The force between an electron and a proton is

Options

A. static electric force Is more effective than gravitational factor
B. gravitational force is more effective than static electric force
C. Both are similar
D. None of the above

Answer

To find the force between an electron and a proton, we can use Coulomb's Law, which describes the electrostatic force between two charged particles. Here’s a step-by-step solution:

### Step 1: Identify the charges
- An electron has a charge of \( q_1 = -e \) (where \( e \approx 1.6 \times 10^{-19} \, \text{C} \)).
- A proton has a charge of \( q_2 = +e \).

### Step 2: Use Coulomb's Law
Coulomb's Law states that the force \( F \) between two point charges is given by the formula:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where:
- \( k = \frac{1}{4 \pi \epsilon_0} \approx 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \) (Coulomb's constant),
- \( r \) is the distance between the charges.

### Step 3: Substitute the values
Assuming the distance \( r \) between the electron and proton is approximately \( 1 \times 10^{-10} \, \text{m} \) (typical atomic scale), we can substitute the values into the equation:
\[ F = k \frac{|(-e)(+e)|}{(1 \times 10^{-10})^2} \]
\[ F = k \frac{e^2}{(1 \times 10^{-10})^2} \]

### Step 4: Calculate the force
Substituting \( e \) and \( k \):
\[ F = \left(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\right) \frac{(1.6 \times 10^{-19})^2}{(1 \times 10^{-10})^2} \]
\[ F = (8.99 \times 10^9) \frac{2.56 \times 10^{-38}}{1 \times 10^{-20}} \]
\[ F = (8.99 \times 10^9) \times (2.56 \times 10^{-18}) \approx 2.30 \times 10^{-8} \, \text{N} \]

### Step 5: Compare with gravitational force
The gravitational force \( F_g \) between an electron and a proton can be calculated using Newton's law of gravitation:
\[ F_g = G \frac{m_e m_p}{r^2} \]
where \( G \approx 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \), \( m_e \approx 9.11 \times 10^{-31} \, \text{kg} \), and \( m_p \approx 1.67 \times 10^{-27} \, \text{kg} \).

Calculating this gives:
\[ F_g = (6.67 \times 10^{-11}) \frac{(9.11 \times 10^{-31})(1.67 \times 10^{-27})}{(1 \times 10^{-10})^2} \]
\[ F_g \approx 5.52 \times 10^{-53} \, \text{N} \]

### Conclusion
The electrostatic force \( F \approx 2.30 \times 10^{-8} \, \text{N} \) is significantly larger than the gravitational force \( F_g \approx 5.52 \times 10^{-53} \, \text{N} \). Thus, the force between an electron and a proton is much greater than the gravitational force.