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Plan for Today (AP Physics 2)
• Tests back
• Nuclear Pre-quiz
• Lecture/Notes on Nuclear
• Dose sheet
Nuclear Pre-Quiz
What are the types of nuclear
radiation?
• Alpha particles
• Beta Particles
• Gamma Rays
How and why does radiation
occur?
• Unstable nuclei will naturally decay over
time
• When the nuclei decays, it releases
radiation (particles and energy)
Is mass conserved in a
nuclear decay?
• NO!
• Overall, if we are looking at the number
of nucleons, the total stays the same but
if you calculate the mass, it is less
• Mass goes to energy
• E = mc^2
• We finally get to use it
What is half life?
• The time it takes for half of a radioactive
material to decay
When could you receive a
dose of radiation?
• In everyday life
• ALL the time (see sheet)
What would you do if someone
dropped a piece of radioactive
material in your home?
• Depends on what radioactive material it
was
• It’s in smoke detectors, so if it’s a smoke
detector, I guess you say thank you
What happens to food that
has been irradiated?
• Expose to energy
• Works to preserve food, reduce
foodborne illness, slow ripening
• Does not become radioactive – not
exposed to radioactive material (just
energy from) and below threshold
How is carbon dating
performed?
• All living things have some carbon 14
naturally occurring.
• When the organism dies, carbon 14
starts to decay
• Can look at how much carbon 14 is left
and see how long ago the organism lived
(using half-life)
Composition of Matter
All of matter is composed of at least three
fundamental particles (approximations):
Particle
Fig. Sym
Mass
Charge
9.11 x 10-31 kg -1.6 x 10-19 C
Size

Electron
e-
Proton
p
1.673 x 10-27 kg +1.6 x 10-19 C 3 fm
Neutron
n
1.675 x 10-31 kg
0
3 fm
The mass of the proton and neutron are close, but
they are about 1840 times the mass of an electron.
The Atomic Nucleus
Compacted nucleus:
4 protons
5 neutrons
Since atom is electrically neutral, there
must be 4 electrons.
4 electrons
Beryllium Atom
Definitions
A nucleon is a general term to denote a nuclear
particle - that is, either a proton or a neutron.
The atomic number Z of an element is equal to the
number of protons in the nucleus of that element.
The mass number A of an element is equal to the
total number of nucleons (protons + neutrons).
The mass number A of any element is equal to
the sum of the atomic number Z and the number
of neutrons N :
A=N+Z
Some Properties of Nuclei
• All nuclei are composed of protons and neutrons
– Exception is ordinary hydrogen with just a proton
• The atomic number, Z, equals the number of
protons in the nucleus
• The neutron number, N, is the number of neutrons
in the nucleus
• The mass number, A, is the number of nucleons in
the nucleus
– A=Z+N
– Nucleon is a generic term used to refer to either a proton
or a neutron
Symbol Notation
A convenient way of describing an element is by
giving its mass number and its atomic number,
along with the chemical symbol for that element.
A
Z
X
Mass number
Atomic number
 Symbol 
9
For example, consider beryllium (Be): 4
Be
Symbolism
A
Z
• Symbol:
X
– X is the chemical symbol of the element
• Example:
»
»
»
»
Mass number is 27
Atomic number is 13
Contains 13 protons
Contains 14 (27 – 13) neutrons
27
13
Al
– The Z may be omitted since the element can
be used to determine Z
Example 1: Describe the nucleus of a lithium
atom which has a mass number of 7 and an
atomic number of 3.
A = 7; Z = 3; N = ?
N=A–Z= 7-3
neutrons: N = 4
Protons:
Z=3
Electrons: Same as Z
7
3
Li
Lithium Atom
Isotopes of Elements
Isotopes are atoms that have the same number
of protons (Z1= Z2), but a different number of
neutrons (N). (A1  A2)
3
2
He
Helium - 3
Isotopes
of helium
4
2
He
Helium - 4
Nuclides
Because of the existence of so many
isotopes, the term element is sometimes
confusing. The term nuclide is better.
A nuclide is an atom that has a definite
mass number A and Z-number. A list of
nuclides will include isotopes.
The following are best described as nuclides:
3
2
He
4
2
He
12
6
C
13
6
C
Mass
• It is convenient to use unified mass units, u,
to express masses
– 1 u = 1.660 559 x 10-27 kg
– Based on definition that the mass of one atom of
C-12 is exactly 12 u
• Mass can also be expressed in MeV/c2
– From ER = m c2
– 1 u = 931.494 MeV/c2
Atomic Mass Unit, u
One atomic mass unit (1 u) is equal to onetwelfth of the mass of the most abundant
form of the carbon atom--carbon-12.
Atomic mass unit: 1 u = 1.6606 x 10-27 kg
Common atomic masses:
Proton: 1.007276 u
Neutron: 1.008665 u
Electron: 0.00055 u
Hydrogen: 1.007825 u
Exampe 2: The average atomic mass of
Boron-11 is 11.009305 u. What is the mass
of the nucleus of one boron atom in kg?
11
5
B = 11.009305
Electron: 0.00055 u
The mass of the nucleus is the atomic mass
less the mass of Z = 5 electrons:
Mass = 11.009305 u – 5(0.00055 u)
1 boron nucleus = 11.00656 u
 1.6606 x 10-27 kg 
m  11.00656 u 

