Question

Two protons are separated by a distance of 1 nanometer. The magnitudes of gravitational, electromagnetic and strong nuclear forces between them are denoted by $F_G$, $F_E$ and $F_S$ respectively. Select the correct option.

• A. $F_E \gt F_G \gt F_S$
• B. $F_E \gt F_S \gt F_G$
• C. $F_S \gt F_G \gt F_E$
• D. $F_S \gt F_E \gt F_G$

Hint:

Remember that the strong nuclear force falls off exponentially with distance ($F_S \propto e^{-r/r_0}$).
At $1\text{ nm}$, it is mathematically much smaller than even the gravitational force, which only falls off as $1/r^2$.

Answer 1

The Correct Option is A

Step 1: Note the separation.
The two protons sit $1$ nanometre apart, which is $10^{-9}$ m. This is far larger than a nucleus, an important clue for the strong force.

Step 2: Rule out the strong force at this range.
The strong nuclear force only acts over about $10^{-15}$ m. At a nanometre, which is a million times bigger, it has completely died away, so $F_S$ is essentially zero here.

Step 3: Compare the two remaining forces.
Both the electromagnetic and gravitational forces follow an inverse square law, so at the same distance their ratio is fixed and distance cancels out.

Step 4: Recall their relative strength.
For two protons the electric repulsion overwhelms the gravitational pull by a factor of roughly $10^{36}$. So $F_E$ is hugely bigger than $F_G$.

Step 5: Place the forces in order.
So $F_E$ is the largest, $F_G$ is next, and $F_S$ is effectively the smallest because it has vanished at this distance.

Step 6: Write the ranking.
The correct ordering is electromagnetic, then gravitational, then strong. \[ \boxed{F_E \gt F_G \gt F_S} \]