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Atomic, Nuclear and
Particle Physics
Topic 7.1 Discrete energy and radioactivity
Image from http://www.onlineopinion.com.a...
What is an atom?
• Can you explain why you know
that matter is made of atoms?
• How do you know?
• Why is it important?
• ...
Energy Levels
Thomas Melville was the first to study
the light emitted by various gases.
He used a flame as a heat source,...
The new type of spectrum consisted of
a series of bright lines separated by
dark gaps.
This spectrum became known as a lin...
In other words, the spectrum was
characteristic of the type of gas,
a kind of "fingerprint" of the
element or compound.
Th...
Emission Spectra
Absorption Spectra
What do you notice about these?
TOK
Spectra can be categorised as either
emission or absorption spectra.
An emission spectrum is, as the name
suggests, a spec...
An absorption spectrum is just the
opposite, consisting of a bright,
continuous spectrum covering the full
range of visibl...
Evidence
What causes line spectra?
You always get line spectra from
atoms that have been excited in
some way, either by he...
Line spectra are caused by changes in
the energy of the electrons.
Large, complicated atoms like neon
give very complex li...
Planck and Einstein's quantum theory
of light gives us the key to
understanding the regular patterns in
line spectra.
The ...
The electron, has the most
potential energy when it is on the
upper level, or excited state.
When the electron is on the l...
The diagram can show an electron in an
excited atom dropping from the excited
state to the ground state.
This energy jump,...
The potential energy that the electron has
lost is given out as a photon.
This energy jump corresponds to a specific
frequ...
THE BOHR MODEL OF
THE ATOM
In 1911 Bohr ignored all the previous
descriptions of the electronic
structure as they were bas...
THE BOHR MODEL OF
THE ATOM
Bohr assumed that the energy
carried by an electron was also
quantized.
From this assumption, h...
THE BOHR MODEL OF
THE ATOM
0
+
-
free e-
} bound e-
e n e r g y le v e ls
B o h r a t o m
THE BOHR MODEL OF
THE ATOM
An electron can be moved to a higher
energy level by…
1. INCOMING PHOTON- Must be of
exactly th...
THE BOHR MODEL OF
THE ATOM
IONIZATION- energy required to
remove an electron from the
atom.
Example: the ionization energy...
THE BOHR MODEL OF
THE ATOM
Let’s prove this using
the following
formula…
• LYMAN SERIES
En-Em = hf
(13.6 –0.85)(1.6X10-
19...
THE BOHR MODEL OF
THE ATOM
• BALMER SERIES
En-Em = hf
(3.4 –0.85)(1.6X10-19
)=hc/λ
λ=4.87X10-7
m
= 487 nm
This is Blue Lig...
EXAMPLE 1
Use the first three energy levels for
the electron in hydrogen to
determine the energy and hence
wavelength of t...
EXAMPLE 1 SOLUTION
From the diagram, the atom can
be excited to the first (n = 2)
and second
(n = 3) excited states. From
...
EXAMPLE 1 SOLUTION
n = 3 n = 1, Ephoton
= E3
- El
• = -1.51 - (-13.6)
• = 12.09eV
 
n = 2 n = l, Ephoton
= E2
- E1
• = -3....
EXAMPLE 1 SOLUTION
n = 3 n = 2, Ephoton
= E3
- E2
• = -1.51 - (-3.4)
• = 1.89 eV n = 3
n = 2
n = 1
EXAMPLE 1 SOLUTION
To find the wavelengths of the
three photons, use
Note: convert eV to J
E = ie. =
E
hf
hc hc
=
λ
λ
EXAMPLE 1 SOLUTION
n=3 n=l,
• = 1.024 x 10 -7
m
• = 102 nm (ultraviolet)
λ =
6.6 x 10 x 3 x 10
12.09 x 1.6 x 10
-34 -8
-19
EXAMPLE 1 SOLUTION
n=2 n=l, λ=
• = 1.21 x 10-7
m
• = 121nm (ultraviolet)
n=3 n=2, λ=
= 6.55 X 10-7
m
= 655 nm (visible-red...
EXAMPLE 1
SOLUTION
Note that we have two
Lyman series lines
(those ending in the
ground state) and
one Balmer line
(ending...
