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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

Question: Two tiny, spherical water drops, with identical charges of-1.00脳10-16C, have a center-to-center separation of 1.00 cm. (a) What is the magnitude of the electrostatic force acting between them? (b) How many excess electrons are on each drop, giving it its charge imbalance?

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