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 solve the question regarding the maximum number of sub-shells, orbitals, and electrons for the 4th energy level of an atom, we can follow these steps:

### Step 1: Determine the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the atom. For the 4th energy level, we have:
- \( n = 4 \)

### Step 2: Calculate the Maximum Number of Sub-shells (L)
The maximum number of sub-shells is determined by the formula \( L = n - 1 \). Therefore:
- \( L = 4 - 1 = 3 \)

The possible values of L are:
- \( L = 0 \) (s sub-shell)
- \( L = 1 \) (p sub-shell)
- \( L = 2 \) (d sub-shell)
- \( L = 3 \) (f sub-shell)

Thus, the maximum number of sub-shells for \( n = 4 \) is:
- **4 sub-shells** (4s, 4p, 4d, 4f)

### Step 3: Calculate the Number of Orbitals
Each sub-shell has a specific number of orbitals:
- For the 4s sub-shell: 1 orbital
- For the 4p sub-shell: 3 orbitals
- For the 4d sub-shell: 5 orbitals
- For the 4f sub-shell: 7 orbitals

Now, we sum the orbitals:
- Total orbitals = \( 1 + 3 + 5 + 7 = 16 \)

Thus, the maximum number of orbitals for the 4th energy level is:
- **16 orbitals**

### Step 4: Calculate the Maximum Number of Electrons
Each orbital can hold a maximum of 2 electrons. Therefore, to find the total number of electrons:
- Total electrons = Number of orbitals × 2
- Total electrons = \( 16 \times 2 = 32 \)

Thus, the maximum number of electrons for the 4th energy level is:
- **32 electrons**

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