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Chapter 22: Problem 21

A proton, an alpha particle (a bare helium nucleus), and a singly ionized helium atom are accelerated through a \(100-\mathrm{V}\) potential difference. How much energy does each gain?

Short Answer

Expert verified
The proton gains \(1.6 \times 10^{-17}\) J of energy, the alpha particle gains \(3.2 \times 10^{-17}\) J of energy, and the singly ionized helium atom gains \(1.6 \times 10^{-17}\) J of energy.

Step by step solution

01

Recall the energy-voltage relation

The energy gained by a particle being accelerated through a potential difference can be calculated by the equation \( E = q \cdot V \), where \( E \) is the energy, \( q \) is the charge, and \( V \) is the potential difference or voltage. Therefore, the task is to find the charges of the proton, alpha particle, and singly ionized helium atom.
02

Calculate the energy gained by the proton

The charge of a proton is +1e (or \(1.6 \times 10^{-19}\) C) and the potential difference is 100V. Substituting these values into the formula gives: \( E_p = 1 \cdot 100 = 100e \) or \(1.6 \times 10^{-17}\) J.
03

Calculate the energy gained by the alpha particle

An alpha particle is a helium nucleus, stripped of its electrons, thus it has a charge of +2e (or \(3.2 \times 10^{-19}\) C). Substituting into the formula gives: \( E_{\alpha} = 2 \cdot 100 = 200e \) or \(3.2 \times 10^{-17}\) J.
04

Calculate the energy gained by the singly ionized helium

A singly ionized helium atom has lost an electron and so has a charge of +1e. Using the formula, \( E_{He^+} = 1 \cdot 100 = 100e \) or \(1.6 \times 10^{-17}\) J.

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Most popular questions from this chapter

In considering the potential of an infinite flat sheet, why isn't it useful to take the zero of potential at infinity?

A sphere of radius \(R\) carries a nonuniform but spherically symmetric volume charge density that results in an electric field in the sphere given by \(\vec{E}=E_{0}(r / R)^{2} \hat{r},\) where \(E_{0}\) is a constant. Find the potential difference from the sphere's surface to its center.

Two points \(A\) and \(B\) lie \(15 \mathrm{cm}\) apart in a uniform electric field, with the path \(A B\) parallel to the field. If the potential difference \(\Delta V_{A B}\) is \(840 \mathrm{V},\) what's the field strength?

The potential at the surface of a 10 -cm-radius sphere is \(4.8 \mathrm{kV}\) What's the sphere's total charge, assuming charge is distributed in a spherically symmetric way?

A thin spherical shell has radius \(R\) and total charge \(Q\) distributed uniformly over its surface. Find the potential at its center.
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