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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脳10鈭�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脳102鈥塏

b) The acceleration of the particle isa=7.7脳1028鈥�ms2

Step by step solution

01

Write the given data

Consider the given chemical equation as:

U238鈫�Th234+He4

Separation between Th234andHe4 is9脳10鈭�15鈥尘

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脳109鈥�Nm2C2)(2脳1.60脳10鈭�19鈥塁)(90脳1.60脳10鈭�19鈥�C)(9.0脳10鈭�15鈥尘)2=5.1脳102鈥塏

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鈥檚 second law leads to

a=Fm=5.1脳102鈥塏4(1.67脳10鈭�27鈥塳驳)=7.7脳1028鈥�ms2

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Most popular questions from this chapter

A particle of charge Qis fixed at the origin of an x-ycoordinate system. Att=0a particle (m=0.800g,鈥�q=4.00渭颁) is located on the xaxis atx=20.0cm, moving with a speed of50.0m/sin the positive ydirection. For what value of Qwill the moving particle execute circular motion? (Neglect the gravitational force onthe particle.)

How far apart must two protons be if the magnitude of the electrostatic force acting on either one due to the other is equal to the magnitude of the gravitational force on a proton at Earth鈥檚 surface?

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=(q2L2蟺蔚0mg)1/3gives the equilibrium separation xof the balls.

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

In Fig. 21-26, particle 1 of charge +1.0渭Cand particle 2 of charge -3.0鈥�渭Care 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?

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.)
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