EXAMPLE 1
SOLUTION
Those from the Lyman
series produce lines in
the ultra-violet part of
the spectrum while the
line in th...
Nuclear Structure
Mass Number
The total number of protons and
neutrons in the nucleus is called
the mass number (or nucleon
number).
Nucleon
Protons and neutrons are called
nucleons.
Each is about 1800 times more
massive than an electron, so
virtually all...
Atomic Number
All materials are made from about 100
basic substances called elements.
An atom is the smallest `piece' of a...
Isotopes
Every atom of oxygen has a
proton number of 8. That is, it has
8 protons (and so 8 electrons to
make it a neutral...
Some oxygen atoms have a
nucleon number of 17 or 18.
16
8O and 17
8O are both oxygen
atoms.
They are called isotopes of
ox...
Since the isotopes of an element
have the same number, of
electrons, they must have the
same chemical properties.
The atom...
Evidence for Neutrons
The existence of isotopes is evidence for the
existence of neutrons because there is no
other way to...
Interactions in the
Nucleus
Electrons are held in orbit by the force of
attraction between opposite charges.
Protons and n...
What is radiation?
• What does it do?
• Where does it come from?
• How can we use it?
• Can we stop it?
• How do we protec...
Radioactivity
In 1896, Henri Becquerel
discovered, almost by accident,
that uranium can blacken a
photographic plate, even...
Then Marie and Pierre Curie
discovered more radioactive elements
including polonium and radium.
Scientists soon realised t...
Alpha, Beta and Gamma
Properties
Properties 2
The diagram on the right shows
how the different types are
affected by a magnetic field.
The alpha beam is a ...
The beta particles are much lighter than the alpha
particles and have a negative ( ) charge, so they‑
are deflected more, ...
Ionising Properties
α particles,‑ β particles and‑ γ ray photons‑
are all very energetic particles.
We often measure their...
Why do the 3 types of
radiation have different
penetrations?
Since the α-particle is a heavy,
relatively slow moving parti...
the β particle‑ is a much lighter
particle than the α particle and it‑
travels much faster.
Since it spends just a short t...
A γ ray photon‑ interacts weakly with
matter because it is uncharged and
therefore it is difficult to stop.
A γ ray photon...
Stability
If you plot the neutron number N
against the proton number Z for
all the known nuclides, you get
the diagram sho...
Can you see that the stable nuclides of
the lighter elements have approximately
equal numbers of protons and neutrons?
How...
It is the strong nuclear force that holds
the nucleons together, but this is a very
short range force.
The repulsive elect...
More neutrons are needed to hold the
nucleus together (although adding too
many neutrons can also cause
instability).
Ther...
Alpha Decay
An alpha particle is a helium nucleus‑
and is written 4
2He or 4
2α.
It consists of 2 protons and 2
neutrons.
...
The nuclear equation is
A
Z X → A-4
Z-2 Y + 4
2α.
Note that the top numbers
balance on each side of the
equation. So do th...
Beta Decay
Many radioactive nuclides
(radio nuclides) decay by‑
β emission.‑
This is the emission of an
electron from the ...
What happens is this:
one of the neutrons changes into
a proton (which stays in the
nucleus) and an electron (which
is emi...
The nuclear equation is
A
Z X → A
Z+I Y + 0
-1e
Notice again, the top numbers
balance, as do the bottom ones.
A radio nuclide‑ above the
stability line decays by
β emission.‑
Because it loses a neutron and
gains a proton, it moves
d...
Gamma Decay
Gamma emission does not‑
change the structure of the
nucleus, but it does make the
nucleus more stable
because...
Decay chains
A radio nuclide often produces an unstable‑
daughter nuclide.
The daughter will also decay, and the
process w...
When determining the
products of deacy
series, the same
rules apply as in
determining the
products of alpha and
beta, or a...
Half Life
Suppose you have a sample of 100
identical nuclei.
All the nuclei are equally likely to
decay, but you can never...
Does this mean that we can never
know the rate of decay?
No, because for any particular
radio nuclide there is a certain‑
...
Iodine 131 is a radioactive‑
isotope of iodine.
The chart on the next slide
illustrates the decay of a sample
of iodine 13...
To begin with, there are 40 million undecayed nuclei.
