An electron with values 4,3,-2 and +1/2 for the set of four quantum numbers n,l,m^landm^s respectively.

Options

A. 4s orbital
B. 4p orbital
C. 4d orbital
D. 4f orbital

Answer

To solve the question regarding the quantum numbers of an electron, we will analyze the given values step by step.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The given quantum numbers are:
- Principal quantum number (n) = 4
- Azimuthal quantum number (l) = 3
- Magnetic quantum number (m) = -2
- Spin quantum number (ms) = +1/2

2. **Determine the Principal Quantum Number (n)**:
- The principal quantum number (n) indicates the energy level of the electron. Here, n = 4 means the electron is in the 4th energy level.

3. **Determine the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number (l) indicates the shape of the orbital. The values of l correspond to different types of orbitals:
- l = 0 corresponds to s orbitals
- l = 1 corresponds to p orbitals
- l = 2 corresponds to d orbitals
- l = 3 corresponds to f orbitals
- Since l = 3, this indicates that the electron is in an f orbital.

4. **Determine the Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) specifies the orientation of the orbital in space. It can take values from -l to +l.
- For l = 3, the possible values of m are -3, -2, -1, 0, +1, +2, +3. The given m = -2 is valid.

5. **Determine the Spin Quantum Number (ms)**:
- The spin quantum number (ms) indicates the spin of the electron. The possible values are +1/2 or -1/2.
- Here, ms = +1/2 is valid.

6. **Identify the Orbital**:
- Combining the information from the principal quantum number and the azimuthal quantum number, we conclude that the electron is in the 4f orbital.

### Final Answer:
The electron with the given quantum numbers is in the **4f orbital**.

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