Which of the following quantum numbers may be the same for an electron present in 3p and 5p orbitals? 

Options

A. Principal quantum number
B. Azimuthal quantum number
C. Magnetic quantum number
D. Spin quantum number

Answer

To determine which quantum numbers may be the same for an electron present in the 3p and 5p orbitals, we need to analyze the quantum numbers associated with these orbitals.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The four quantum numbers are:
- Principal quantum number (n)
- Azimuthal quantum number (l)
- Magnetic quantum number (m)
- Spin quantum number (s)

2. **Determine Quantum Numbers for 3p Orbital**:
- For the 3p orbital:
- Principal quantum number (n) = 3
- Azimuthal quantum number (l) = 1 (since p orbitals have l = 1)
- Magnetic quantum number (m) can take values from -l to +l: m = -1, 0, +1
- Spin quantum number (s) can be either +1/2 or -1/2

3. **Determine Quantum Numbers for 5p Orbital**:
- For the 5p orbital:
- Principal quantum number (n) = 5
- Azimuthal quantum number (l) = 1 (same as for 3p)
- Magnetic quantum number (m) can take values from -l to +l: m = -1, 0, +1
- Spin quantum number (s) can be either +1/2 or -1/2

4. **Compare Quantum Numbers**:
- **Principal Quantum Number (n)**:
- For 3p, n = 3; for 5p, n = 5. These are different.
- **Azimuthal Quantum Number (l)**:
- For both 3p and 5p, l = 1. These are the same.
- **Magnetic Quantum Number (m)**:
- For both orbitals, m can be -1, 0, or +1. These can be the same.
- **Spin Quantum Number (s)**:
- For both orbitals, s can be +1/2 or -1/2. These can be the same.

5. **Conclusion**:
- The quantum numbers that may be the same for an electron present in the 3p and 5p orbitals are:
- Azimuthal quantum number (l)
- Magnetic quantum number (m)
- Spin quantum number (s)

Thus, the answer is that the azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s) can be the same for electrons in the 3p and 5p orbitals.