Two protons are separated by distance r - AQA - A-Level Physics - Question 15 - 2021 - Paper 2

The gravitational force (F_g) between two protons is given by Newton's law of gravitation:

$F_g = G \frac{m_1 m_2}{r^2}$ where:

• $G$ is the gravitational constant ($6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$)
• $m_1$ and $m_2$ are the masses of the protons (approximately $1.67 \times 10^{-27}$ kg each).

Substituting the values:

$F_g = 6.67 \times 10^{-11} \frac{(1.67 \times 10^{-27})^2}{r^2}$

To find X, we can divide the electrostatic force by the gravitational force:

$X = \frac{F_e}{F_g} = \frac{8.99 \times 10^9 \frac{(1.6 \times 10^{-19})^2}{r^2}}{6.67 \times 10^{-11} \frac{(1.67 \times 10^{-27})^2}{r^2}}$

Simplifying this gives:

$X = \frac{8.99 \times 10^9 \times (1.6 \times 10^{-19})^2}{6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2}$

Calculating the constants, we find:

$X \approx 10^{36}$

Thus, the best estimate for X is option C: $10^{36}$.