For the `4^(th)` energy level of an atom , the maximum number of sub-shells, orbitals and electrons are

Options

A. `-4,8,16`
B. `-4,-4,32`
C. `4,16,32`
D. `-4,-4,16`

Answer

To determine the maximum number of sub-shells, orbitals, and electrons in the 4th energy level of an atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Energy Level**:
- The given energy level is the 4th energy level (n = 4).

2. **Determine the Number of Sub-shells**:
- The number of sub-shells in a given energy level (n) is equal to n.
- For n = 4, the sub-shells are:
- 4s
- 4p
- 4d
- 4f
- Therefore, the total number of sub-shells = 4.

3. **Calculate the Number of Orbitals in Each Sub-shell**:
- Each type of sub-shell has a specific number of orbitals:
- **4s**: 1 orbital
- **4p**: 3 orbitals (Px, Py, Pz)
- **4d**: 5 orbitals
- **4f**: 7 orbitals
- Total number of orbitals = 1 (from 4s) + 3 (from 4p) + 5 (from 4d) + 7 (from 4f) = 16 orbitals.

4. **Determine the Maximum Number of Electrons**:
- Each orbital can hold a maximum of 2 electrons.
- Therefore, the total number of electrons in 16 orbitals = 16 orbitals × 2 electrons/orbital = 32 electrons.

### Final Answers:
- Maximum number of sub-shells: **4**
- Maximum number of orbitals: **16**
- Maximum number of electrons: **32**