The acceleration of electron due to mutual attraction between electron and a proton when they are 1.6 Angstroms apart is

Options

A. `10^24 m/s^2`
B. `10^23 m/s^2`
C. `10^22 m/s^2`
D. `10^25 m/s^2`

Answer

To find the acceleration of an electron due to the mutual attraction between the electron and a proton when they are 1.6 Angstroms apart, we can follow these steps:

### Step 1: Convert the distance from Angstroms to meters
1 Angstrom (Å) = \(1 \times 10^{-10}\) meters. Therefore,
\[ 1.6 \, \text{Å} = 1.6 \times 10^{-10} \, \text{m} \]

### Step 2: Use Coulomb's Law to calculate the electrostatic force
Coulomb's Law states that the electrostatic force \(F\) between two charges is given by:
\[ F = k \frac{q_1 q_2}{r^2} \]
Where:
- \(k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2\) (Coulomb's constant)
- \(q_1 = q_2 = 1.6 \times 10^{-19} \, \text{C}\) (charge of electron and proton)
- \(r = 1.6 \times 10^{-10} \, \text{m}\)

Substituting the values:
\[ F = 9 \times 10^9 \frac{(1.6 \times 10^{-19})^2}{(1.6 \times 10^{-10})^2} \]

### Step 3: Calculate the force
Calculating the numerator:
\[ (1.6 \times 10^{-19})^2 = 2.56 \times 10^{-38} \]
Calculating the denominator:
\[ (1.6 \times 10^{-10})^2 = 2.56 \times 10^{-20} \]
Now substituting back into the force equation:
\[ F = 9 \times 10^9 \frac{2.56 \times 10^{-38}}{2.56 \times 10^{-20}} = 9 \times 10^9 \times 10^{-18} = 9 \times 10^{-9} \, \text{N} \]

### Step 4: Calculate the acceleration of the electron
The acceleration \(a\) can be calculated using Newton's second law:
\[ a = \frac{F}{m} \]
Where:
- \(m = 9.1 \times 10^{-31} \, \text{kg}\) (mass of the electron)

Substituting the values:
\[ a = \frac{9 \times 10^{-9}}{9.1 \times 10^{-31}} \]

### Step 5: Solve for acceleration
Calculating the acceleration:
\[ a \approx 9.89 \times 10^{22} \, \text{m/s}^2 \]
This can be approximated to \(10^{22} \, \text{m/s}^2\).

### Final Answer
The acceleration of the electron due to mutual attraction between the electron and proton when they are 1.6 Angstroms apart is approximately:
\[ \boxed{10^{22} \, \text{m/s}^2} \]