Ch 16- Nuclear reactions are among the
most powerful energy sources in nature.
Behaviour of the nucleus
 What is radioactivity?
 Where does the huge energy released in a nuclear
reaction come from?
 How can stars create elements?
 99.9 % of the mass of atom concentrated in the nucleus
(10-15m= 1 femtometer)
 All nuclear reactions happen within the nucleus
 Nuclear reactions create new elements
 Bombarding nitrogen gas with alpha particles
transmutes (changes) nitrogen into oxygen and
produces hydrogen nuclei.
Nucleus contains positively charged protons and neutral
neutrons. Protons and neutrons are called nucleons.
 Atomic Number, Z: the number of protons in a nucleus
 Neutron Number, N: the number of neutrons in the
nucleus
 Atomic Mass Number, A: the number of nucleons in the
nucleus, Z + N
If X any element
A
Z
Atomic Mass
number
X
35
17
Cl
34
17
Cl
Atomic number
Or Cl-35 and isotope Cl-34
Ex: Chlorine has 17 protons and 18 neutrons and the
isotope has 17 protons and 17 neutrons.
[How to use periodic table]-show examples
Ex: O-16, Th-234, H-1, carbon-14, U-234. Find A, Z, N
Ex
[Rem:#protons for an element never changes.
Isotopes – elements with same number of protons (Z)
but differing in number of neutrons (N).
Ex: H-1 , deuterium H-2, and tritium H-3
Have same chemical properties but different physical
properties. one isotope of an element may be highly
radioactive, while another is stable.
Atomic Mass Units- instead of kg for the mass
1 amu or u = 1.66 x 10-27 kg See formula sheet
Forces in the Nucleus
 The gravitational attraction is vastly weaker than the
electrostatic force of repulsion, so gravity cannot be the
force that holds a nucleus together.
 Strong nuclear force binds (glues) nucleons together in
the nucleus. It is fundamental force of nature, like gravity
and the electrostatic force. It has a very short range and
acts on both neutrons and protons, but does not affect
electrons. To separate protons and neutrons from each
other, we need to overcome the strong nuclear force.
Mass-energy Equivalence
E=mc
2
E is energy in J, m is mass in kg, and c is the speed of light
in m/s.
 This formula converts mass ↔ energy. Energy is mass
and mass is energy. The conversion factor is c2
Ex: What is the energy equivalent for
a. an electron,
b. a proton,
c. helium-4.
d. 1 g
Ex: What is the energy equivalent for 1 u?
Ex: What is the mass equivalent for 1.55 x 1012 J
Ex: calculate the energy equivalent for 0.0029 u in J and eV.
Ex: Show that MeV/c2 has a unit of kg.
In a microsecond about 700 grams of
uranium 235 made a nuclear fission, then the
energy equal to the energy of 15 thousand
tons of TNT dynamite was radiated.
Binding Energy
binding energy is the difference between the total energy
of the individual nucleons and the energy of the nucleus
with the nucleons bound together:
Eb = Enucleons - Enucleus
Enucleons is the sum of the energies of the nucleons.
Enucleus is the energy of the nucleus.
 Binding energy is a small fraction of u.
 The law of conservation of energy in nuclear
reactions states: the total of the energy and the energy
equivalent of the mass in the system is constant.
Mass Defect (mc2)
 mass of the nucleons of a nucleus separately are greater
than the mass of the nucleus.
 the assembled nucleus has less energy than the separate
protons and neutrons that make it up.
 The difference(defect) is the binding energy of the
nucleus. Binding energy is equal to this mass defect.
Ex - The mass of an assembled helium nucleus (42 He) is
6.6443x10-27 kg
mp=1.6726x10-27 kg
mn=1.6749x10-27 kg
(a) What is the mass defect of the helium-4 nucleus?