8 days later, half of these have disintegrated.
With the number of u...
Definition
The half life of a radioactive‑
isotope is the time taken for half
the nuclei present in any given
sample to de...
Activity and half life‑
In a radioactive sample, the
average number of
disintegrations per second is
called the activity.
...
The graph on the next slide of the
next page shows how, on
average, the activity of a sample
of iodine 131 varies with tim...
Definition 2
The half life of a radioactive‑
isotope is the time taken for the
activity of any given sample to
fall to hal...
Exponential Decay
Any quantity that reduces by the
same fraction in the same period
of time is called an exponential
decay...
Radioactive Decay
Radioactive decay is a
completely random process.
No one can predict when a
particular parent nucleus wi...
Radioactive Decay
We can define a constant for the
decay of a particular isotope,
which is called the half-life.
This is d...
Radioactive Decay
From a nuclear point of view, the
half-life of a radioisotope is the
time it takes half of the atoms
of ...
Radioactive Decay
An example would be the half-life
of tritium (3
H), which is 12.5
years.
For a 100g sample, there will b...
Radioactive Decay
The decay
curve is
exponentia
l.The only
difference
from one
sample to
another is
the value
for the half-
Radioactive Decay
Below is a decay curve for 14
C.
Determine the half-life for 14
C.
Radioactive Decay
The half-life does not indicate
when a particular atom will
decay but how many atoms will
decay in a lar...
Radioactive Decay
If a sample contains N
radioactive nuclei,
we can express the statistical
nature of the decay rate
(-dN/...
Radioactive Decay
in which λ, the
disintegration or decay
constant, has a
characteristic value for
every radionuclide. Thi...
Radioactive Decay
-dN/dt = λN
Collect like terms
dN/N = -λdt
Integrate
ln N = -λt + c
But c = ln N0
So, ln N = -λt + ln N0...
Radioactive Decay
Solving for t½
yields, that is when N =
N0/2
λt1/2 = 0.693
t1/2 = 0.693/ λ
λ
2ln
2
1 =t or
2
1
2ln
t
=λ
Radioactive Decay
The half-life of an isotope can be
determined by graphing the
activity of a radioactive
sample,over a pe...
Radioactive Decay
The graph of activity vs time can
be graphed in other ways
As the normal graph is
exponential it does no...
Radioactive Decay
Radioactive Decay
If we take the natural log of N =
Noe-λt
we get:
ln N = ln No -λt
The slope of the line will
determine t...
Radioactive Decay
The accuracy in determining the
half-life depends on the number
of disintegrations that occur per
unit t...
Radioactive Decay
For very long half-life isotopes
i.e. millions of years
Only a small number of events will
take place ov...
Radioactive Decay
Standard is produced by
reputable organisations
i.e. International Atomic Energy
Agency
Calibrated stand...
Radioactive Decay
With very short half-life isotopes,
the isotope may disintegrate
entirely before it is
measured.Time is ...
EXAMPLE 1
(a) Radium-226 has a half-life of
1622 years. A sample contains
25g of this radium isotope. How
much will be lef...
EXAMPLE 1 SOLUTION
(a) 3244 years is 2 half lives
(2 x 1622)
N= No(1/2)n
= 25 x (1/2)2
= 25 x (1/4)
=6.25
EXAMPLE 1 SOLUTION
(b)The activity of a radioactive
sample is directly proportional
to the number of remaining
atoms of th...
EXAMPLE 2
A Geiger counter is placed near a
source of short lifetime
radioactive atoms, and the
detection count for 30-sec...
EXAMPLE 2
• Interval Count
• 1. 12456
• 2. 7804
• 3. 5150
• 4. 3034
• 5. 2193
• 6. 1278
• 7. 730
EXAMPLE 2 SOLUTION
The data are
plotted on a
graph with
the point
placed at
the end of
the time
interval
since the
count
EXAMPLE 2 SOLUTION
A line of best fit is
drawn through the
points, and the
time is determined
for a count rate of
12 000 i...
EXAMPLE 2 SOLUTION
t(12 000) = 30s
t( 6000) = 72s, so
t1/2
(1) = 42s
t( 3000) = 120s, so
t1/2
(2) = 48s
 The time differen...
