An ion with mass number `56` contains `3` units of positive charge and `30.4%` more neutrons then electrons. Assign the symbol to this ion.

Options

A. `""_(26)^(56)Fe^(3+)`
B. `""_(26)^(56)Fe^(2+)`
C. `""_(27)^(56)Co^(2+)`
D. `""_(27)^(58)Co^(3+)`

Explanation

To solve the problem step by step, we need to determine the symbol of the ion based on the given information:

1. **Identify the mass number and charge**:
The mass number (A) is given as 56, and the ion has a charge of +3.

2. **Define variables**:
Let the number of electrons in the ion be denoted as \( a \). Since the ion has a +3 charge, the number of protons (Z) will be \( a + 3 \).

3. **Relate neutrons to electrons**:
The problem states that the number of neutrons (N) is 30.4% more than the number of electrons. This can be expressed mathematically as:
\[ N = a + 0.304a = 1.304a \]

4. **Use the mass number formula**:
The mass number is the sum of protons and neutrons:
\[ A = Z + N \]
Substituting the expressions for Z and N, we get:
\[ 56 = (a + 3) + (1.304a) \]

5. **Combine like terms**:
Simplifying the equation:
\[ 56 = a + 3 + 1.304a \]
\[ 56 = 2.304a + 3 \]

6. **Isolate \( a \)**:
Subtract 3 from both sides:
\[ 53 = 2.304a \]
Now, divide by 2.304:
\[ a \approx \frac{53}{2.304} \approx 23 \]

7. **Calculate the number of protons**:
Since \( a \) (the number of electrons) is approximately 23, the number of protons is:
\[ Z = a + 3 = 23 + 3 = 26 \]

8. **Determine the element**:
The atomic number (Z) of 26 corresponds to the element Iron (Fe).

9. **Write the symbol of the ion**:
Since the ion has a +3 charge, the symbol for this ion will be:
\[ \text{Fe}^{3+} \]

### Final Answer:
The symbol for the ion is \( \text{Fe}^{3+} \).