1
u


m = 1.83 x 10-26 kg
Mass and Energy
Recall Einstein’s equivalency formula for m and E:
E  mc ; c  3 x 10 m/s
2
8
The energy of a mass of 1 u can be found:
E = (1 u)c2 = (1.66 x 10-27 kg)(3 x 108 m/s)2
E = 1.49 x 10-10 J
When converting
amu to energy:
Or
E = 931.5 MeV
c  931.5
2
MeV
u
Example 3: What is the rest mass energy of
a proton (1.007276 u)?
E = mc2 = (1.00726 u)(931.5 MeV/u)
Proton: E = 938.3 MeV
Similar conversions show other
rest mass energies:
Neutron: E = 939.6 MeV
Electron: E = 0.511 MeV
Summary of Masses
Masses
Particle
kg
u
MeV/c
2
Proton
1.6726 x 10-27 1.007276
938.28
Neutron 1.6750 x 10-27 1.008665
939.57
Electron 9.109 x 10-31
5.486x10-4 0.511
The Mass Defect
The mass defect is the difference between
the rest mass of a nucleus and the sum of
the rest masses of its constituent nucleons.
The whole is less than the sum of the parts!
Consider the carbon-12 atom (12.00000 u):
Nuclear mass = Mass of atom – Electron masses
= 12.00000 u – 6(0.00055 u)
= 11.996706 u
The nucleus of the carbon-12 atom has this mass.
(Continued . . .)
Mass Defect (Continued)
Mass of carbon-12 nucleus: 11.996706
Proton: 1.007276 u
Neutron: 1.008665 u
The nucleus contains 6 protons and 6 neutrons:
6 p = 6(1.007276 u) = 6.043656 u
6 n = 6(1.008665 u) = 6.051990 u
Total mass of parts: = 12.095646 u
Mass defect mD = 12.095646 u – 11.996706 u
mD = 0.098940 u
The Binding Energy
The binding energy EB of a nucleus is the
energy required to separate a nucleus into
its constituent parts.
EB = mDc2 where c2 = 931.5 MeV/u
The binding energy for the carbon-12 example is:
EB = (0.098940 u)(931.5 MeV/u)
Binding EB for C-12:
EB = 92.2 MeV
Binding Energy per Nucleon
An important way of comparing the nuclei of
atoms is finding their binding energy per nucleon:
Binding energy EB =  MeV 


per nucleon
A
 nucleon 
For our C-12 example A = 12 and:
EB 92.2 MeV
MeV

 7.68 nucleon
A
12
Formula for Mass Defect
The following formula is useful for mass defect:
Mass defect
mD
mD   ZmH  Nmn   M 
mH = 1.007825 u;
mn = 1.008665 u
Z is atomic number; N is neutron number;
M is mass of atom (including electrons).
By using the mass of the hydrogen atom, you avoid
the necessity of subtracting electron masses.
Example 4: Find the mass defect for the He
nucleus of helium-4. (M = 4.002603 u)
4
2
Mass defect
mD
mD   ZmH  Nmn   M 
ZmH = (2)(1.007825 u) = 2.015650 u
Nmn = (2)(1.008665 u) = 2.017330 u
M = 4.002603 u (From nuclide tables)
mD = (2.015650 u + 2.017330 u) - 4.002603 u
mD = 0.030377 u
Example 4 (Cont.) Find the binding energy per
nucleon for helium-4. (mD = 0.030377 u)
EB = mDc2 where c2 = 931.5 MeV/u
EB = (0.030377 u)(931.5 MeV/u) = 28.3 MeV
A total of 28.3 MeV is required To tear apart
the nucleons from the He-4 atom.
Since there are four nucleons, we find that
EB 28.3 MeV

 7.07
A
4
MeV
nucleon
Curve shows that
EB increases with
A and peaks at
A = 60. Heavier
nuclei are less
stable.
Green region is for
most stable atoms.
Binding Energy per nucleon
Binding Energy Vs. Mass Number
8
6
4
2
50
100 150 200 250
Mass number A
For heavier nuclei, energy is released when they
break up (fission). For lighter nuclei, energy is
released when they fuse together (fusion).
Summary
Fundamental atomic and nuclear particles
Particle
Fig. Sym
Mass
Charge
9.11 x 10-31 kg -1.6 x 10-19 C
Size

Electron
e
Proton
p
1.673 x 10-27 kg +1.6 x 10-19 C 3 fm
Neutron
n
1.675 x 10-31 kg
0
3 fm
The mass number A of any element is equal to
the sum of the protons (atomic number Z) and
A=N+Z
the number of neutrons N :
Summary Definitions:
A nucleon is a general term to denote a nuclear
particle - that is, either a proton or a neutron.
The mass number A of an element is equal to the
total number of nucleons (protons + neutrons).
Isotopes are atoms that have the same number
of protons (Z1= Z2), but a different number of
neutrons (N). (A1  A2)
A nuclide is an atom that has a definite mass
number A and Z-number. A list of nuclides will
include isotopes.
Summary (Cont.)
Symbolic notation
for atoms
Mass defect
A
Z
X
Mass number
Atomic number
 Symbol 
mD
mD   ZmH  Nmn   M 
Binding
energy
EB = mDc2 where c2 = 931.5 MeV/u
Binding Energy EB =  MeV 


per nucleon
A
 nucleon 