Conceptual Physics

(Sean Pound) #1

38.16 - Sample problem: radioactive decay


Variables


What is the strategy?



  1. The Į and ȕ particles have known charge and known mass number. Subtract these from the atomic number and the mass number of
    the parent nucleus to determine the daughter nucleus’s values of Z and A.


Physics principles and equations


AnĮ particle consists of 2 protons and 2 neutrons. Its mass number is four.


A negative ȕ particle consists of one electron. When the parent nucleus emits it, the number of protons increases by one and its mass number
is unchanged.


Step-by-step solution


We will use the notation Z 0 and A 0 to denote the initial values of the proton number and the mass number, Z 1 and A 1 to denote their values
after the first decay step, Z 2 and A 2 to denote their values after the second decay step, and Z 3 and A 3 to denote their values after the third and
final decay step.


After the first decay process, the nucleus has 88 protons and 228 nucleons in total. This is radon-228, which then emits a negative ȕ particle.


After the second decay process, there is a nucleus with 89 protons and 228 nucleons in total. This is actinium-228, which then decays by
emitting another negative ȕ particle.


After the third decay process, the nucleus has 90 protons, and a total of 228 nucleons. The end result after the three decays is again thorium
because the number of its protons is again 90. After the three decays, the element is thorium-228. This lighter thorium isotope then continues
to decay in a series of Į and ȕ decays until it becomes the stable isotope lead-208.


A thorium-232 nucleus (Z = 90, A =


232) is radioactive and decays by first


emitting an alpha particle, then two


negative beta particles. What are the


atomic number and the mass number


of the daughter nucleus after each of


these three decay steps?


atomic number, number of
protons

Z


mass number, total number of
protons and neutrons

A


Step Reason


1. Z 0 = 90 initial values


2. Z 1 = Z 0 – 2 Į emission decreases nuclear charge


3. A 1 = A 0 – 4 Į emission decreases nuclear mass


Step Reason


4. Z 1 = 88 initial values


5. Z 2 = Z 1 + 1 ȕ emission increases nuclear charge


6. A 2 = A 1 ȕ emission does not affect nuclear mass


Step Reason


7. Z 2 = 89 initial values


8. Z 3 = Z 2 + 1 ȕ emission increases nuclear charge


9. A 3 = A 2 ȕ emission does not affect nuclear mass


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