Helium nucleus contains two protons and two neutrons
Mass defect=(mass of protons +mass of neutrons)(mass of assembled nucleus)=6.6950x10-27 6.643x10-27=5.07x10-29 kg
(b)What is the binding energy of the helium nucleus?
E= mdefectc2= (5.07x10-29)(3.00x108)2=4.56x10-12 J
Ex- What is the mass defect and binding energy of C-12
mc=12.00 amu
mp=1.6726x10-27 kg
mn=1.6749x10-27 kg
mass of individual protons= 6 x 1.6726x10-27=
mass of individual neutrons= 6 x 1.6749x10-27=
Total mass of individual protons and neutrons=
Mass defect(formula)=(mass of protons +mass of
neutrons)-(mass of assembled nucleus)
=
Binding energy (formula)=mdefect x c2
=1.485 x 10-11 J
16.2 Radioactive Decay
 Becquerel, 1896, discovered radioactive decay while
conducting an experiment with uranium.
 He observed while uranium is locked in a drawer away
from sunlight, its radiation fogged photographic plate.
 Some of the radiation deflected when tested with
magnetic and electric fields.
 Atoms emit radiation to become more stable.
 Curie, husband and wife, studied radiation from uranium,
thorium and more active radium, polonium and found
that:
 The intensity of radiation from uranium compounds
was not affected by the other elements in the
compound, heat, powdered, or dissolved or pressure
only depends on the quantity of uranium.
 Concluded radioactivity comes from uranium nucleus.
 Rutherford identified four forms of nuclear radiation:
Alpha (α), Beta negative( β-) , Beta positive ( β+),
gamma (γ)
Radioactive decay of nucleus
Nuclear Radiation is affected by magnetic fields
Four kinds of nuclear radiation
http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/radioa7.swf
1. Alpha particles, symbolized by α or 2 He
 They are positively charged particles
containing helium nuclei.
 They are ejected at a high speed but
have a penetration range of only a
few centimeters in air.
 They are stopped by a thin sheet of
aluminum foil.
4

Ex:
20
11Na
16

9F
4
+ 2He
Na is called parent element and F is called daughter
element.
http://www.wwnorton.com/college/Chemistry/gilbert/tutorials/ch2.htm
All radioactive decays obey conservation laws:
1. momentum
2. energy+mass
3. Electric charge: total charge before the decay = total
charge after decay (the values of Z must balance on
both sides of the equation)
4. Atomic Mass Number: Total of the atomic mass
number for the original nucleus = Atomic mass number
of final products. ( the values of A must balance on
both sides of the equation)
A
Z
X
Y 
A4
Z 2
4
2
Ex:
234
90
Th
A (atomic mass number) is balanced 238 = 4+234
Z (charge) is balanced 92 = 90+2
Ex: The isotope 235U decays into another element, emitting an alpha
particle. What is the element?(write the nuclear decay balanced equation)
Ex: Polonium-212 undergoes alpha decay. Write balanced decay
equation)
Energy –mass, and momentum is conserved
during alpha decay
Mass-energy is conserved
mparentc2 = mdaughterc2 + malphac2 + Ek-alpha
Energy is released because mass decreases, mass defect,
and the difference is converted to energy.
Momentum is conserved(linear)
malpha x valpha = mdaughter x vdaughter
2. Beta-negative particles decay, β They are a stream of electrons
released from nucleus
 Some beta particles are able to
penetrate several millimeters of
aluminum.
0
 denoted by 1 e or 1 
 Neutron changes into a proton and an electron. (conservation of
charge) 0=+1-1
0
antineutrino
X
Y  v
A
A
0
Z
Z 1
1
Ex: Beta(β-) decay of C-14
 Applying conservation of energy showed another particle,
antineutrino, must exist to balance the energy both sides.
 Antineutrino,
v
, and neutrino,

,are neutral particles.
Ex: Write balanced beta-negative decay for thallium-208 (Z=81).
Antineutrino is also released.
Weak nuclear force – involves the transformation of a
neutron into a proton and electron. It is less powerful than
strong nuclear force.
