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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. 21-39, two tiny conducting balls of identical mass mand identical charge hang from non-conducting threads of length L. Assume that u is so small that tan u can be replaced by its approximate equal, sin u.

(a) Show thatx=(q2L2πε0mg)1/3gives the equilibrium separation xof the balls.

(b) If L=120cm,and, x=5.0cmwhat is|q|?

Two small, positively charged spheres have a combined charge of5.0×10−5 C. If each sphere is repelled from the other by an electrostatic force of1.0Nwhen the spheres are2.0mapart, what is the charge on the sphere with the smaller charge?

What must be the distance between point charge q1=26.0μc and point chargerole="math" localid="1661869629566" q2=-47.0μc for the electrostatic force between them to have a magnitude of 5.70 N ?

In Fig. 21-44, what are the (a) magnitude and (b) direction of the net electrostatic force on particle 4 due to the other three particles? All four particles are fixed in the xy−plane, and,q1=−3.20×10−19 C,,q2=+3.20×10−19 C,q3=+6.40×10−19 C,q4=+3.20×10−19 C,θ1=35.00,d1=3.00 cmand d2=d3=2.00 cm.

Question: In Fig. 21-41, three identical conducting spheres form an equilateral triangle of side length d=20.0 cm. The sphere radii are much smaller thand, and the sphere charges are, qA=-2.00nC,qB=-4.00nC,andqc=+8.00nC.

(a) What is the magnitude of the electrostatic force between spheresAandC?

The following steps are then taken:AandBare connected by a thin wire andthen disconnected;Bis grounded by the wire, and the wire is then removed;BandCare connected by the wire and then disconnected. What now are the magnitudes of the electrostatic force (b) between spheresAandCand (c) between spheresBandC?
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