The total number of m values for `n = 4` is

Options

A. 8
B. 16
C. 12
D. 20

Explanation

To find the total number of m values for \( n = 4 \), we can follow these steps:

### Step 1: Understand the quantum numbers
The principal quantum number \( n \) indicates the energy level of an electron in an atom. For each value of \( n \), there are different types of orbitals (s, p, d, f) that can exist.

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

### Step 3: Calculate the m values for each l
For each value of \( l \), the magnetic quantum number \( m \) can take values from \( -l \) to \( +l \), including zero. The total number of \( m \) values for each \( l \) is given by \( 2l + 1 \).

- For \( l = 0 \) (s orbital):
- \( m \) values: \( 0 \) (Total = 1)

- For \( l = 1 \) (p orbital):
- \( m \) values: \( -1, 0, +1 \) (Total = 3)

- For \( l = 2 \) (d orbital):
- \( m \) values: \( -2, -1, 0, +1, +2 \) (Total = 5)

- For \( l = 3 \) (f orbital):
- \( m \) values: \( -3, -2, -1, 0, +1, +2, +3 \) (Total = 7)

### Step 4: Sum the total m values
Now, we can sum the total number of \( m \) values from each type of orbital:
- Total \( m \) values = \( 1 + 3 + 5 + 7 = 16 \)

### Final Answer
The total number of m values for \( n = 4 \) is **16**.

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