The distance of closest approach of a certain nucleus is 7.2 fm and it has a charge of `1.28 xx 10^(-17)` C. The number of neutrons inside the nucleus of an atom is

Options

A. 111
B. 142
C. 140
D. 132

Explanation

To solve the problem, we need to determine the number of neutrons in a nucleus given the charge and the distance of closest approach. Here’s a step-by-step solution:

### Step 1: Understand the Given Information
- Distance of closest approach (R) = 7.2 fm = \(7.2 \times 10^{-15}\) m
- Charge of the nucleus (Q) = \(1.28 \times 10^{-17}\) C

### Step 2: Calculate the Atomic Mass (A)
The radius of the nucleus can be related to the atomic mass (A) using the formula:
\[ R = R_0 A^{1/3} \]
Where \(R_0\) is a constant approximately equal to \(1.25 \, \text{fm}\).

Rearranging the formula to find A:
\[ A = \left(\frac{R}{R_0}\right)^3 \]
Substituting the values:
\[ A = \left(\frac{7.2 \, \text{fm}}{1.25 \, \text{fm}}\right)^3 \]
Calculating the ratio:
\[ \frac{7.2}{1.25} = 5.76 \]
Now, calculating \(A\):
\[ A = (5.76)^3 \approx 191 \]

### Step 3: Calculate the Number of Protons (Z)
The number of protons can be calculated using the formula:
\[ Z = \frac{Q}{e} \]
Where \(e\) (the charge of an electron) is approximately \(1.6 \times 10^{-19}\) C.
Substituting the values:
\[ Z = \frac{1.28 \times 10^{-17} \, \text{C}}{1.6 \times 10^{-19} \, \text{C}} \approx 80 \]

### Step 4: Calculate the Number of Neutrons (N)
The number of neutrons can be found using the formula:
\[ N = A - Z \]
Substituting the values:
\[ N = 191 - 80 = 111 \]

### Final Answer
The number of neutrons inside the nucleus is **111**.

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