Two electrons are separated by a distance of `1Å`. What is the Coulomb force between them?

Options

A. `2.3xx10^(-8)N`
B. `4.6xx10^(-8)N`
C. `1.5xx10^(-8)N`
D. None of these

Explanation

To find the Coulomb force between two electrons separated by a distance of 1 Å (1 Ångström = \(1 \times 10^{-10}\) meters), we can use Coulomb's law, which is given by the formula:

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

Where:
- \(F\) is the magnitude of the force between the charges,
- \(k\) is Coulomb's constant, approximately \(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\),
- \(q_1\) and \(q_2\) are the magnitudes of the charges,
- \(r\) is the distance between the charges.

### Step-by-Step Solution:

1. **Identify the charges**:
Since we are dealing with electrons, the charge of each electron (\(q\)) is:
\[ q = -1.6 \times 10^{-19} \, \text{C} \]
Therefore, \(q_1 = q_2 = e = 1.6 \times 10^{-19} \, \text{C}\).

2. **Convert the distance**:
The distance \(r\) is given as 1 Ångström:
\[ r = 1 \, \text{Å} = 1 \times 10^{-10} \, \text{m} \]

3. **Substitute values into Coulomb's law**:
Now we can substitute the values into the formula:
\[ F = \frac{(8.99 \times 10^9) \cdot (1.6 \times 10^{-19}) \cdot (1.6 \times 10^{-19})}{(1 \times 10^{-10})^2} \]

4. **Calculate the denominator**:
\[ (1 \times 10^{-10})^2 = 1 \times 10^{-20} \]

5. **Calculate the numerator**:
\[ (1.6 \times 10^{-19}) \cdot (1.6 \times 10^{-19}) = 2.56 \times 10^{-38} \]
Therefore, the numerator becomes:
\[ 8.99 \times 10^9 \cdot 2.56 \times 10^{-38} = 2.30 \times 10^{-28} \]

6. **Combine the results**:
Now substituting back into the formula:
\[ F = \frac{2.30 \times 10^{-28}}{1 \times 10^{-20}} = 2.30 \times 10^{-8} \, \text{N} \]

7. **Final Result**:
The magnitude of the Coulomb force between the two electrons is:
\[ F \approx 2.3 \times 10^{-8} \, \text{N} \]
The direction of the force is repulsive since both charges are negative.