Explain why the gravitational force can be ignored for sub-atomic particles - Leaving Cert Physics - Question i - 2017

The gravitational force is negligible for sub-atomic particles due to the extremely small mass of these particles compared to their electromagnetic interactions.

The magnitude of gravitational force can be approximated using Newton's law of gravitation:

F_g = rac{G imes m_1 imes m_2}{r^2}

where:

• $F_g$ is the gravitational force,
• $G$ is the gravitational constant ($6.67 imes 10^{-11} ext{ N(m/kg)}^2$),
• $m_1$ and $m_2$ are the masses of the particles, and
• $r$ is the distance between their centers.

In comparison, electromagnetic forces, which dominate at the subatomic level, can be described by Coulomb's law:

F_e = k rac{q_1 q_2}{r^2}

where:

• $F_e$ is the electromagnetic force,
• $k$ is Coulomb's constant ($8.99 imes 10^9 ext{ Nm}^2/ ext{C}^2$), and
• $q_1$ and $q_2$ are the charges of the particles.

Given that the electromagnetic force between charged particles is significantly stronger than the gravitational force, it can be concluded that, for subatomic interactions, gravitational effects can be ignored.