The number of orbitals in the quantum level n = 4 is

Options

A. 4
B. 9
C. 16
D. 18

Answer

To determine the number of orbitals in the quantum level \( n = 4 \), we can follow these steps:

### Step 1: Understand the Quantum Levels
Quantum levels (or shells) are denoted by the principal quantum number \( n \). Each level can contain one or more sub-levels (or subshells), which are designated as \( s, p, d, f \).

### Step 2: Identify the Subshells for \( n = 4 \)
For \( n = 4 \), the possible subshells are:
- 4s
- 4p
- 4d
- 4f

### Step 3: Determine the Number of Orbitals in Each Subshell
Each subshell contains a specific number of orbitals:
- The \( s \) subshell has 1 orbital.
- The \( p \) subshell has 3 orbitals.
- The \( d \) subshell has 5 orbitals.
- The \( f \) subshell has 7 orbitals.

### Step 4: Calculate the Total Number of Orbitals
Now, we can add the number of orbitals from each subshell:
- Total orbitals = Number of orbitals in \( 4s \) + Number of orbitals in \( 4p \) + Number of orbitals in \( 4d \) + Number of orbitals in \( 4f \)
- Total orbitals = \( 1 + 3 + 5 + 7 = 16 \)

### Conclusion
The total number of orbitals in the quantum level \( n = 4 \) is **16**.

---