Chapter 20:  Nuclear Chemistry

 

 

Section 20-1: Balancing Nuclear Equations

Section 20-2: Nuclear Kinetics and Half-Life

Chapter 20 Practice Exercises and Review Quizzes

 

 

 

 

 

 

Section 20-1:  Balancing Nuclear Equations


During a nuclear reaction, the nuclei of the isotopes involved will undergo a change in composition.  Each particle involved in a nuclear reaction will be represented as follows, where Z is the atomic number and A is the mass number:

 

 

When a nuclear reaction is balanced, the sum of the Z values for the reactants must equal the sum of the Z values for the products.  Likewise, the sum of the A values for the reactants must equal the sum of the A values for the products.  Note that charges are typically omitted when nuclear reactions are written.

 

Types of radioactive decay include:

 

A. Alpha decay (or alpha emission) = nucleus of an isotope X emits a helium-4 nucleus to produce a new isotope Y.  The equation is balanced as follows:

 

 

B. Beta decay (or beta emission) = nucleus of an isotope X emits a particle equivalent to an electron to produce a new isotope Y.  The equation is balanced as follows:

 

 

C. Positron decay (or positron emission) = nucleus of an isotope X emits a particle equivalent to an electron, but with a positive charge, to produce a new isotope Y.  The equation is balanced as follows:

 

 

D. Electron capture = electron from an inner orbital is absorbed into the nucleus of isotope X to produce a new isotope Y.  The equation is balanced as follows:

 

 

In each case above, the identity of the isotope Y can be determined by matching the atomic number of Y with an element on the periodic table:

 

Sample Exercise 20A:

 

Write balanced equations for the following nuclear reactions:

 

a. Uranium-235 decays by alpha emission.

b. Rubidium-87 decays by beta emission.

c. Potassium-38 decays by positron emission.

d. Iron-55 decays by electron capture.  

 

Solution:

 

 

A nuclear reaction may also be initiated by bombarding a sample of an isotope with particles such as neutrons or protons in order to produce a new isotope.  Other particles may be produced in the process as well.  The symbols for a neutron and a proton are as follows:

 

 

Sample Exercise 20B:

 

Neutron bombardment of nitrogen-14 produces a proton and a new isotope.  Write a balanced equation for this nuclear reaction.

 

Solution:

 

 

 

 

Section 20-2:  Nuclear Kinetics and Half-Life


Radioactive decay is first-order.  Given the initial quantity (Qi) of a radioactive isotope in any unit (such as grams, moles, or number of atoms), the final quantity (Qf) can be calculated using the following equation:

 

ln Qf = -kt + ln Qi

 

The half-life (t1/2) of a radioactive isotope is the time required for the isotope to decay to half its initial quantity.  Using the equation above, we can derive the relationship between half-life and the rate constant k by substituting 0.5Qi for Qf  and t1/2 for t:

 

ln (0.5Qi) = -kt1/2 + ln Qi

kt1/2 = ln (Qi /0.5Qi) = ln 2

t1/2 = ln 2/k = 0.693/k and k = 0.693/t1/2

 

Replacing k with 0.693/t1/2 in the equation ln Qf = -kt + ln Qi, we obtain the following equation:

 

ln Qf  = -(0.693/t1/2)t + ln Qi

 

Sample Exercise 20C:

 

The half-life of bromine-80 is 18 minutes.  What mass of bromine-80 will remain if a 96 gram sample decays for 25 minutes?

 

Solution:


 

If the equation ln Qf = -(0.693/t1/2)t + ln Qi is solved for t, we obtain:

 

t = (t1/2/0.693)ln (Qi/Qf)

 

Sample Exercise 20D:

 

The half-life of potassium-40 is 1.25 x 109 years.  How much time is required for a 9.48 mol sample of potassium-40 to decay to 1.22 mol?  

 

Solution:

 

 

We can also solve for t1/2 as follows:

 

Sample Exercise 20E:

 

A sample of radon-222 containing 6.54 x 1025 atoms requires 17.6 days to decay to 2.66 x 1024 atoms.  Calculate the half-life of radon-222.

 

Solution:

 

 

 

 

 

Chapter 20 Practice Exercises and Review Quizzes:

 

20-1) Write balanced equations for the following nuclear reactions:

 

a. Lead-196 decays by electron capture.

b. Phosphorus-28 decays by positron emission.

c. Radium-226 decays by alpha emission.

d. Zinc-73 decays by beta emission.  

 

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20-1)

 

 

20-2) Proton bombardment of magnesium-26 produces an alpha particle and a new isotope.  Write a balanced equation for this nuclear reaction.

 

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20-2)

 

 

20-3) The half-life of oxygen-13 is 0.00870 seconds.  How many moles of oxygen-13 will remain if a 38.4 mol sample decays for 0.0125 seconds?

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20-3)

 

 

20-4) The half-life of iodine-131 is 8.04 days.  How much time is required for a sample containing 6.56 x 1023 iodine-131 atoms to decay to 1.26 x 1023 atoms?

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20-4)

 

 

20-5) A 48 gram sample of magnesium-28 requires 69 hours to decay to 5.0 grams.  Calculate the half-life of magnesium-28.

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20-5)

 

 

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