Give the number of identical orbitals in d subshell is a given energy level and the values for their m quantum numbers

Explanation

To solve the question regarding the number of identical orbitals in the d subshell at a given energy level and the values for their magnetic quantum numbers (m), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Number for the d Subshell**:
- The azimuthal quantum number (l) for the d subshell is 2. This is a fundamental property of the d subshell.

2. **Calculate the Number of Orbitals in the d Subshell**:
- The formula to find the number of orbitals in any subshell is given by:
\[ \text{Number of orbitals} = 2l + 1 \]
- Substituting the value of l for the d subshell:
\[ \text{Number of orbitals} = 2(2) + 1 = 4 + 1 = 5 \]
- Therefore, there are 5 identical orbitals in the d subshell.

3. **List the d Orbitals**:
- The five d orbitals are:
- \(d_{xy}\)
- \(d_{yz}\)
- \(d_{zx}\)
- \(d_{x^2 - y^2}\)
- \(d_{z^2}\)

4. **Determine the Values of the Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) can take values from \(-l\) to \(+l\). For l = 2:
\[ m = -2, -1, 0, +1, +2 \]
- Thus, the values of m for the d orbitals are:
- \(m = -2\) for \(d_{xy}\)
- \(m = -1\) for \(d_{yz}\)
- \(m = 0\) for \(d_{zx}\)
- \(m = +1\) for \(d_{x^2 - y^2}\)
- \(m = +2\) for \(d_{z^2}\)

### Final Answer:
- The number of identical orbitals in the d subshell is **5**.
- The values for their magnetic quantum numbers (m) are: **-2, -1, 0, +1, +2**.