Question

Two protons are kept at a distance of \(40\times10^{-10}\text{ m}\). \(F_n\) is the nuclear force and \(F_e\) is the electrostatic force between them. Then

• A. \(F_n \gg F_e\)
• B. \(F_n = F_e\)
• C. \(F_n \ll F_e\)
• D. \(F_n \ne F_e\)

Hint:

Nuclear force is very strong but very short-range. It becomes negligible when separation is much larger than \(10^{-15}\ \text{m}\).

Answer 1

The Correct Option is C

Concept:
There are two important forces between protons: \[ F_e = \text{electrostatic repulsive force} \] \[ F_n = \text{nuclear attractive force} \] Electrostatic force is a long-range force, while nuclear force is a very short-range force. The nuclear force acts effectively only when nucleons are separated by a distance of the order: \[ 10^{-15}\ \text{m} \]

Step 1: Write the given separation.
Given distance between two protons: \[ r=40\times10^{-10}\ \text{m} \] Simplify: \[ r=4.0\times10^{-9}\ \text{m} \]

Step 2: Compare with range of nuclear force.
Range of nuclear force is approximately: \[ 10^{-15}\ \text{m} \] Given separation is: \[ 4.0\times10^{-9}\ \text{m} \] This is much greater than: \[ 10^{-15}\ \text{m} \] So at this separation, nuclear force is almost negligible.

Step 3: Understand electrostatic force at this distance.
Electrostatic force follows Coulomb's law: \[ F_e=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^2} \] It can act even at distances much larger than nuclear range. So electrostatic force is still present.

Step 4: Compare \(F_n\) and \(F_e\).
Since nuclear force is negligible: \[ F_n \approx 0 \] But electrostatic force exists: \[ F_e \ne 0 \] Therefore: \[ F_n \ll F_e \]

Step 5: Check the options.
Option (A) is incorrect because nuclear force is not stronger at such large distance.
Option (B) is incorrect because the two forces are not equal.
Option (C) is correct because nuclear force is negligible compared to electrostatic force.
Option (D) is vague, while option (C) gives the correct comparison. Hence, the correct answer is: \[ \boxed{(C)\ F_n \ll F_e} \]