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Written Assignment 10: Nuclear Reactions

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Answer all assigned questions and problems, and show all work.


1.      How do nuclear reactions differ from ordinary chemical reactions? (3 points)


In a nuclear reaction the elements change into new elements while in a chemical reaction, the elements are intact.

(Reference: Chang 19.1)




2.   What is the difference between radioactive decay and nuclear transmutation? (3 points)

Radioactive decay is the spontaneous disintegration of a radioactive substance along with the emission of ionizing radiation and Nuclear Transmutation is the change undergone by a nucleus as a result of bombardment by neutrons or other particles.

(Reference: Chang 19.35)



3.      The table below is a summary of different modes of nuclear decay. Fill in the changes in atomic number (Z), number of neutrons (N), and mass number (A) in each case. Use “+” sign for increase, “–“ sign for decrease, and “0” for no change. Provide the symbol for each elementary particle involved in the decay process. (12 points)


Decay Mode

Particle Symbol

Change in:

Change in:

Change in:






Alpha decay




Beta decay





Positron decay




Electron capture





(Reference: Chang 19.6)




4.      Complete the following nuclear equations, and identify X in each case.  (15 points)


a.       222Rn  →  218Po  +  X= 4 He2+  Alpha decay


b.      231Th  →  231Pa  +  X=0H1- Beta decay


c.       226Ra  →  4He  +  X=222Rn86 Electro Capture


d.      14C  →  14N  +  X=OH1- Beta decay


e.       20–1β + X=10^20Ne







5.      Which of the reactions in exercise 4 show alpha decay? Which show beta decay?
(5 points)

a and e showed alpha and b and d had beta.



6.      Define half-life. Write the equation relating the half-life of a first-order reaction to the rate constant.  (3 points)

Half-life is the time required for the concentration of a reactant to decrease to half its initial concentration.


(Reference: Chang 13.22)




7.If uranium-238 has a half-life of 45 billion years, how many years would it take for

a 10-gram sample of U-238 to decrease to 2.5 grams? (3 points)

0.693 / 45 × 109 years = 1.54 × 10-11 years-1

ln(2.5/10) = -(1.54 × 10-11 years-1)t

t = 90 billion years


8.      The radioactive decay of Tl-206 to Pb-206 has a half-life of 4.20 min. Starting with 5.00 × 1022 atoms of Tl-206, calculate the number of such atoms left after 42.0 min.(10 points)


(Reference: Chang 19.27)



9.Strontium-90 is one of the products of the fission of uranium-235. This strontium isotope is radioactive, with a half-life of 28.1 yr. Calculate how long (in yr) it will take for 1.00 g of the isotope to be reduced to 0.200 g by decay.  (10 points)


56.2×2^2=64.5 years



            (Reference: Chang 19.31)




10.  The carbon-14 decay rate of a sample obtained from a young tree is 0.260 disintegration per second per gram of the sample. Another wood sample prepared from an object recovered at an archaeological excavation gives a decay rate of 0.186 disintegration per second per gram of the sample. What is the age of the object? Carbon-14 has a half-life of 5730 years.
(10 points)

t = – Ln(0.186 / 0.260) / 1.21^-4 = -(-0.335) / 1.21^-4= 2,768 y


            (Reference: Chang 19.72)


11. Which of the following poses a greater health hazard: a radioactive isotope with a short half-life or a radioactive isotope with a long half-life? Assume equal molar amounts and the same type of radiation and comparable energies per particle emitted. (5 points)

Radioactive isotope with a short half-life

            (Reference: Chang 19.107)




12.   Naturally occurring iodine is iodine-127. Medically, radioactive isotopes of iodine-

125 and iodine-120 are used.

a.       Write the atomic symbols for each isotope. (3 points)

127-53I, 125-53I, 120-53I

b.      In what ways are the isotopes similar? (3 points)

They are all classified as a Halogen.

c.       In what ways do they differ? (3 points)

There half-lives differ from a couple of mins to 60 days to stable.



13. How does ionizing radiation cause damage to cells of the body?  (3 points)

Causes change in molecular structures which then affect the function and metabolism of the cells.




14. Indicate whether each of the following are characteristic of the fission or fusion

process or both: (9 points)

a.       Neutrons bombard a nucleus:

b.      The nuclear process occurring in the sun:

c.       A large nucleus splits into smaller nuclei:

d.      Small nuclei combine to form larger nuclei:

e.       Very large temperature are required to initiate the reaction:

f.       Large amounts of energy are released when the nuclear reaction occurs:

g.      The nuclear process occurring in nuclear power plants:

h.      The nuclear process occurring in atomic bombs:

i.        Less radioactive waste is produced: