__Chapter 20: Nuclear Chemistry
__

**
**

__Section 20-1:Ê Balancing Nuclear Equations__

__Section 20-2:Ê 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 (Q

ln Q* _{f}* = -kt + ln Q

The half-life (t_{1/2}) 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 0.5Q* _{i}* for Q

ln (0.5Q* _{i}*) = -kt

kt_{1/2 }=
ln (Q* _{i}* /0.5Q

t_{1/2 }=
ln 2/k = 0.693/k and k = 0.693/t_{1/2}

Replacing k with 0.693/t_{1/2} in the equation ln Q* _{f}* =
-kt + ln Q

**ln Q_{f} = -(0.693/t_{1/2})t + ln Q_{i}
**

__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 Q* _{f}* = -(0.693/t

**t = (t _{1/2}/0.693)ln (Q_{i}/Q_{f})
**

__Sample Exercise 20D:
__

The half-life of potassium-40 is
1.25 x 10^{9} 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 t_{1/2} as follows:

__Sample Exercise 20E:
__

A sample of radon-222 containing
6.54 x 10^{25} atoms requires 17.6 days to decay to 2.66 x 10^{24} 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.

__Click for Solution__

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

__Click for Solution__

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?

__Click for Solution__

20-4) The half-life of iodine-131
is 8.04 days. How much time is
required for a sample containing 6.56 x 10^{23} iodine-131 atoms to
decay to 1.26 x 10^{23} atoms?

__Click for Solution__

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.

__Click for Solution__