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Chapter 42: Q89P (page 1307)

What is the likely mass number of a spherical nucleus with a radius of 3.6 fm as measured by electron-scattering methods?

Short Answer

Expert verified

The likely mass number of the nucleus is 27.

Step by step solution

01

Given data

Radius of the nucleus, r = 3.6 fm

02

Understanding the concept of nuclear radius

The nuclear radius, R, can be defined as the distance from the center to the point where the density has decreased to half its original value. In calculation, the radius is directly proportional to the one-third power of the mass number of the nucleus.

Formula:

The radius of an atom of mass number, A in a nucleus

r=r0A1/3.........(1)wherer0=1.2fm

03

Calculation of the mass number

Using the given data in equation (1), we can get the mass number of the spherical nucleus as follows:

A=rr03=3.6fm1.2fm3=27

Hence, the likely mass number is 27.

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Most popular questions from this chapter

What is the binding energy per nucleon of the rutherfordium isotope Rf104259? Here are some atomic masses and the neutron mass.

Rf104259259.10563uH11.007825un1.008665u

Nuclear radii may be measured by scattering high energy (high speed) electrons from nuclei. (a) What is the de-Broglie wavelength for 200MeV electrons? (b) Are these electrons suitable probes for this purpose?

The isotope K40can decay to either C40aor A40r; assume both decays have a half-life of 1.26脳109y. The ratio of the Caproduced to Ar theproduced is 8.54/1 = 8.54. A sample originally had onlyK40. It now has equal amounts ofK40andA40r; that is, the ratio of Kto Aris 1/1 = 1. How old is the sample? (Hint:Work this like other radioactive-dating problems, except that this decay has two products.)

The half-life of a radioactive isotope is 140d. How many days would it take for the decay rate of a sample of this isotope to fall to one-fourth of its initial value?

Under certain rare circumstances, a nucleus can decay by emitting a particle more massive than an alpha particle. Consider the decays Ra223鈫�Pb209+C12andRa223鈫�Ra219+He4

Calculate the Qvalue for the (a) first and (b) second decay and determine that both are energetically possible. (c) The Coulomb barrier height for alpha-particle emission is 30.0 MeV. What is the barrier height for14Cemission ? (Be careful about the nuclear radii.) The needed atomic masses are

Ra223223.01850uC1414.00324uRa20920.98107uC44.00260uRa219219.00948u
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