EXAMPLE 2 SOLUTION
Since we have two
values, an
average is taken.
t s1 2
42 48
2
45/ =
+
=
Background radiation
• Can you
overdose on
radiation?
https://www.flickr.com/photos/oregonstateuniversity/8528630449
• The Four Forces in Nature by relative strength
Fundamental Interactions
Type Relative
Strength
(2 p in
nucleus)
Field Pa...
An analogy is used to help understand
how a force can be experienced due
to exchange of a particle….
Imagine Harry & Juliu...
Fundamental
Interactions
If they grab the pillow out of the
other’s hand to exchange pillows
They are pulled towards each
other
An attractive
force...
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7.1

  1. 1. Atomic, Nuclear and Particle Physics Topic 7.1 Discrete energy and radioactivity Image from http://www.onlineopinion.com.au/view.asp? article=15900
  2. 2. What is an atom? • Can you explain why you know that matter is made of atoms? • How do you know? • Why is it important? • How do we collect evidence of them? • Why do you need to know about models of atom that we no longer “believe”? TOK
  3. 3. Energy Levels Thomas Melville was the first to study the light emitted by various gases. He used a flame as a heat source, and passed the light emitted through a prism. Melville discovered that the pattern produced by light from heated gases is very different from the continuous rainbow pattern produced when sunlight passes through a prism.
  4. 4. The new type of spectrum consisted of a series of bright lines separated by dark gaps. This spectrum became known as a line spectrum. Melvill also noted the line spectrum produced by a particular gas was always the same.
  5. 5. In other words, the spectrum was characteristic of the type of gas, a kind of "fingerprint" of the element or compound. This was a very important finding as it opened the door to further studies, and ultimately led scientists to a greater understanding of the atom.
  6. 6. Emission Spectra Absorption Spectra What do you notice about these? TOK
  7. 7. Spectra can be categorised as either emission or absorption spectra. An emission spectrum is, as the name suggests, a spectrum of light emitted by an element. It appears as a series of bright lines, with dark gaps between the lines where no light is emitted.
  8. 8. An absorption spectrum is just the opposite, consisting of a bright, continuous spectrum covering the full range of visible colours, with dark lines where the element literally absorbs light. The dark lines on an absorption spectrum will fall in exactly the same position as the bright lines on an emission spectrum for a given element, such as neon or sodium.
  9. 9. Evidence What causes line spectra? You always get line spectra from atoms that have been excited in some way, either by heating or by an electrical discharge. In the atoms, the energy has been given to the electrons, which then release it as light.
  10. 10. Line spectra are caused by changes in the energy of the electrons. Large, complicated atoms like neon give very complex line spectra, so physicists first investigated the line spectrum of the simplest possible atom, hydrogen, which has only one electron.
  11. 11. Planck and Einstein's quantum theory of light gives us the key to understanding the regular patterns in line spectra. The photons in these line spectra have certain energy values only, so the electrons in those atoms can only have certain energy values.
  12. 12. The electron, has the most potential energy when it is on the upper level, or excited state. When the electron is on the lower level, or ground state, it has the least potential energy.
  13. 13. The diagram can show an electron in an excited atom dropping from the excited state to the ground state. This energy jump, or transition, has to be done as one jump. It cannot be done in stages. This transition is the smallest amount of energy that this atom can lose, and is called a quantum (plural = quanta).
  14. 14. The potential energy that the electron has lost is given out as a photon. This energy jump corresponds to a specific frequency (or wavelength) giving a specific line in the line spectrum. E = hf This outlines the evidence for the existance of atomic energy levels.
  15. 15. THE BOHR MODEL OF THE ATOM In 1911 Bohr ignored all the previous descriptions of the electronic structure as they were based on classical physics. This allowed the electron to have any amount of energy. Planck and Einstein used the idea of quanta for the energy carried by light.
  16. 16. THE BOHR MODEL OF THE ATOM Bohr assumed that the energy carried by an electron was also quantized. From this assumption, he formed three postulates (good intelligent guesses) from which he developed a mathematical description.
  17. 17. THE BOHR MODEL OF THE ATOM 0 + - free e- } bound e- e n e r g y le v e ls B o h r a t o m
  18. 18. THE BOHR MODEL OF THE ATOM An electron can be moved to a higher energy level by… 1. INCOMING PHOTON- Must be of exactly the same energy as E2 – E1 2. INCOMING ELECTRON- remaining energy stays with the incoming electron. 3. HEAT- gives the electron vibrational energy.
