An orbital is occupied by an electrons with the quantum numbers n = 4, l = 1. How many orbitals of this type are found in a multi- electron atom ?

Options

A. (a) 4p, 3
B. (b) 4s, 1
C. (c) 4d, 5
D. (d) 4p, 6

Answer

To solve the question of how many orbitals are found in a multi-electron atom for an electron with quantum numbers n = 4 and l = 1, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The principal quantum number (n) is given as 4.
- The azimuthal quantum number (l) is given as 1.

2. **Determine the Subshell**:
- The azimuthal quantum number (l) indicates the type of subshell.
- For l = 0, the subshell is s; for l = 1, the subshell is p; for l = 2, the subshell is d; and for l = 3, the subshell is f.
- Since l = 1, we are dealing with the 4p subshell.

3. **Find the Magnetic Quantum Number (m_l)**:
- The magnetic quantum number (m_l) can take values from -l to +l, including zero.
- Therefore, for l = 1, m_l can be -1, 0, or +1.

4. **Count the Number of Orbitals**:
- The possible values of m_l (-1, 0, +1) correspond to three different orbitals in the p subshell.
- Thus, there are a total of 3 orbitals in the 4p subshell.

5. **Conclusion**:
- Therefore, the number of orbitals of the type 4p in a multi-electron atom is **3**.

### Final Answer:
The number of orbitals of the type 4p in a multi-electron atom is **3**.