The maximum number of electrons in p-orbital with n=5, m=1 is

Options

A. 6
B. 2
C. 14
D. 10

Explanation

To determine the maximum number of electrons in a p-orbital with the principal quantum number \( n = 5 \) and magnetic quantum number \( m = 1 \), we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number \( n \) indicates the energy level of the electron. Here, \( n = 5 \) means we are dealing with the 5th energy level.

**Hint:** The principal quantum number \( n \) can take positive integer values (1, 2, 3, ...).

### Step 2: Determine the Azimuthal Quantum Number (l)
For p-orbitals, the azimuthal quantum number \( l \) is equal to 1. This indicates that we are dealing with p-orbitals.

**Hint:** The azimuthal quantum number \( l \) for different orbitals is defined as follows:
- s-orbital: \( l = 0 \)
- p-orbital: \( l = 1 \)
- d-orbital: \( l = 2 \)
- f-orbital: \( l = 3 \)

### Step 3: Identify the Magnetic Quantum Number (m)
The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \). For \( l = 1 \):
- Possible values of \( m \) are: \( -1, 0, +1 \)

Since we are given \( m = 1 \), we are specifically referring to one of the three p-orbitals.

**Hint:** The magnetic quantum number \( m \) defines the orientation of the orbital in space.

### Step 4: Determine the Maximum Number of Electrons in the p-Orbital
Each orbital can hold a maximum of 2 electrons (due to the spin quantum number, which can be +1/2 or -1/2). Since we are focusing on the p-orbital with \( m = 1 \), this specific orbital can hold a maximum of 2 electrons.

**Hint:** Each orbital can accommodate 2 electrons, one with spin up and one with spin down.

### Conclusion
The maximum number of electrons in the p-orbital with \( n = 5 \) and \( m = 1 \) is **2**.

**Final Answer:** 2