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Chapter 2: Problem 88

Use Coulomb's law, \(F=k Q_{1} Q_{2} / d^{2},\) to calculate the electric force on an electron \(\left(Q=-1.6 \times 10^{-19} \mathrm{C}\right)\) exerted by a single proton if the particles are \(0.53 \times 10^{-10} \mathrm{~m}\) apart. The constant \(k\) in Coulomb's law is \(9.0 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\). (The unit abbreviated \(\mathrm{N}\) is the newton, the SI unit of force.)

Short Answer

Expert verified
The electric force exerted by a single proton on an electron, when the particles are \(0.53 \times 10^{-10} m\) apart, is approximately \(5.12 \times 10^{-9} N\).

Step by step solution

01

Identify given information

We are given the following information: - Charge of an electron: \(Q_1 = -1.6 \times 10^{-19} C\) - Charge of a proton: \(Q_2 = 1.6 \times 10^{-19} C\) (we know the magnitude of the charge is equal to the charge of an electron, but with the opposite sign) - Distance between the electron and proton: \(d = 0.53 \times 10^{-10} m \) - Coulomb's constant: \(k = 9.0 \times 10^9 N \cdot m^2 / C^2\)
02

Apply Coulomb's Law formula

Using the given charges, distance, and Coulomb's constant, we can now find the electric force between the electron and the proton by applying Coulomb's Law: \[ F = \frac{k \cdot Q_1 \cdot Q_2}{d^2} \]
03

Substitute the given values

Now substitute the values in the formula: \[ F = \frac{(9.0 \times 10^9 N \cdot m^2 / C^2)(-1.6 \times 10^{-19} C)(1.6 \times 10^{-19} C)}{(0.53 \times 10^{-10} m)^2} \]
04

Solve for the electric force

Simplify the expression and solve for the electric force: \[ F = \frac{(9.0 \times 10^9)(16 \times 10^{-38})}{2.809 \times 10^{-20}} \] \[ F = \frac{14.4 \times 10^{-28}}{2.809 \times 10^{-20}} \] \[ F = 5.12 \times 10^{-9} N \] The electric force exerted by a single proton on an electron, when the particles are \(0.53 \times 10^{-10} m\) apart, is approximately \(5.12 \times 10^{-9} N\).

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Most popular questions from this chapter

Assume that you encounter the following sentences in your reading. What is the chemical formula for each substance mentioned? (a) Sodium hydrogen carbonate is used as a deodorant. (b) Calcium hypochlorite is used in some bleaching solutions. (c) Hydrogen cyanide is a very poisonous gas. (d) Magnesium hydroxide is used as a cathartic. (e) \(\operatorname{Tin}(\mathrm{II})\) fluoride has been used as a fluoride additive in toothpastes. (f) When cadmium sulfide is treated with sulfuric acid, fumes of hydrogen sulfide are given off.

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