3. Beta-positive (β+) decay: nuclear decay involving
emission of a positron. Positron is an antimatter to the
electron. It has exactly same properties except opposite
charge. A neutrino is released during β+ decay. No change
to A but Z reduced by 1
0
0
1
1
Ex: Nitrogen-13 transmutes by β+ decay. Write balanced
reaction.
4. Gamma rays decay, γ
 e
 They are electromagnetic radiation (speed=3.00x108 m/s) with very
short wavelengths.
 Their wavelengths and energy can vary.
 High-energy gamma rays can penetrate at least 30 cm lead or 2 km
of air.
 Gamma decay does not change the element or its A and Z numbers
A
Z
X X 
A
Z
0
0
Ex: Th-230 emits gamma rays to be more stable.
Natural Transmutations
The process of changing one element into another by alpha, beta or
gamma decay is called natural transmutation.
Radioactive decay series. The process of successive
decays until reaching a stable nucleus.
Example:
Fill spaces with α
U  ...... Th  ...... Pa  ...... U  ..... Th
238
92
, , or γ
234
234
234
90
91
92
Example
Beta-positive decay
230
90
22
11 Na
+10e + 1022Ne
Ex
m defect= mi – mf =21.994436 x 1.66 x 10-27 – 21.991385 x 1.66 x
10-27
= 5.065466 x 10-30 kg
E released= m defect x c2= 4.558194 x 10-13 J
Write balanced nuclear reaction and what type is this decay?
22
11 Na
+10e + 1022Ne
Radioactive decay
1. Complete the missing in the following chart.
Element #protons #neutrons
16
8
8
8O
H-2
1
1
Strontium38
52
90
35
17
18
17 Cl
197
79
118
79Au
234
92
142
92 U
Carbon6
8
14
2. Complete the following nuclear reactions
Th24     
ans: 22688Ra
Ra  222
86 Rn    
ans: 42He
Pb 10 e    
ans:21283Bi
a.
230
90
b.
226
88
c.
212
82
C     10
d.
14
6
e.
227
90
f.
Th     00 


55
  10  25
Mn
ans:147N
ans: 22790Th
ans: 5524Cr
3. Write the nuclear equation for the transmutation by alpha decay for
226
234
92 U and 82 Pb
234
92
U  23090 Th
226
222
80Hg
82 Pb 
+ 42He
+ 42He
4. Write the nuclear equation for the transmutation by beta decay for
210
and 83 Bi
210
83
Bi  0-1e
56
24
Cr
+21084PO
5. Write the full nuclear fusion reaction for two deuterium (H-2) atoms to
form He-3.
2
1H
+ 21H  32He + 10n
Solve Workbook Q#17-30
16.4 Fission and Fusion
Two distinct types of reactions can release energy from nuclei.
1.Nuclear fission
splitting of a heavier nucleus into lighter nuclei. Often,
fission results from a free neutron colliding with a large
nucleus.
235
1
144
90
1
92 U+ 0 n
56 Ba+
36 Kr +2 0n +Energy
Fission reaction gives off energy equal to the difference in
mass between the original nucleus and the total mass of the
products. Mass-energy is conserved. Energy is released
because total matter decreases
ΔE = (mf - mi) x c2
mi is total mass of the original nucleus, kg
mf is total mass of the product(s), kg
Ex: Calculate the energy released by the fission reaction
Mass of U-235= 235.043 930 u
Mass of neutron=1.008 665 u
Mass of Ba-141=140.914 412 u
Mass of Kr-92=91.926 156 u
[Ans: 1.733 x 108 eV]
2.Nuclear fusion
When two low-mass nuclei combine to form a single nucleus
Example
2
2
3
1
1H+ 1 H 2He+ 0n+energy
 This is one of the reactions that occur in the sun.
 To sustain nuclear fusion, high temperatures are
required. This is because both nuclei are positive
to overcome repulsion force.