  19. 19. THE BOHR MODEL OF THE ATOM IONIZATION- energy required to remove an electron from the atom. Example: the ionization energy required to remove an electron from its ground state (K=1) for Hydrogen is 13.6 eV.
  20. 20. THE BOHR MODEL OF THE ATOM Let’s prove this using the following formula… • LYMAN SERIES En-Em = hf (13.6 –0.85)(1.6X10- 19 )=hc/λ λ=9.7X10-8 m (98nm) This is UV Light 0 - 2 - 4 - 6 - 8 - 1 0 - 1 2 - 1 4 2 energy(eV) L y m a n s e r ie s B a lm e r s e r ie s P a s c h e n s e r ie s g r o u n d s ta te 1 s t e x c ite d s ta te n = 3 n = 1 n = 2 n = 4 n = 5 n = ∞ io n iz e d a to m ( e le c tr o n u n b o u n d a n d f r e e to ta k e a n y e n e r g y ) ( K s h e ll) ( L s h e ll) ( M s h e ll) ( N s h e ll) - 1 3 .6 - 3 .4 - 1 .5 1 - 0 .8 5
  21. 21. THE BOHR MODEL OF THE ATOM • BALMER SERIES En-Em = hf (3.4 –0.85)(1.6X10-19 )=hc/λ λ=4.87X10-7 m = 487 nm This is Blue Light. 0 - 2 - 4 - 6 - 8 - 1 0 - 1 2 - 1 4 2 energy(eV) L y m a n s e r ie s B a lm e r s e r ie s P a s c h e n s e r ie s g r o u n d s t a t e 1 s t e x c it e d s t a t e n = 3 n = 1 n = 2 n = 4 n = 5 n = ∞ io n iz e d a t o m ( e le c t r o n u n b o u n d a n d f r e e t o t a k e a n y e n e r g y ) ( K s h e ll) ( L s h e ll) ( M s h e ll) ( N s h e ll) - 1 3 .6 - 3 .4 - 1 .5 1 - 0 .8 5
  22. 22. EXAMPLE 1 Use the first three energy levels for the electron in hydrogen to determine the energy and hence wavelength of the lines in its line emission spectrum. n = 3 n = 2 n = 1- 1 3 .6 e V - 3 .4 e V - 1 .5 1 e V
  23. 23. EXAMPLE 1 SOLUTION From the diagram, the atom can be excited to the first (n = 2) and second (n = 3) excited states. From these, it will return to the ground state emitting a photon. The electron can make the following transitions:
  24. 24. EXAMPLE 1 SOLUTION n = 3 n = 1, Ephoton = E3 - El • = -1.51 - (-13.6) • = 12.09eV   n = 2 n = l, Ephoton = E2 - E1 • = -3.4 - (-13.6) • = 10.2eV
  25. 25. EXAMPLE 1 SOLUTION n = 3 n = 2, Ephoton = E3 - E2 • = -1.51 - (-3.4) • = 1.89 eV n = 3 n = 2 n = 1
  26. 26. EXAMPLE 1 SOLUTION To find the wavelengths of the three photons, use Note: convert eV to J E = ie. = E hf hc hc = λ λ
  27. 27. EXAMPLE 1 SOLUTION n=3 n=l, • = 1.024 x 10 -7 m • = 102 nm (ultraviolet) λ = 6.6 x 10 x 3 x 10 12.09 x 1.6 x 10 -34 -8 -19
  28. 28. EXAMPLE 1 SOLUTION n=2 n=l, λ= • = 1.21 x 10-7 m • = 121nm (ultraviolet) n=3 n=2, λ= = 6.55 X 10-7 m = 655 nm (visible-red) 19- 834 10x1.6x10.2 10x3x10x6.6 − 19- 834 10x1.6x1.89 10x3x10x6.6 −
  29. 29. EXAMPLE 1 SOLUTION Note that we have two Lyman series lines (those ending in the ground state) and one Balmer line (ending in the first excited state). n = 3 n = 2 n = 1
  30. 30. EXAMPLE 1 SOLUTION Those from the Lyman series produce lines in the ultra-violet part of the spectrum while the line in the Balmer series produces a line in the visible part of the spectrum. n = 3 n = 2 n = 1
  31. 31. Nuclear Structure
  32. 32. Mass Number The total number of protons and neutrons in the nucleus is called the mass number (or nucleon number).
