How many electrons in an atom can have n = 3, l = 1, m =-1 and `s = + 1//2`

Options

A. 1
B. 2
C. 4
D. 6

Answer

To determine how many electrons in an atom can have the given set of quantum numbers (n = 3, l = 1, m = -1, s = +1/2), we can follow these steps:

### Step 1: Understand the Quantum Numbers
- **n (Principal Quantum Number)**: Indicates the energy level or shell of the electron. Here, n = 3 means we are looking at the third shell.
- **l (Azimuthal Quantum Number)**: Indicates the subshell. For l = 1, this corresponds to the p subshell.
- **m (Magnetic Quantum Number)**: Indicates the orientation of the orbital. For m = -1, this refers to one specific orbital within the p subshell.
- **s (Spin Quantum Number)**: Indicates the spin of the electron. A value of +1/2 indicates one specific spin orientation.

### Step 2: Identify the Subshell and Orbitals
- The 3p subshell (since n = 3 and l = 1) can hold a maximum of 6 electrons (2 electrons per orbital, and there are 3 orbitals: m = -1, 0, +1).

### Step 3: Determine the Specific Orbital
- The magnetic quantum number m = -1 corresponds to one of the three orbitals in the 3p subshell.

### Step 4: Consider the Spin Quantum Number
- The spin quantum number s = +1/2 indicates that we are considering one specific electron with a particular spin in the m = -1 orbital.

### Step 5: Conclusion
- Since each electron in an atom must have a unique set of quantum numbers, and we are specifying m = -1 and s = +1/2, there can only be **one electron** that fits this exact set of quantum numbers.

### Final Answer
Thus, the number of electrons in an atom that can have the quantum numbers n = 3, l = 1, m = -1, and s = +1/2 is **1**.

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