```Do Now (3/17/14):
1. What are some words and images
that come to mind when you hear
2. What is an isotope?
3. What makes an isotope different
than its element?
4/23/12 
Lesson Objectives
Describe nuclear reactions
and perform balancing of
nuclear reactions by solving
problems.
by solving problems.
Nuclear reaction
A reaction in which the
number of protons or
neutrons in the nucleus
of an atom changes.
Atomic number
Number of protons
in the nucleus of the
atom
Mass number
Sum of protons and
neutrons in the
nucleus of the atom
Alpha decay
process in which the
nucleus of an atom
emits an alpha
particle
Alpha Particle
Nucleus of
a helium
atom
Beta decay
when a neutron is changed to a
proton within the nucleus of an
atom, and a beta particle and
an antineutrino are emitted
Gamma decay
that takes place when the
nucleus of an atom emits a
gamma ray.
Isotope
 Atomic nuclei having the same number of protons but
different number of neutrons
Isotopes
 All elements have more than one isotope
 Some isotopes of all elements are radioactive
 Some half-lives are so short that the isotope is not found
naturally
A Half-Life Is the Time Required for ½ the Atoms
of a Substance to Undergo Radioactive Decay
Applet Animation
T1/2 = time for half the sample
to disintegrate
---------------------------------------Assume T1/2 = 5 years
---------------------------------------Number of nuclei present at
time t = 0:
N0 = 1000
--------------------------------------When t = 5 yrs, N = 50
t = 10 yrs, N = 250
t = 20 yrs, N = 125.
Calculate the half-life animation
Applet Animation
Half Life:
 Half-life: time needed for half of remaining mass of
element to decay
t  (#halflives)T1
2
Example #1:
Fermium-253 has a half-life of
sample is considered to be
completely decayed after 10
half-lives. How much time will
elapse for this sample to be
considered gone?
Decay Rate
 T1/2=half life
 λ=decay rate
0.693

T1
2
Example #2:
The half life of Zn-71 is
2.4 minute. If one had 100
g at the beginning, what
is the decay rate of Zn-71?
Mass remaining
m  m0e
 m=mass remaining
 Original mass
 t
Example #3:
The half life of Zn-71 is 2.4
minute. If one had 100 g at
the beginning, how many
grams would be left after 7.2
minutes elapsed?
Practice:
Use the rest of class to
work on the paper:
problems: #2,5,6, and 7
Do Now (4/24/12):
 Pd-100 has a half-life of 3.6 days. If one had 6.02x1023
atoms at the start, how many atoms would be present
Do Now (4/24/12):
U-238 has a half-life of 4.46x109
years. How much U-238 should
10
be present in a sample 2.5 x10
years old, if 2 grams were
present initially?
Using Logarithms
m  m0e
 t
m
 t
e
m0
Using Logarithms
m
 t
e
m0
 m 
ln  t
m0 
Using Logarithms
 Solving for λ:
 m 
ln 
m0 

t
Using Logarithms
 Solving for t:
 m 
ln 
m0 
t

Decay series animation
The Uranium Decay Series
The only radium that exists today
is that which is created as a result
of the decay of uranium.
Carbon-14 Production
Neutron enters nucleus and kicks out a proton.
0n
1
+ 7N14 ---------> 6C14 + 1p1
Carbon-14 Enters the Ecosystem
Carbon Dating
 Since living organisms continually exchange carbon with the atmosphere
in the form of carbon dioxide, the ratio of C-14 to C-12 approaches that of
the atmosphere.
 From the known half-life of carbon-14 and the number of carbon atoms in
a gram of carbon, you can calculate the number of radioactive decays to
be about 15 decays per minute per gram of carbon in a living organism.
Measuring the Age of Organic
Matter
A German tourist in the
Italian Alps discovered
the remains of the
"Iceman" in the ice of a
glacier in 1991.
Calculating the Iceman's Age
The current activity per gram of
carbon half what it would be if
the Iceman were alive.
Since the half-life of carbon-14
5700 years old.
N(t) = population at time t
N(0) = population at time zero
N0 = N(0)
 = decay constant
N(t) = N0 e-t
Example: N0 = 1000
 = 2 x 10-3 years -1
When will N = 200?
N = N0 e-t
(1)
e-t = N /N0
(2)
ln (e-t) = ln (N /N0)
(3)
- t = ln (N /N0)
(4)
t = - [ln (N /N0)] / 
(5)
= - [ln (200/1000)] /2 x10-3 (6)
= 805 years
Half-Life Problem
The half-life of a radioactive substance is
10 hours. What is the decay constant, ?
-------------------------------------------------------N = N0 e-t
(1)
0.50 N0 = N0 e-10
e-10 = 0.50
(2)
(3)
ln(e-10) = ln(0.50)
-10  = -0.693
 = 0.0693 hrs-1
(4)
(5)
(6)
Half-Life Problem
From the previous problem, how much time will it
take for the sample's activity to fall to only 20% of
what it was originally?
---------------------------------------------N = 0.20 N0
(7)
0.20 N0 = N0 e-0.0693 t
-0.0693 t = ln (0.20)
t = 23 hours
(8)
(9)
Decay Constant and Half-Life
N = N0 e-t
(1)
0.50 N0 = N0 e-T
(T = half-life)
e-T = 0.50
(3)
ln(e-T) = ln(0.50)
-T = -0.693
(4)
(5)
T = 0.693/
 = 0.693/T
(2)
(6)
(7)
Half-Life Example
38Sr
90
(strontium-90) has a half-life of 28.5 years.
How long will it take for 98% of a sample of
strontium-90 to disappear?
----------------------------------------------------------------- = 0.693/T1/2
= 0.693 / 28.5
= 0.0243 years-1
0.02 = e-0.0243 t
t = - ln(0.02) /0.0243 years-1
= 161 years
A = number of disintegrations
per second, activity
A = N
One becquerel (Bq) is one
disintegration per second.
One curie is the number of
disintegrations per second (the
"activity") of one gram of radium, or
about 3.7 x 10 10 Bq.
20 rads of X-rays doesn't do the
same damage to humans as 20
---------------------------------------------Rem: an absolute biological
damage unit
Dose
(rems)
Effect
50-300
Sickness
400-500
Lethal 50% (LD50)
Above 600
Lethal 100% (LD100)
(Relative Biological Effectiveness)
a-particles
R
20
Neutrons
10
Protons
10
b-particles
1
g-rays
1
X-rays
1
Example:
will kill a person?
-----------------------------600 rems is fatal
RBE for protons is 10
Number of rads = 600 / 10
= 60
Example:
One joule of energy per
kilogram is absorbed in the
form of neutrons.
Will this prove fatal?
Uranium in earth's crust decays to radium,
Radon is an odorless, tasteless, lighter-thanair gas which rises from the ground through
cracks and fissures in the earth into homes.
When breathed, the alphaemitting radon can cause cancer of the lung.
Radon is the single greatest source of