The ratio of electric force between two electrons to two protons separated by the same distance in air is .

Options

A. `10^(0)`
B. `10^(6)`
C. `10^(4)`
D. None of these

Answer

To solve the problem of finding the ratio of the electric force between two electrons to that between two protons separated by the same distance in air, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Electric Force**:
The electric force \( F \) between two point charges is given by Coulomb's Law:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where \( k \) is the electrostatic constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges.

2. **Identify the Charges**:
- The charge of an electron \( (q_e) \) is \( -e \) (approximately \( -1.6 \times 10^{-19} \) C).
- The charge of a proton \( (q_p) \) is \( +e \) (approximately \( +1.6 \times 10^{-19} \) C).

3. **Calculate the Electric Force Between Two Electrons**:
Using Coulomb's Law for two electrons:
\[ F_{ee} = k \frac{|q_e q_e|}{r^2} = k \frac{|-e \cdot -e|}{r^2} = k \frac{e^2}{r^2} \]

4. **Calculate the Electric Force Between Two Protons**:
Using Coulomb's Law for two protons:
\[ F_{pp} = k \frac{|q_p q_p|}{r^2} = k \frac{|e \cdot e|}{r^2} = k \frac{e^2}{r^2} \]

5. **Find the Ratio of the Forces**:
Now we find the ratio of the electric force between two electrons to that between two protons:
\[ \text{Ratio} = \frac{F_{ee}}{F_{pp}} = \frac{k \frac{e^2}{r^2}}{k \frac{e^2}{r^2}} = \frac{e^2/r^2}{e^2/r^2} = 1 \]

6. **Conclusion**:
The ratio of the electric force between two electrons to that between two protons is:
\[ \text{Ratio} = 1 \]