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An electron and a proton are about 10-10 m apart. Their relative motion is chiefly determined by
1. gravitational forces
2. electrical forces
3. nuclear forces
4. magnetic forces

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Correct Answer - Option 2 : electrical forces

CONCEPT:

Gravitational force Electric force Magnetic force Nuclear force
Gravitational force is the force of attraction between two masses. It is one of the four fundamental forces of nature.

When two charges are kept close to each other a force acts between them. The force between the two charges is called an electric force.

When two magnetic poles are kept close to each other a force acts between them. The force between the two magnetic poles is called magnetic force.

The nuclear force is the force that binds the protons and neutrons in a nucleus together. The range of a nuclear force is 10-15 m.

It is the weakest of the four. It is always of attraction nature.

Like charges repel each other while the unlike charges attract each other.

Like poles repel each other while the unlike poles attract each other.

This force can exist between protons and protons, neutrons and protons or neutrons.

EXPLANATION:

  • The electron and the proton are 10-10 m apart.
  • We know that the range of a nuclear force is 10-15 m and the electron and the proton are 10-10 m apart so there will be no nuclear force.
  • For magnetic force, the charges must be in motion so there will be no magnetic force between the charges.
  • By coulombs law, the electric force between the electron and the proton is given as,

\(⇒ F_{e}=\frac{kee}{r^{2}}\)

Where e = 1.6×10-19 C and k = 9 × 109 Nm2/C2 (For vacuum)

\(⇒ F_{e}=\frac{9×10^9×(1.6×10^{-19})^2}{10^{{-20}}}\)

⇒ Fe = 23.04×10-9 N     -----(1)

  • The gravitational force between the electron and the proton is given as,

\(⇒ F_{g}=\frac{Gm_em_p}{r^{2}}\)

Where G = 6.67×10-11 Nm2/kg2, me = 9.1×10-31 kg, mp = 1.67×10-27 kg and r = 10-10m

\(⇒ F_{g}=\frac{6.67×10^{-11}×9.1×10^{-31}×1.67×10^{-27}}{10^{-20}}\)

⇒ Fg = 10.14×10-49 N     -----(2)

  • By equation 1 and equation 2 it is clear that the electric force is much much higher than the gravitational force. So the net effect between the electron and the proton will be due to the electric force.
  • So their relative motion is chiefly determined by an electrical force.
  • Hence, option 2 is correct.

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