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Chapter 21: Q69P (page 629)

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 is9.0×10−15m, what are the magnitudes of (a) the electrostatic

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

Short Answer

Expert verified

a) The electrostatic force between them isF=5.1×102 N

b) The acceleration of the particle isa=7.7×1028 ms2

Step by step solution

01

Write the given data

Consider the given chemical equation as:

U238→Th234+He4

Separation between Th234andHe4 is9×10−15 m

02

(a) Calculate the magnitudes of the electrostatic force between them

The nucleus of Helium has 2 protons and that of thorium has 90.

F=kq2d2=(9×109 Nm2C2)(2×1.60×10−19 C)(90×1.60×10−19 C)(9.0×10−15 m)2=5.1×102 N

03

(b) Calculate the magnitudes of the acceleration of the particle

Estimating the helium nucleus mass as that of 4 protons (actually, that of 2

Protons and 2 neutrons, but the neutrons have approximately the same mass), Newton’s second law leads to

a=Fm=5.1×102 N4(1.67×10−27 kg)=7.7×1028 ms2

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Most popular questions from this chapter

In Fig. 21-26, particle 1 of charge +1.0μCand particle 2 of charge -3.0 μCare held at separation L=10.0cm on an x-axis. If particle 3 of unknown charge q3is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) xand (b) ycoordinates of particle 3?

The charges and coordinates of two charged particles held fixed in an x-yplane are q1=+3.0mC,x1=3.5cm,y1=0.50cm,and q2=-4.0mC,x2=-2.0cm,y2=1.5 cm.Find the (a) magnitude and (b) direction of the electrostatic force on particle 2 due to particle 1. At what (c) xand (d) ycoordinates should a third particle of charge q3=+4.0 mC be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero?

Figure 21-11 shows four situations in which five charged particles are evenly spaced along an axis. The charge values are indicated except for the central particle, which has the same charge in all four situations. Rank the situations according to the magnitude of the net electrostatic force on the central particle, greatest first.

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Fig. 21-22a). The electrostatic force acting on sphere 2 due to sphere 1 isF→.Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Fig. 21-22b), then to sphere 2 (Fig. 21-22c), and finally removed (Fig. 21-22d). The electrostatic force that now acts on sphere 2 has magnitudeF'. What is the ratioF'/F?

Figure 21-21 shows four situations in which a central proton is partially surrounded by protons or electrons fixed in place along a half-circle. The anglesθare identical; the anglesareϕ also. (a) In each situation, what is the direction of the net force on the central proton due to the other particles? (b) Rank the four situations according to the magnitude of that net force on the central proton, greatest first.
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