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Chapter 21: Q72P (page 629)

An electron is projected with an initial speedvi=3.2脳105鈥�msdirectly toward a very distant proton that is at rest. Because the proton mass is large relative to the electron mass, assume that the proton remains at rest. By calculating the work done on the electron by the electrostatic force, determine the distance between the two particles when the electron instantaneously has speed2vi.

Short Answer

Expert verified

The distance between the particles is r=1.64脳10鈭�9鈥尘.

Step by step solution

01

 Step 1: Given

The initial speed of the particle isvi=3.2脳105鈥�ms.

02

Determine the concept

According to the principle of conservation of energy, energy is neither creatednor destroyed.It may only transform from one type to another

03

Calculate the distance between the two particles when the electron instantaneously has speed2vi

Since the total energy is conserved the required relation is:

12mevi2=12mevf2鈭�ke2rf

Here,rfis the distance between the electron and the proton.

Forvf=2vi, and forrfsolve as:

rf=2ke2me(vf2鈭�vi2)rf=2ke23mevi2

rf=2(9脳109鈥�Nm2C2)(1.60脳10鈭�19鈥塁)23(9.11脳10鈭�31鈥塳驳)(3.20脳105鈥�ms)2=1.64脳10鈭�9m

.

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Most popular questions from this chapter

In crystals of the salt cesium chloride, cesium ions Cs+form the eight corners of a cube and a chlorine ion Cl鈭�is at the cube鈥檚 center (Fig. 21-36). The edge length of the cube is 0.40nm. The Cs+ions are each deficient by one electron (and thus each has a charge of role="math" localid="1661790179659" 鈭�e), and the Cl鈭�ion has one excess electron (and thus has a charge of -e). (a)What is the magnitude of the net electrostatic force exerted on the Cl鈭�ion by the eight Cs+ions at the corners of the cube? (b) If one of theCs+ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on theCl鈭�ion by the seven remainingCs+ions?

Figure 21-18 shows four situations in which particles of charge +qor -qare fixed in place. In each situation, the particles on the xaxis are equidistant from the yaxis. First, consider the middle particle in situation 1; the middle particle experiences an electrostatic force from each of the other two particles. (a) Are the magnitudes Fof those forces the same or different? (b) Is the magnitude of the net force on the middle particle equal to, greater than, or less than 2F? (c) Do the xcomponents of the two forces add or cancel? (d) Do their ycomponents add or cancel? (e) Is the direction of the net force on the middle particle that of the canceling components or the adding components? (f) What is the direction of that net force? Now consider the remaining situations: What is the direction of the net force on the middle particle in (g) situation 2, (h) situation 3, and (i) situation 4? (In each situation, consider the symmetry of the charge distribution and determine the canceling components and the adding components.)

In Fig. 21-29a, three positively charged particles are fixed on an x-axis. Particles Band Care so close to each other that they can be considered to be at the same distance from particle A. The net force on particle Adue to particles Band Cis 2.014脳10鈭�23Nin the negative direction of the x-axis. In Fig. 21- 29b, particle Bhas been moved to the opposite side of Abut is still at the same distance from it. The net force on Ais now2.877脳10鈭�24N in the negative direction of the x-axis. What is the ratio qC/qB?

In the radioactive decay of Eq. 21-13, a U238 nucleus transforms

toTh234and an ejectedHe4. (These are nuclei, not atoms, and thus

electrons are not involved.) When the separation between and

4He is9.0脳10鈭�15m, what are the magnitudes of (a) the electrostatic

force between them and (b) the acceleration of the particle?

How many electrons would have to be removed from a coin to leave it with a charge of +1.0脳10鈭�7C ?
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