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

The gravitational force ($F_g$) between two protons can be calculated using Newton's law of gravitation:
$F_g = G \frac{m_1 m_2}{r^2}$
Where:

• $G$ is the gravitational constant, approximately $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$
• $m_1$ and $m_2$ are the masses of the protons, approximately $1.67 \times 10^{-27} \text{ kg}$.

Substituting these values:
$F_g \approx 6.674 \times 10^{-11} \frac{(1.67 \times 10^{-27})^2}{r^2}$

To find $X$, we take the ratio of the electrostatic force to the gravitational force:
$X = \frac{F_e}{F_g} = \frac{k_e \frac{q_1 q_2}{r^2}}{G \frac{m_1 m_2}{r^2}} = \frac{k_e \cdot q_1 \, q_2}{G \cdot m_1 \, m_2}$
Substituting the constants:
$X \approx \frac{(8.99 \times 10^9)(1.6 \times 10^{-19})^2}{(6.674 \times 10^{-11})(1.67 \times 10^{-27})^2}$ Calculating this gives an approximate value of $X \approx 10^{36}$.

Therefore, the best estimate for $X$ is $10^{36}$. The correct answer is C.