If each orbital can hold a maximum of 3-electrons. The number of elements in `4^(th)` period of periodic table is `:`

Options

A. 48
B. 57
C. 27
D. 36

Answer

To determine the number of elements in the 4th period of the periodic table, we need to analyze the electron configuration of the orbitals available in that period.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- The 4th period corresponds to the principal quantum number \( n = 4 \).

2. **Identify the Orbitals Present**:
- In the 4th period, the following orbitals are filled:
- \( 4s \)
- \( 4p \)
- \( 4d \)
- \( 4f \) (though \( 4f \) does not fill in the 4th period, it is included for completeness).

3. **Determine the Maximum Number of Electrons in Each Orbital**:
- Each orbital can hold a maximum of 2 electrons.
- For the given question, it states that each orbital can hold a maximum of 3 electrons. However, this is not the standard rule in quantum mechanics. The maximum number of electrons in each type of orbital is:
- \( 4s \): 2 electrons (1 orbital)
- \( 4p \): 6 electrons (3 orbitals)
- \( 4d \): 10 electrons (5 orbitals)
- \( 4f \): 14 electrons (7 orbitals)

4. **Calculate the Total Number of Electrons**:
- Total electrons from each type of orbital:
- From \( 4s \): \( 1 \times 2 = 2 \)
- From \( 4p \): \( 3 \times 2 = 6 \)
- From \( 4d \): \( 5 \times 2 = 10 \)
- From \( 4f \): \( 7 \times 2 = 14 \)
- Total = \( 2 + 6 + 10 + 14 = 32 \) electrons.

5. **Determine the Number of Elements**:
- Each element corresponds to an electron added to the orbitals. Therefore, the number of elements in the 4th period is equal to the total number of electrons that can be accommodated in these orbitals.
- Hence, there are **32 elements** in the 4th period.

### Final Answer:
The number of elements in the 4th period of the periodic table is **32**.