Question

In hydrogen atom an electron revolves around a proton (in nucleus) at a distance 'r' m. The intensity of electric field due to the proton at distance 'r' is $5 \times 10^{11}\ \text{NC}^{-1}$, the magnitude of force between the electron and proton is [charge on electron = $1.6 \times 10^{-19}\ \text{C}$]

• A. $4 \times 10^8\ \text{N}$
• B. $8 \times 10^8\ \text{N}$
• C. $4 \times 10^{-8}\ \text{N}$
• D. $8 \times 10^{-8}\ \text{N}$

Hint:

Don't waste time using Coulomb's law ($\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^2}$) to solve for the radius $r$. The electric field term $E$ already encapsulates the constant and the distance factor ($\frac{1}{4\pi\varepsilon_0}\frac{q_{\text{proton}}}{r^2}$), so a single direct multiplication ($F = qE$) is all that is required.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem states that an electron moves in an orbit around a proton source. We are given the electric field intensity ($E$) created by the central proton at that specific orbital radius, along with the fundamental charge of an electron ($q$). We need to find the electrostatic force acting on the electron.

Step 2: Key Formula or Approach:
The electrostatic force ($F$) experienced by a point charge $q$ placed in an external electric field $E$ is given by the fundamental relation:
$$F = q \cdot E$$

Step 3: Detailed Explanation:
Let's list the known parameters provided in the problem statement:
Electric field intensity at radius $r$: $E = 5 \times 10^{11}\ \text{NC}^{-1}$ Charge magnitude of the electron: $q = 1.6 \times 10^{-19}\ \text{C}$ Substitute these values directly into our force formula:
$$F = (1.6 \times 10^{-19}\ \text{C}) \times (5 \times 10^{11}\ \text{NC}^{-1})$$ Multiply the coefficients together and combine the powers of 10:
$$F = (1.6 \times 5) \times 10^{-19 + 11}$$ $$F = 8.0 \times 10^{-8}\ \text{N}$$ This calculation gives the exact magnitude of the electrostatic attraction between the two particles.

Step 4: Final Answer:
The magnitude of the force between the electron and proton is $8 \times 10^{-8}\ \text{N}$, matching option (D).