 The first manufactured use of the energy of
nuclear fusion was in the fusion bomb, popularly
called the hydrogen bomb.
 Radioisotopes can be formed from stable isotopes
by bombarding with alpha particles, neutrons,
electrons or gamma rays.
Ereleasd= (mi – mf) x c2
Ex: Balance the equation.
4
27
1
30
2He + 13Al 0n+
15P
Balance the equation.
Potential Hazards of Nuclear Radiation
Radiation Sickness: Radiation can ionize cellular
material. This ionization disrupts the complex biochemistry
of the body
Genetic Damage: High-energy particles and gamma rays
can alter DNA, and lead to the development of cancers or
harmful mutations.
The introduction of radioactive isotopes into the food chain
is also a serious concern. (Read TXT pg 808)
The fundamental forces in nature
1. Gravitational force-weakest force
2. Electromagnetic force
3. Weak nuclear force
4. Strong nuclear force- strongest force.
16.3 Radioactive Decay Rates and half-life graph
Why inject patients with radioactive dyes.
How do we know this fossil is 5000 years old
 A half-life is the time required for one half of the
atoms in any radioisotope to decay.
http://www.colorado.edu/physics/2000/isotopes/radioactive_decay3.html#lifetime
http://lectureonline.cl.msu.edu/~mmp/applist/decay/decay.htm
 The half-lives of isotopes vary from element to
element. It is unique to the isotope.
Radium-226 has a half-life 1600 years. It means, it
takes 1600 years of a given half quantity of Ra-226
to decay.
 The level of radioactivity shown by a radioactive
substance is proportional to the mass of the
substance.
The level of radioactivity emitted by an isotope may be
measured by means of a device such as a Geiger counter.
The reading will be in becquerels (Bq), the amount of
radiation per second (grams per sec or mL/day or L/ year).
The disintegrations are unaffected by changes in
temperature or pressure or the compound.
Standard graph for Radioactive decay (same
shape for all isotopes)
Ex:
Time(d)
Radioactive Mass(g)
0
100
24
50
48
25
72
12.5
96
6.25
Half-life is 24 days
A sample graph for the decay sodium-24 is given below.
Using the above graph, find
half-life.
t1/2= About 15 h
The decay started with 400
counts/h. The time
corresponding to 200
counts/h is 15h
The formulas used are:

n
Time
T

half  life T 1
2

N
the
T1/2=15 h
1
 N  ( )n
2
n= number of half-lives
T1/2= time for half-life (s, min, h, year .....)
N0=Initial activity at t=0
N= Activity after a period of time
From graph:
T1/2= 8 days
Physics 30- Half-life practice:
Name:…………
1. The half-life of a radioactive isotope is 2.5 years. What would be its
activity after 5.0 y if the activity of the original sample is 3.2x103 Bq?
n=time/half-life=5.0/2.5 =2.0
N=No(1/2)n
N=3.2x103(1/2)2
=8.0x102 Bq
2. The half-life of a radioactive isotope is 6.8 years. If the activity of the
original sample is 4.9x105 Bq, what would be its activity after 100
years?
18 Bq (Follow the method in the example 1)
3. What fraction of Polonium-210 will remain after 172 days if it has a halflife of 138 days?
Assume N0=1.00 0r 100
0.422 or 42.2%
4. If the activity of a sample is 28 Bq and 8.0 h later the activity is 18 Bq,
what is the half-life of the sample?
N=N0(1/2)n
18=28(1/2)n
18/28= (1/2)n
0.643=(1/2)n
log0.643=nlog0.5
n=log0.643/log0.5
n=0.637
n=Time/half-life
=8.0/0.637
=13 h
5. The half-life of radium-226 is 1.6x103years. How long will it take for
20.0 mg of radium-226 to decay to 2.50 mg?
Use the method in question 4.
4.8x103 years.
