Question

Why is the gravitational force usually ignored in problems involving particles such as electrons and protons?

Answer 1

Answer:

Because the mass of electrons and protons is very small

Explanation:

The gravitational force exerted between two objects is given by:

$F=G\frac{m_1 m_2}{r^2}$

where

$G=6.67 \cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant

m1 and m2 are the masses of the two objects

r is the distance between the two objects

The mass of a proton and of an electron is very small, so the gravitational force involved in case of such particles is very weak. Let's calculate for example the gravitational attraction between one proton and one electron at a distance of r = 1 m. We have:

- Proton mass: $m_1 = 1.67 \cdot 10^{-27}kg$

- Electron mass: $m_2 = 9.11\cdot 10^{-31}kg$

So, the gravitational force between the two particles is:

$F=(6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2})\frac{(1.67\cdot 10^{-27}kg)(9.11\cdot 10^{-31} kg)}{(1 m)^2}=1.01\cdot 10^{-67}N$

Which is a very weak force.

By comparison, let's calculate instead the electromagnetic force between a proton and an electron (both having a charge of $q=1.6\cdot 10^{-19}C$) still separated by a distance of r = 1 m. We have:

$F=k\frac{q_1 q_2}{r^2}=(9.0\cdot 10^9 Nm^2C^{-2})\frac{(1.6\cdot 10^{-19}C)(1.6\cdot 10^{-19}C)}{(1 m)^2}=2.3\cdot 10^{-28}N$

Which we see is much stronger than the gravitational force (almost by a factor $10^{40}$