):
- For \( l = 0 \) (s subshell):
- Number of orbitals = \( 2(0) + 1 = 1 \)
- For \( l = 1 \) (p subshell):
- Number of orbitals = \( 2(1) + 1 = 3 \)
- For \( l = 2 \) (d subshell):
- Number of orbitals = \( 2(2) + 1 = 5 \)
- For \( l = 3 \) (f subshell):
- Number of orbitals = \( 2(3) + 1 = 7 \)

### Step 4: Total the number of orbitals
Now, we can sum the number of orbitals from each subshell:
- Total number of orbitals = \( 1 + 3 + 5 + 7 = 16 \)

### Step 5: Conclusion
In the shell with \( n = 4 \):
- Number of subshells = 4 (s, p, d, f)
- Number of orbitals = 16

Thus, the answer is:
- **Number of subshells: 4**
- **Number of orbitals: 16**