The nucleus of helium atom contains two protons that are separated by distance `3.0xx10^(-15)m`. The magnitude of the electrostatic force that each proton exerts on the other is

Options

A. 20.6 N
B. 25.6 N
C. 15.6 N
D. 12.6 N

Explanation

To calculate the magnitude of the electrostatic force that each proton exerts on the other, we can use Coulomb's Law, which is given by the formula:

\[ F = k \frac{q_1 q_2}{r^2} \]

Where:
- \( F \) is the electrostatic force between the charges,
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Step-by-step Solution:

1. **Identify the charges:**
Each proton has a charge of \( q = 1.6 \times 10^{-19} \, \text{C} \).

2. **Determine the distance:**
The distance between the two protons is given as \( r = 3.0 \times 10^{-15} \, \text{m} \).

3. **Substitute the values into Coulomb's Law:**
Since both protons have the same charge, we can set \( q_1 = q_2 = q \):
\[ F = k \frac{q^2}{r^2} \]
Substituting the known values:
\[ F = 9 \times 10^9 \, \frac{\text{N m}^2}{\text{C}^2} \cdot \frac{(1.6 \times 10^{-19} \, \text{C})^2}{(3.0 \times 10^{-15} \, \text{m})^2} \]

4. **Calculate \( q^2 \):**
\[ (1.6 \times 10^{-19})^2 = 2.56 \times 10^{-38} \, \text{C}^2 \]

5. **Calculate \( r^2 \):**
\[ (3.0 \times 10^{-15})^2 = 9.0 \times 10^{-30} \, \text{m}^2 \]

6. **Substitute \( q^2 \) and \( r^2 \) back into the equation:**
\[ F = 9 \times 10^9 \cdot \frac{2.56 \times 10^{-38}}{9.0 \times 10^{-30}} \]

7. **Calculate the fraction:**
\[ \frac{2.56 \times 10^{-38}}{9.0 \times 10^{-30}} = 2.84 \times 10^{-9} \]

8. **Calculate the force \( F \):**
\[ F = 9 \times 10^9 \cdot 2.84 \times 10^{-9} = 25.56 \, \text{N} \]

9. **Round the answer:**
The magnitude of the electrostatic force that each proton exerts on the other is approximately \( 25.6 \, \text{N} \).

### Final Answer:
The magnitude of the electrostatic force that each proton exerts on the other is \( 25.6 \, \text{N} \).