n, l and m values of the `2p_(z)` orbital are

Options

A. 3,2,1
B. 2,1,0
C. 1,2,0
D. 2,0,1

Answer

To determine the quantum numbers \( n \), \( l \), and \( m \) for the \( 2p_z \) orbital, we will follow these steps:

### Step 1: Identify the Principal Quantum Number (\( n \))
The principal quantum number \( n \) indicates the energy level of the electron in an atom. For the \( 2p_z \) orbital, the number "2" indicates that the principal quantum number is:
\[ n = 2 \]

### Step 2: Determine the Azimuthal Quantum Number (\( l \))
The azimuthal quantum number \( l \) defines the shape of the orbital. The values of \( l \) can range from \( 0 \) to \( n-1 \). For \( p \) orbitals, \( l \) is always \( 1 \):
\[ l = 1 \]

### Step 3: Find the Magnetic Quantum Number (\( m \))
The magnetic quantum number \( m \) describes the orientation of the orbital in space. The possible values of \( m \) range from \( -l \) to \( +l \), including zero. For \( l = 1 \):
\[ m = -1, 0, +1 \]
Since we are specifically looking for the \( z \) orientation, we take:
\[ m = 0 \quad \text{(for the } p_z \text{ orbital)} \]

### Final Answer
Thus, the quantum numbers for the \( 2p_z \) orbital are:
- \( n = 2 \)
- \( l = 1 \)
- \( m = 0 \)