Two electrones each of mass `9.1xx10^(31)` kg are at a distance of 10 A. calculate the gravitational force of attraction between them. Given `1 A=10^(-10) m`.

Explanation

To calculate the gravitational force of attraction between two electrons, we can use Newton's law of universal gravitation, which states:

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

Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant, approximately \( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the electrons),
- \( r \) is the distance between the centers of the two masses.

### Step 1: Identify the mass of the electrons
Given:
- Mass of each electron, \( m_1 = m_2 = 9.1 \times 10^{-31} \, \text{kg} \).

### Step 2: Convert the distance from Angstroms to meters
Given:
- Distance \( r = 10 \, \text{A} \).
- We know that \( 1 \, \text{A} = 10^{-10} \, \text{m} \).

Thus,
\[ r = 10 \, \text{A} = 10 \times 10^{-10} \, \text{m} = 10^{-9} \, \text{m}. \]

### Step 3: Substitute the values into the formula
Now substituting the values into the gravitational force formula:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
\[ F = \frac{(6.67 \times 10^{-11}) \cdot (9.1 \times 10^{-31}) \cdot (9.1 \times 10^{-31})}{(10^{-9})^2}. \]

### Step 4: Calculate \( r^2 \)
Calculating \( r^2 \):
\[ r^2 = (10^{-9})^2 = 10^{-18} \, \text{m}^2. \]

### Step 5: Substitute \( r^2 \) into the formula
Now substituting \( r^2 \) back into the formula:
\[ F = \frac{(6.67 \times 10^{-11}) \cdot (9.1 \times 10^{-31}) \cdot (9.1 \times 10^{-31})}{10^{-18}}. \]

### Step 6: Calculate the numerator
Calculating the numerator:
\[ (9.1 \times 10^{-31}) \cdot (9.1 \times 10^{-31}) = 8.27 \times 10^{-61}. \]
Thus,
\[ F = \frac{(6.67 \times 10^{-11}) \cdot (8.27 \times 10^{-61})}{10^{-18}}. \]

### Step 7: Calculate the force
Now, calculating the force:
\[ F = (6.67 \times 8.27) \times 10^{-11 - 61 + 18} \]
\[ F = 55.2 \times 10^{-54} \]
\[ F = 5.52 \times 10^{-53} \, \text{N}. \]

### Final Answer
The gravitational force of attraction between the two electrons is approximately:
\[ F \approx 5.52 \times 10^{-53} \, \text{N}. \]