Nuclear Physics and Radioactivity
AP Physics
Chapter 30
Nuclear Physics and Radioactivity
30.1 Structure and properties of the Nucleus
30.1 Structure and Property of the Nucleus
Nucleus is composed of two
particles
Proton – positive charge
Neutron – neutral
Together they are called nucleons
30.1
kgxm
Cxq
p
p
27
19
1067262.1
10602.1
kgxmn271067493.1
30.1 Structure and Property of the Nucleus
To present this information we use the symbol form
Z – number of protons (atomic number)
A – atomic mass (not average)
The number of Neutrons (N) is
Sometime written without the Z, as that information is redundant
30.1
XAZ
ZAN XA
30.1 Structure and Property of the Nucleus
Isotopes – the same element, but different numbers of neutrons or mass number
These isotopes would be
Not all isotopes are equally
common
C-12 is 98.9%
C-13 is 1.1%
Called the Natural Abundance 30.1
He52 He6
2 He72 He8
2
30.1 Structure and Property of the Nucleus
Masses of atoms are determined using a mass spectrometer
The mass is given
in unified atomic
mass units (u)
Carbon – 12 is
given the mass
of 12.000000u
30.1
ump 007276.1
umn 008665.1
30.1 Structure and Property of the Nucleus
Masses are often given in electron volts
This is derived from Einstein’s equation
Using the mass of a proton
And placing into Einstein’s equation
30.1
2mcE
ukgxprotonu
protonkgxu /1066054.1
/007276.1
/1067262.10000.1 27
27
JxsmxukgxE 102827 104924.1)/109979.2(/1066054.1
25.9311031.9106022.1
1104924.1 8
1910
cMeVeVx
Jx
eVJxE
Nuclear Physics and Radioactivity
30.2 Binding Energy and Nuclear Forces
30.2 Binding Energy and Nuclear Forces
The total mass of a stable nucleus is always less than the sum of the masses of its separate protons and neutrons
The difference is mass is
the binding energy
So for example the mass of
Helium 4 is 4.002603u
30.2
uxuxux enp 03297916.4)00054858.02()008665.12()007276.12(
uuu 0303761.0002603.403297916.4
MeVu
MeVu 30.28
1
5.9310303761.0
30.2 Binding Energy and Nuclear Forces
This is the energy needed to break apart the nucleus
To be a stable nucleus, the mass must be less than the parts
The binding energy per
nucleon is the total
binding energy divided
by A
30.2
30.2 Binding Energy and Nuclear Forces
Strong Nuclear Force – attractive force between all nucleons
Drops to essentially zero if the distance between the nucleons is greater than 10-15m
Occur by the exchange of a particle called a meson
Weak Nuclear Force – very weak, show in types of radioactive decay
30.2
Nuclear Physics and Radioactivity
30.3 Radioactivity
30.3 Radioactivity
Henri Becquerel (1896) uranium darkens photographic plates
Radioactive decay – unstable nuclei
fall apart with
the emission of
radiation
30.3
30.3 Radioactivity
Rays can be classified into three catagories
1. Alpha () – barely penetrates paper
2. Beta () – penetrates up to 3mm of aluminium
3. Gamma () – penetrates several cm of lead
30.3
Nuclear Physics and Radioactivity
30.4 Alpha Decay
30.4 Alpha Decay
An alpha particle is a helium nucleus
When an atom undergoes alpha
decay it loses 2 protons and 2
Neutrons
Reactions are written
30.4
HeRnRa 42
222862
22688
30.4 Alpha Decay
Parent nucleus – the original
Daughter nucleus – nucleus of new atom
Transmutation – change of one element into another
Basic form for alpha decay is
The alpha particle is ejected because it has a very large binding energy and is difficult to break apart
30.4
HeRnRa 42
222862
22688 HeNN A
ZAZ
42
420
Nuclear Physics and Radioactivity
30.5 Beta Decay
30.5 Beta Decay
Beta particle (-) – electron
Also produces an
antineutrino
Antineutrino – has no
charge and almost
no mass
The result of the decay is that a neutron becomes a proton 30.5
30.5 Beta Decay
For Carbon – 14 decay
Or the general form which would be
The electron does not come form the electron cloud, but from the decay of a neutron into a proton
It is identical to any other electron
30.5
veNC 147
146
veNN AZ
AZ
10
30.5 Beta Decay
Unstable isotopes with too few neutrons compared to their number of protons decay by emitting a positron
Positron – same mass as an
electron, positive charge
This is an example of an antiparticle (antimatter)
The decay pattern is30.5
e
veNN AZ
AZ
10
Nuclear Physics and Radioactivity
30.6 Gamma Decay
30.6 Gamma Decay
Gamma Ray – photon of
EMR
A nucleus can be in an
excited state like an
electron
When it drops down it emits a ray
Much larger than for electrons
For a given decay the ray has the same energy
30.6
30.6 Gamma Decay
The nucleus may enter an excited state by
Violent collision with another particle
The particle after a decay is often in an excited state
The equation can be
written
30.6
NN AZ
AZ 10
Nuclear Physics and Radioactivity
30.7 Conservation of Nucleon Number
30.7 Conservation of Nucleon Number
In radioactive decay all conservation laws are true
1. Energy
2. Linear Momentum
3. Angular Momentum
4. Electric Charge
Law of Conservation of Nucleon Number – the number of nucleons (protons or neutrons) remains the same, although they may change type
30.7
Nuclear Physics and Radioactivity
30.8 Half-Life and Decay Rate
30.8 Half-Life and Rate of Decay
Individual radioactive nuclei in a random process
Based on probability we can approximate the number of nuclei in a sample that will decay
Where is the decay constant30.8
tNN tNN Nt
N
30.8 Half-Life and Rate of Decay
The greater the decay constant, the greater the rate of decay
The more radioactive it is
The equation can be solved for N using calculus and we get
Where N0 is the initial number of nuclei present
N is the number remaining after time t
The number of decays per unit time is called the activity or rate of decay
30.8
teNN 0
30.8 Half-Life and Rate of Decay
Half-Life – the time it takes for half the original amount of parent isotope to decay (T½)
30.8
693.02ln
21 T
Nuclear Physics and Radioactivity
30.9 Calculations Involving Decay Rates and Half-Life
30.9 Calc. Involving Decay Rates and Half-Life
Carbon-14 has a half-life of 5730 yr. What is the activity of a sample that contains 1022 nuclei?
1 decay/s is called a becquerel (Bq)
30.9
693.0
21 T
21
693.0
T sx
yrsxyr/1083.3
)/10156.3)(5730(
693.0 127
Nt
N
sdecayxsxt
N/1083.3)10)(/1083.3( 102222
30.9 Calc. Involving Decay Rates and Half-Life
1.49mg of Nitrogen-13 has a half life of 600s.
a. How many nuclei are present?
b. What is the initial activity?
30.9
1623
60 109.6
0.13
10022.61049.1 x
g
nucleixgxN
sxT
/1016.1600
693.0693.0 3
21
sdecayxxsxNt
N/108)109.6)(/1016.1( 13163
30.9 Calc. Involving Decay Rates and Half-Life
1.49mg of Nitrogen-13 has a half life of 600s.
c. What is the activity after 3600s?6 half lives
If this had not been a perfect half life we would have used
30.9
1262113 1025.1))(108( xx
tet
N
t
N
0
Nuclear Physics and Radioactivity
30.10 Decay Series
30.10 Decay Series
Decay Series – a successive set of decay
30.10
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