6. An experiment was performed to determine the
half-life of technetium-99.
The activity was measured
over a 24 h period and the results are recorded below.
Time(h) Activity(kBq)
0
17.0
3
12.2
6
8.9
9
6.5
12
4.5
15
3.2
18
2.3
21
1.5
24
1.1
(a) Plot a graph of
activity vs time
(b)Using the graph,
determine the half-life.
(c)Predict the activity for
19 h
7. In an experiment, a researcher studied the decay of Po-210, which
decays by the alpha emission and releases a stable Pb-206 atom. The
half-life of Po-210 is 138.4 days. The mass of the Po-210 sample at the
start of the experiment was 34.0g.
(a)Write an equation for the alpha-decay of Po-210
(b)What will be the amount Po-210 remaining after 415.2 days?
(c)At the end of the experiment, the amount of Po-210 remaining was
1.06 g. What is the duration of the experiment?
Physics 30- Half-life practice:
Name:…………
1. The half-life of a radioactive isotope is 2.5 years. What would be its activity after 5.0 y if the activity of
the original sample is 3.2x103 Bq?
2. The half-life of a radioactive isotope is 6.8 years. If the activity of the original sample is 4.9x105 Bq, what
would be its activity after 100 years?
3. What fraction of Polonium-210 will remain after 172 days if it has a half-life of 138 days? Assume
N0=1.00 0r 100
4. If the activity of a sample is 28 Bq and 8.0 h later the activity is 18 Bq, what is the half-life of the sample?
5. The half-life of radium-226 is 1.6x103years. How long will it take for 20.0 mg of radium-226 to decay to
2.50 mg?
6. An experiment was performed to determine the half-life of
technetium-99. The activity was measured over a 24 h period
and the results are recorded below.
a) Plot a graph of activity vs. time
b) Using the graph, determine the half-life.
c) Predict the activity for 19 h.
Time (h)
0
3
6
9
12
15
18
21
24
Activity (kBq)
17.0
12.2
8.9
6.5
4.5
3.2
2.3
1.5
1.1
7. In an experiment, a researcher studied the decay of Po-210, which decays by the alpha emission and
releases a stable Pb-206 atom. The half-life of Po-210 is 138.4 days. The mass of the Po-210 sample at
the start of the experiment was 34.0g.
a. Write an equation for the alpha-decay of Po-210
b. What will be the amount Po-210 remaining after 415.2 days?
c. At the end of the experiment, the amount of Po-210 remaining was 1.06 g. What is the
duration of the experiment?
Radioactive Decay and half-life
1. Write the nuclear balanced equation for the following alpha decay:
Ra-226
Th-230
2. Write the nuclear balanced equation for the following beta decay:
Pb-214
Cr-56
3. The half-life of strontium-90 is 28 years. After 280 years, how would the intensity of a sample
compare to the original intensity of the sample (in %)
4. A 1.00 microgram sample of radioactive material decays to 0.25 microgram after 48 hours. What is
the half-life of this material?
5. Nitrogen-14 has a nuclear mass of 14.00307u. What is its mass defect and binding energy?
mp=1.007825u
mn=1.008665u
me=0.000549u
6. If a fission reaction produced 5.6 x 1012 J of energy, how much mass was converted into energy?
7. The loss in mass in fission reaction is 0.010g. How much energy will have been produced?
8. Two hundred atoms of uranium-235 split. If each atom releases 3.2 x 10-8 J when fission occurs, what
nuclear mass was converted into energy?
9. The nuclear equation for the fusion of two isotopes of hydrogen is shown. (Written below each
isotope is its mass in unit called the atomic mass unit (amu)). If 1 amu=1.66 x 10-27 kg, calculate the
nuclear energy released in the reaction by comparing the total mass before and after the reaction.
H
+
H

He
+
n
(2.01410 amu)
(2.01410 amu)
(3.01603 amu)
(1.000867 amu)
Solve Workbook Q#31-36