If element with particle quantum number `ngt4` were not allowed in nature , the number of possible element would be

Options

A. 60
B. 32
C. 4
D. 64

Explanation

To solve the problem, we need to determine the number of possible elements if elements with a principal quantum number \( n \) greater than 4 are not allowed.

### Step-by-Step Solution:

1. **Identify Allowed Quantum Numbers**:
Since \( n \) must be less than or equal to 4, the allowed principal quantum numbers are \( n = 1, 2, 3, \) and \( 4 \).

2. **Calculate the Maximum Number of Electrons for Each Shell**:
The maximum number of electrons that can occupy a shell is given by the formula:
\[ \text{Number of electrons} = 2n^2 \]
We will calculate this for each allowed value of \( n \).

- For \( n = 1 \):
\[ \text{Electrons} = 2(1^2) = 2 \]

- For \( n = 2 \):
\[ \text{Electrons} = 2(2^2) = 8 \]

- For \( n = 3 \):
\[ \text{Electrons} = 2(3^2) = 18 \]

- For \( n = 4 \):
\[ \text{Electrons} = 2(4^2) = 32 \]

3. **Sum the Maximum Number of Electrons**:
Now, we add the maximum number of electrons from all the shells:
\[ \text{Total Electrons} = 2 + 8 + 18 + 32 \]

Performing the addition:
\[ \text{Total Electrons} = 60 \]

4. **Conclusion**:
Therefore, if elements with a principal quantum number \( n > 4 \) are not allowed, the total number of possible elements is 60.

### Final Answer:
The number of possible elements would be **60**.