Find the electric force between two protons separated by a distance of 1 fermi `(1fermi = 10^(15)m).` The protons in a nucleus remain at a separation of this order.

Options

A. 230N
B. 2300N
C. 23000N
D. None of the Above

Explanation

To find the electric force between two protons separated by a distance of 1 fermi (1 fermi = \(10^{-15}\) m), we can use Coulomb's law, which states that the electric force \(F\) between two point charges is given by the formula:

\[ F = \frac{k \cdot |Q_1 \cdot Q_2|}{r^2} \]

Where:
- \(F\) is the electric force,
- \(k\) is Coulomb's constant (\(k \approx 9 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
- \(Q_1\) and \(Q_2\) are the charges of the protons,
- \(r\) is the distance between the charges.

### Step-by-Step Solution:

**Step 1: Identify the charge of a proton.**
The charge of a proton \(Q\) is:
\[ Q = 1.6 \times 10^{-19} \, \text{C} \]

**Step 2: Identify the distance between the protons.**
The distance \(r\) is given as:
\[ r = 1 \, \text{fermi} = 10^{-15} \, \text{m} \]

**Step 3: Substitute the values into Coulomb's law.**
Using Coulomb's law, we can substitute \(Q_1 = Q_2 = Q\) and \(r\) into the formula:
\[ F = \frac{k \cdot Q^2}{r^2} \]
Substituting the known values:
\[ F = \frac{9 \times 10^9 \cdot (1.6 \times 10^{-19})^2}{(10^{-15})^2} \]

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

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

**Step 6: Substitute \(Q^2\) and \(r^2\) back into the formula.**
Now substituting \(Q^2\) and \(r^2\) into the force equation:
\[ F = \frac{9 \times 10^9 \cdot 2.56 \times 10^{-38}}{10^{-30}} \]

**Step 7: Simplify the equation.**
\[ F = 9 \times 10^9 \cdot 2.56 \times 10^{-8} \]
\[ F = 23.04 \, \text{N} \]

Thus, the electric force between the two protons is approximately:
\[ F \approx 23.04 \, \text{N} \]