  33. 33. Nucleon Protons and neutrons are called nucleons. Each is about 1800 times more massive than an electron, so virtually all of an atom's mass is in its nucleus.
  34. 34. Atomic Number All materials are made from about 100 basic substances called elements. An atom is the smallest `piece' of an element you can have. Each element has a different number of protons in its atoms: it has a different atomic number (sometimes called the proton number). The atomic number also tells you the number of electrons in the atom.
  35. 35. Isotopes Every atom of oxygen has a proton number of 8. That is, it has 8 protons (and so 8 electrons to make it a neutral atom). Most oxygen atoms have a nucleon number of 16. This means that these atoms also have 8 neutrons.This is 16 8O.
  36. 36. Some oxygen atoms have a nucleon number of 17 or 18. 16 8O and 17 8O are both oxygen atoms. They are called isotopes of oxygen. Isotopes are atoms with the same proton number, but different nucleon numbers.
  37. 37. Since the isotopes of an element have the same number, of electrons, they must have the same chemical properties. The atoms have different masses, however, and so their physical properties are different.
  38. 38. Evidence for Neutrons The existence of isotopes is evidence for the existence of neutrons because there is no other way to explain the mass difference of two isotopes of the same element. By definition, two isotopes of the same element must have the same number of protons, which means the mass attributed to those protons must be the same. Therefore, there must be some other particle that accounts for the difference in mass, and that particle is the neutron. TOK
  39. 39. Interactions in the Nucleus Electrons are held in orbit by the force of attraction between opposite charges. Protons and neutrons (nucleons) are bound tightly together in the nucleus by a different kind of force, called the strong, short- range nuclear force. There are also Coulomb interaction between protons. Due to the fact that they are charged particles.
  40. 40. What is radiation? • What does it do? • Where does it come from? • How can we use it? • Can we stop it? • How do we protect ourselves? TOK
  41. 41. Radioactivity In 1896, Henri Becquerel discovered, almost by accident, that uranium can blacken a photographic plate, even in the dark. Uranium emits very energetic radiation it is radioactive.‑
  42. 42. Then Marie and Pierre Curie discovered more radioactive elements including polonium and radium. Scientists soon realised that there were three different types of radiation. These were called alpha (α), beta (β), and gamma (γ) rays from the first three letters of the Greek alphabet.
  43. 43. Alpha, Beta and Gamma
  44. 44. Properties
  45. 45. Properties 2 The diagram on the right shows how the different types are affected by a magnetic field. The alpha beam is a flow of positively (+) charged particles, so it is equivalent to an electric current. It is deflected in a direction given by Fleming's left hand rule the‑ ‑ rule used for working out the direction of the force on a current carrying wire in a‑ magnetic field.
  46. 46. The beta particles are much lighter than the alpha particles and have a negative ( ) charge, so they‑ are deflected more, and in the opposite direction. Being uncharged, the gamma rays are not deflected by the field. Alpha and beta particles are also affected by an electric field in other words, there is a force on‑ them if they pass between oppositely charged plates.
  47. 47. Ionising Properties α particles,‑ β particles and‑ γ ray photons‑ are all very energetic particles. We often measure their energy in electron volts (eV) rather than joules.‑ Typically the kinetic energy of an α particle‑ is about 6 million eV (6 MeV). We know that radiation ionises molecules by `knocking' electrons off them. As it does so, energy is transferred from the radiation to the material. The next diagrams show what happens to an α particle‑
  48. 48. Why do the 3 types of radiation have different penetrations? Since the α-particle is a heavy, relatively slow moving particle‑ with a charge of +2e, it interacts strongly with matter. It produces about 1 x 105 ion pairs per cm of its path in air. After passing through just a few cm of air it has lost its energy.
