The maximum number of electrons that can exists in the orbital for which n = 3., 1 = 1 and m = -1 is :

Options

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

Answer

To determine the maximum number of electrons that can exist in the orbital for which \( n = 3 \), \( l = 1 \), and \( m = -1 \), 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, \( n = 3 \) means we are dealing with the third energy level.

**Hint:** The principal quantum number \( n \) indicates the main energy level of the electron in an atom.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number \( l \) defines the shape of the orbital. For \( l = 1 \), the corresponding orbital is a p-orbital.

**Hint:** The azimuthal quantum number \( l \) can take values from \( 0 \) to \( n-1 \). For \( l = 0 \) it's s, \( l = 1 \) is p, \( l = 2 \) is d, and \( l = 3 \) is f.

### Step 3: Determine the Magnetic Quantum Number (m)
The magnetic quantum number \( m \) specifies the orientation of the orbital. For \( l = 1 \), the possible values of \( m \) are \( -1, 0, +1 \). Since we are given \( m = -1 \), we are focusing on one specific p-orbital.

**Hint:** The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \), giving a total of \( 2l + 1 \) orbitals for each value of \( l \).

### Step 4: Calculate the Maximum Number of Electrons
Each orbital can hold a maximum of 2 electrons (due to the Pauli exclusion principle). Since we are considering the specific orbital defined by \( n = 3 \), \( l = 1 \), and \( m = -1 \), there is only one orbital available.

**Hint:** Remember that each orbital can hold a maximum of 2 electrons, regardless of the quantum numbers.

### Step 5: Conclusion
Therefore, the maximum number of electrons that can exist in the orbital for which \( n = 3 \), \( l = 1 \), and \( m = -1 \) is **2 electrons**.

**Final Answer:** 2 electrons.