The electrostatic force between protons is how many times stronger than gravitational force.

Options

A. `10^(34)`
B. `10^(35)`
C. `10^(36)`
D. `10^(37)`

Answer

To find how many times stronger the electrostatic force between protons is compared to the gravitational force, we can follow these steps:

### Step 1: Write the formulas for electrostatic and gravitational forces.
The electrostatic force \( F_e \) between two protons can be expressed using Coulomb's law:
\[ F_e = k \frac{q^2}{r^2} \]
where:
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q \) is the charge of a proton (\( 1.6 \times 10^{-19} \, \text{C} \)),
- \( r \) is the distance between the protons.

The gravitational force \( F_g \) between two protons can be expressed using Newton's law of gravitation:
\[ F_g = G \frac{m^2}{r^2} \]
where:
- \( G \) is the gravitational constant (\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)),
- \( m \) is the mass of a proton (\( 1.67 \times 10^{-27} \, \text{kg} \)).

### Step 2: Set up the ratio of the forces.
To find how many times stronger the electrostatic force is compared to the gravitational force, we take the ratio:
\[ \frac{F_e}{F_g} = \frac{k \frac{q^2}{r^2}}{G \frac{m^2}{r^2}} = \frac{k \cdot q^2}{G \cdot m^2} \]
Notice that the \( r^2 \) terms cancel out.

### Step 3: Substitute the known values.
Now we substitute the known values into the equation:
\[ \frac{F_e}{F_g} = \frac{9 \times 10^9 \cdot (1.6 \times 10^{-19})^2}{6.67 \times 10^{-11} \cdot (1.67 \times 10^{-27})^2} \]

### Step 4: Calculate the numerator and denominator.
First, calculate the numerator:
\[ 9 \times 10^9 \cdot (1.6 \times 10^{-19})^2 = 9 \times 10^9 \cdot 2.56 \times 10^{-38} = 23.04 \times 10^{-29} \]

Now calculate the denominator:
\[ 6.67 \times 10^{-11} \cdot (1.67 \times 10^{-27})^2 = 6.67 \times 10^{-11} \cdot 2.7889 \times 10^{-54} = 18.60 \times 10^{-65} \]

### Step 5: Divide the results.
Now divide the results from the numerator and denominator:
\[ \frac{F_e}{F_g} = \frac{23.04 \times 10^{-29}}{18.60 \times 10^{-65}} = 1.238 \times 10^{36} \]

### Step 6: Conclusion.
Thus, the electrostatic force between two protons is approximately \( 10^{36} \) times stronger than the gravitational force between them.

### Summary of the solution:
The electrostatic force between protons is \( 10^{36} \) times stronger than the gravitational force.

---