The mass number of an ion is 48. It has 3 units of positive charge. The number of neutrons in the ion exceeds the number of electrons in it by 7. The atomic number of the element is

Options

A. 21
B. 22
C. 24
D. 26

Explanation

To solve the problem step-by-step, we will use the given information about the ion and apply some basic concepts of atomic structure.

### Step 1: Understand the given information
- The mass number of the ion is 48.
- The ion has a charge of +3, indicating it has lost 3 electrons.
- The number of neutrons exceeds the number of electrons by 7.

### Step 2: Define variables
Let:
- \( x \) = atomic number of the element (which is also the number of protons)
- The number of protons = \( x \)
- The number of electrons = \( x - 3 \) (since it has a +3 charge)
- The number of neutrons = \( N \)

### Step 3: Set up the equation for neutrons
According to the problem, the number of neutrons exceeds the number of electrons by 7:
\[ N = (x - 3) + 7 \]
This simplifies to:
\[ N = x + 4 \]

### Step 4: Set up the equation for mass number
The mass number (A) is the sum of the number of protons and neutrons:
\[ A = \text{Number of protons} + \text{Number of neutrons} \]
Given that the mass number is 48, we can write:
\[ 48 = x + N \]
Substituting \( N \) from the previous step:
\[ 48 = x + (x + 4) \]
This simplifies to:
\[ 48 = 2x + 4 \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
1. Subtract 4 from both sides:
\[ 48 - 4 = 2x \]
\[ 44 = 2x \]
2. Divide both sides by 2:
\[ x = 22 \]

### Step 6: Conclusion
The atomic number of the element is \( x = 22 \).

### Final Answer
The atomic number of the element is **22**.

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