  49. 49. the β particle‑ is a much lighter particle than the α particle and it‑ travels much faster. Since it spends just a short time in the vicinity of each air molecule and has a charge of only le, it causes less‑ intense ionisation than the α particle.‑ The β particle produces about 1 x 10‑ 3 ion pairs per cm in air, and so it travels about 1 m before it is absorbed.
  50. 50. A γ ray photon‑ interacts weakly with matter because it is uncharged and therefore it is difficult to stop. A γ ray photon often loses all its‑ energy in one event. However, the chance of such an event is small and on average a γ photon‑ travels a long way before it is absorbed.
  51. 51. Stability If you plot the neutron number N against the proton number Z for all the known nuclides, you get the diagram shown here
  52. 52. Can you see that the stable nuclides of the lighter elements have approximately equal numbers of protons and neutrons? However, as Z increases the `stability line' curves upwards. Heavier nuclei need more and more neutrons to be stable. Can we explain why?
  53. 53. It is the strong nuclear force that holds the nucleons together, but this is a very short range force. The repulsive electric force between the protons is a longer range force. So in a large nucleus all the protons repel each other, but each nucleon attracts only its nearest neighbours.
  54. 54. More neutrons are needed to hold the nucleus together (although adding too many neutrons can also cause instability). There is an upper limit to the size of a stable nucleus, because all the nuclides with Z higher than 83 are unstable.
  55. 55. Alpha Decay An alpha particle is a helium nucleus‑ and is written 4 2He or 4 2α. It consists of 2 protons and 2 neutrons. When an unstable nucleus decays by emitting an α particle‑ it loses 4 nucleons and so its nucleon number decreases by 4. Also, since it loses 2 protons, its proton number decreases by 2
  56. 56. The nuclear equation is A Z X → A-4 Z-2 Y + 4 2α. Note that the top numbers balance on each side of the equation. So do the bottom numbers.
  57. 57. Beta Decay Many radioactive nuclides (radio nuclides) decay by‑ β emission.‑ This is the emission of an electron from the nucleus. But there are no electrons in the nucleus!
  58. 58. What happens is this: one of the neutrons changes into a proton (which stays in the nucleus) and an electron (which is emitted as a β particle).‑ This means that the proton number increases by 1, while the total nucleon number remains the same.
  59. 59. The nuclear equation is A Z X → A Z+I Y + 0 -1e Notice again, the top numbers balance, as do the bottom ones.
  60. 60. A radio nuclide‑ above the stability line decays by β emission.‑ Because it loses a neutron and gains a proton, it moves diagonally towards the stability line, as shown on this graph
  61. 61. Gamma Decay Gamma emission does not‑ change the structure of the nucleus, but it does make the nucleus more stable because it reduces the energy of the nucleus.
  62. 62. Decay chains A radio nuclide often produces an unstable‑ daughter nuclide. The daughter will also decay, and the process will continue until finally a stable nuclide is formed. This is called a decay chain or a decay series. Part of one decay chain is shown below
  63. 63. When determining the products of deacy series, the same rules apply as in determining the products of alpha and beta, or artificial transmutation. The only difference is several steps are involved instead of just one.
  64. 64. Half Life Suppose you have a sample of 100 identical nuclei. All the nuclei are equally likely to decay, but you can never predict which individual nucleus will be the next to decay. The decay process is completely random. Also, there is nothing you can do to `persuade' one nucleus to decay at a certain time. The decay process is spontaneous.
  65. 65. Does this mean that we can never know the rate of decay? No, because for any particular radio nuclide there is a certain‑ probability that an individual nucleus will decay. This means that if we start with a large number of identical nuclei we can predict how many will decay in a certain time interval. TOK
  66. 66. Iodine 131 is a radioactive‑ isotope of iodine. The chart on the next slide illustrates the decay of a sample of iodine 131.‑ On average, 1 nucleus disintegrates every second for every 1000 000 nuclei present.
  67. 67. To begin with, there are 40 million undecayed nuclei. 8 days later, half of these have disintegrated. With the number of undecayed nuclei now halved, the number of disintegrations over the next 8 days is also halved. It halves again over the next 8 days... and so on. Iodine 131 has a‑ half life‑ of 8 days.
  68. 68. Definition The half life of a radioactive‑ isotope is the time taken for half the nuclei present in any given sample to decay.
