Calculate the gravitational force of attraction between a proton of mass `1.67 xx 10^(-27)kg` and an electron of mass `9.1 xx 10^(-31)` kg separated by distance of 1 Fermi ? `G = 6.67 xx 10^(-11) Nm^(2) kg ^(-2)` .

Explanation

To calculate the gravitational force of attraction between a proton and an electron, we will use the formula for gravitational force:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

Where:
- \( F \) is the gravitational force,
- \( G \) is the universal gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two masses.

### Step-by-step Solution:

1. **Identify the given values:**
- Mass of the proton, \( m_1 = 1.67 \times 10^{-27} \, \text{kg} \)
- Mass of the electron, \( m_2 = 9.1 \times 10^{-31} \, \text{kg} \)
- Distance between them, \( r = 1 \, \text{Fermi} = 1 \times 10^{-15} \, \text{m} \)
- Gravitational constant, \( G = 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)

2. **Substitute the values into the formula:**
\[ F = \frac{(6.67 \times 10^{-11}) \cdot (1.67 \times 10^{-27}) \cdot (9.1 \times 10^{-31})}{(1 \times 10^{-15})^2} \]

3. **Calculate the denominator:**
\[ (1 \times 10^{-15})^2 = 1 \times 10^{-30} \]

4. **Calculate the numerator:**
\[ 6.67 \times 10^{-11} \cdot 1.67 \times 10^{-27} \cdot 9.1 \times 10^{-31} \]
- First, multiply \( 1.67 \) and \( 9.1 \):
\[ 1.67 \times 9.1 = 15.197 \]
- Now multiply by \( 6.67 \):
\[ 6.67 \times 15.197 \approx 101.2 \]
- Combine the powers of ten:
\[ 10^{-11} \times 10^{-27} \times 10^{-31} = 10^{-69} \]
- Therefore, the numerator is approximately:
\[ 101.2 \times 10^{-69} \approx 1.012 \times 10^{-67} \]

5. **Now, substitute back into the formula:**
\[ F = \frac{1.012 \times 10^{-67}}{1 \times 10^{-30}} = 1.012 \times 10^{-37} \, \text{N} \]

6. **Final Result:**
\[ F \approx 1.013 \times 10^{-37} \, \text{N} \]

### Final Answer:
The gravitational force of attraction between the proton and the electron is approximately \( 1.013 \times 10^{-37} \, \text{N} \).