A hypothetical ion of element `X` with mass number 40, posses 2 units of positive charge and `23%` more neutrons than electrons. Symbol of the ion is :

Options

A. `(20)^(40)X^(+2)`
B. `(19)^(40)X^(+2)`
C. `(18)^(40)X^(+2)`
D. None of these

Explanation

To solve the problem, we need to determine the symbol of the hypothetical ion of element X based on the given information. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Mass number (A) = 40
- Charge = +2
- Neutrons (N) = 23% more than electrons (E)

2. **Define the Variables:**
- Let the atomic number (Z) represent the number of protons.
- The number of electrons in the ion can be expressed as \( E = Z - 2 \) because the ion has a +2 charge (indicating it has lost 2 electrons).

3. **Express Neutrons in Terms of Electrons:**
- According to the problem, the number of neutrons is 23% more than the number of electrons:
\[ N = E + 0.23E = 1.23E \]
- Substituting \( E \) gives:
\[ N = 1.23(Z - 2) \]

4. **Use the Mass Number Equation:**
- The mass number is the sum of protons and neutrons:
\[ A = Z + N \]
- Substituting the values we have:
\[ 40 = Z + 1.23(Z - 2) \]

5. **Solve for Z:**
- Expanding the equation:
\[ 40 = Z + 1.23Z - 2.46 \]
\[ 40 + 2.46 = 2.23Z \]
\[ 42.46 = 2.23Z \]
\[ Z = \frac{42.46}{2.23} \approx 19.05 \]
- Rounding \( Z \) to the nearest whole number gives \( Z = 19 \).

6. **Calculate the Number of Protons and Neutrons:**
- Number of protons (Z) = 19
- Number of neutrons (N) = \( A - Z = 40 - 19 = 21 \)

7. **Determine the Symbol of the Ion:**
- The symbol of the ion is represented as:
\[ \text{Element}_{\text{mass number}}^{\text{charge}} = \text{X}_{40}^{+2} \]
- The element with atomic number 19 is potassium (K), so the symbol of the ion is:
\[ \text{K}_{40}^{+2} \]

### Final Answer:
The symbol of the ion is \( \text{K}^{2+}_{40} \).

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