Find the maximum coulomb force can act on the electron due to the nucleus in a hydrogen atom.

Explanation

To find the maximum Coulomb force acting on the electron due to the nucleus in a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Coulomb's Law**:
The formula for the Coulomb force \( F \) between two charges is given by:
\[ F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} \]
where:
- \( F \) is the force between the charges,
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges,
- \( \epsilon_0 \) is the permittivity of free space.

2. **Identify the Charges**:
In a hydrogen atom, the nucleus consists of one proton, and the electron has a charge of \( -e \) (where \( e = 1.6 \times 10^{-19} \, C \)). Thus, we have:
\[ q_1 = e = 1.6 \times 10^{-19} \, C \quad \text{and} \quad q_2 = -e = -1.6 \times 10^{-19} \, C \]

3. **Substitute the Values**:
The absolute values of the charges will be used in the formula:
\[ F = \frac{1}{4 \pi \epsilon_0} \frac{(1.6 \times 10^{-19})^2}{r^2} \]

4. **Determine the Minimum Distance**:
The maximum force occurs when the distance \( r \) is at its minimum. For the hydrogen atom, the minimum radius (Bohr radius) is given as:
\[ r = 0.53 \, \text{Å} = 0.53 \times 10^{-10} \, \text{m} \]

5. **Insert the Values into the Formula**:
The value of \( \epsilon_0 \) is approximately \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \). Thus, we can substitute \( \epsilon_0 \) into the equation:
\[ F = \frac{1}{4 \pi (8.85 \times 10^{-12})} \frac{(1.6 \times 10^{-19})^2}{(0.53 \times 10^{-10})^2} \]

6. **Calculate the Force**:
First, compute the constant:
\[ \frac{1}{4 \pi (8.85 \times 10^{-12})} \approx 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \]
Then calculate:
\[ F \approx 9 \times 10^9 \times \frac{(1.6 \times 10^{-19})^2}{(0.53 \times 10^{-10})^2} \]
\[ F \approx 9 \times 10^9 \times \frac{2.56 \times 10^{-38}}{2.809 \times 10^{-21}} \approx 8.2 \times 10^{-8} \, \text{N} \]

### Final Answer:
The maximum Coulomb force acting on the electron due to the nucleus in a hydrogen atom is approximately:
\[ F \approx 8.2 \times 10^{-8} \, \text{N} \]