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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Electric Field and Potential

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Field and Potential

An NaCl molecule is bound by the electric force between the sodium...

An NaCl molecule is bound by the electric force between the sodium and chlorine ions when one electron from sodium is transferred to chlorine. Assuming the ions act as point charges and taking the separation between them to be 2.75×10−8 cm2.75 \times 10^{-8} \text{ cm}, determine the force of attraction between them.

Options

  1. A3.05×10−9 N3.05 \times 10^{-9} \text{ N}
  2. B8.38×10−19 N8.38 \times 10^{-19} \text{ N}
  3. C3.39×10−19 N3.39 \times 10^{-19} \text{ N}
  4. D3.05×10−13 N3.05 \times 10^{-13} \text{ N}

Correct answer

A. 3.05×10−9 N3.05 \times 10^{-9} \text{ N}

Step-by-step solution

The charges on the sodium and chlorine ions are +e+e and −e-e respectively, where e=1.6×10−19 Ce = 1.6 \times 10^{-19} \text{ C}.

The separation between the ions is r=2.75×10−8 cm=2.75×10−10 mr = 2.75 \times 10^{-8} \text{ cm} = 2.75 \times 10^{-10} \text{ m}.

Using Coulomb's law, the force of attraction is given by:

F=14πϵ0q1q2r2F = \dfrac{1}{4\pi\epsilon_0} \dfrac{q_1 q_2}{r^2}

Substituting the values:

F=9×109×(1.6×10−19)2(2.75×10−10)2F = \dfrac{9 \times 10^9 \times (1.6 \times 10^{-19})^2}{(2.75 \times 10^{-10})^2}

F=9×109×2.56×10−387.5625×10−20F = \dfrac{9 \times 10^9 \times 2.56 \times 10^{-38}}{7.5625 \times 10^{-20}}

F=23.04×10−297.5625×10−20F = \dfrac{23.04 \times 10^{-29}}{7.5625 \times 10^{-20}}

F≈3.05×10−9 NF \approx 3.05 \times 10^{-9} \text{ N}
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