An element is isobaric with the inert gas atom `._(18)A^(40)`. The electronic arrangement of the element is `1s^(2) 2s^(2) 2p^(6) 3s^(2) 3p^(2) 4s^(2)`. How many neutrons does each atom of the element carry in its nucleus?

Options

A. 22
B. 20
C. 18
D. 16

Explanation

To solve the problem, we need to determine the number of neutrons in the nucleus of the element that is isobaric with the inert gas atom represented as \( _{18}A^{40} \).

### Step-by-Step Solution:

1. **Identify the Isobaric Element**:
- The given inert gas atom is represented as \( _{18}A^{40} \). This means it has an atomic number (Z) of 18 and a mass number (A) of 40. The element with atomic number 18 is Argon (Ar).

2. **Understand Isobars**:
- Isobars are atoms of different elements that have the same mass number but different atomic numbers. Since the mass number is 40, we need to find another element that also has a mass number of 40.

3. **Determine the Atomic Number of the Isobaric Element**:
- The electronic arrangement given is \( 1s^2 2s^2 2p^6 3s^2 3p^2 4s^2 \).
- Counting the electrons in this configuration:
- \( 1s^2 \) = 2
- \( 2s^2 \) = 2
- \( 2p^6 \) = 6
- \( 3s^2 \) = 2
- \( 3p^2 \) = 2
- \( 4s^2 \) = 2
- Total = \( 2 + 2 + 6 + 2 + 2 + 2 = 20 \)
- Therefore, the atomic number (Z) of the element is 20.

4. **Calculate the Number of Neutrons**:
- The number of neutrons (N) in an atom can be calculated using the formula:
\[ N = A - Z \]
- Here, \( A = 40 \) (mass number) and \( Z = 20 \) (atomic number).
- Substituting the values:
\[ N = 40 - 20 = 20 \]

5. **Conclusion**:
- Each atom of the element carries 20 neutrons in its nucleus.

### Final Answer:
Each atom of the element carries **20 neutrons** in its nucleus.