  69. 69. Activity and half life‑ In a radioactive sample, the average number of disintegrations per second is called the activity. The SI unit of activity is the becquerel (Bq). An activity of, say, 100 Bq means that 100 nuclei are disintegrating per second.
  70. 70. The graph on the next slide of the next page shows how, on average, the activity of a sample of iodine 131 varies with time.‑ As the activity is always proportional to the number of undecayed nuclei, it too halves every 8 days. So `half life' has another meaning‑ as well:
  71. 71. Definition 2 The half life of a radioactive‑ isotope is the time taken for the activity of any given sample to fall to half its original value.
  72. 72. Exponential Decay Any quantity that reduces by the same fraction in the same period of time is called an exponential decay curve. The half life can be calculated from decay curves Take several values and the take an average
  73. 73. Radioactive Decay Radioactive decay is a completely random process. No one can predict when a particular parent nucleus will decay into its daughter. Statistics, however, allow us to predict the behaviour of large samples of radioactive isotopes.
  74. 74. Radioactive Decay We can define a constant for the decay of a particular isotope, which is called the half-life. This is defined as the time it takes for the activity of the isotope to fall to half of its previous value.
  75. 75. Radioactive Decay From a nuclear point of view, the half-life of a radioisotope is the time it takes half of the atoms of that isotope in a given sample to decay. The unit for activity, Becquerel (Bq), is the number of decays per second.
  76. 76. Radioactive Decay An example would be the half-life of tritium (3 H), which is 12.5 years. For a 100g sample, there will be half left (50g) after 12.5 years. After 25 years, one quarter (25g) will be left and after 37.5 years there will be one eighth (12.5g)
  77. 77. Radioactive Decay The decay curve is exponentia l.The only difference from one sample to another is the value for the half-
  78. 78. Radioactive Decay Below is a decay curve for 14 C. Determine the half-life for 14 C.
  79. 79. Radioactive Decay The half-life does not indicate when a particular atom will decay but how many atoms will decay in a large sample. Because of this, there will always be a ‘bumpy’ decay for small samples.
  80. 80. Radioactive Decay If a sample contains N radioactive nuclei, we can express the statistical nature of the decay rate (-dN/dt) is proportional to N:
  81. 81. Radioactive Decay in which λ, the disintegration or decay constant, has a characteristic value for every radionuclide. This equation integrates to: No is the number of radioactive nuclei in a sample at t = 0 and N is the number remaining at any subsequent time t. N dt dN λ=− t oeNN λ− = You have to derive this
  82. 82. Radioactive Decay -dN/dt = λN Collect like terms dN/N = -λdt Integrate ln N = -λt + c But c = ln N0 So, ln N = -λt + ln N0 ln N - ln N0 = -λt N/ N0 = e-λt
  83. 83. Radioactive Decay Solving for t½ yields, that is when N = N0/2 λt1/2 = 0.693 t1/2 = 0.693/ λ λ 2ln 2 1 =t or 2 1 2ln t =λ
  84. 84. Radioactive Decay The half-life of an isotope can be determined by graphing the activity of a radioactive sample,over a period of time
  85. 85. Radioactive Decay The graph of activity vs time can be graphed in other ways As the normal graph is exponential it does not lead to a straight line graph Semi logarithmic graph paper can solve this problem
  86. 86. Radioactive Decay
  87. 87. Radioactive Decay If we take the natural log of N = Noe-λt we get: ln N = ln No -λt The slope of the line will determine the decay constant λ
  88. 88. Radioactive Decay The accuracy in determining the half-life depends on the number of disintegrations that occur per unit time. Measuring the number of disintegrations for very long or short half-life isotopes could cause errors.
  89. 89. Radioactive Decay For very long half-life isotopes i.e. millions of years Only a small number of events will take place over the period of a year Specific activity is used Activity of sample is measured against a calibrated standard
  90. 90. Radioactive Decay Standard is produced by reputable organisations i.e. International Atomic Energy Agency Calibrated standard measures the accuracy of the detector making sure it is accurate Specific activity and atomic mass of isotope is then used to calculate the half-life
  91. 91. Radioactive Decay With very short half-life isotopes, the isotope may disintegrate entirely before it is measured.Time is therefore of the essence As most of these isotopes are artificial. Produce them in or near the detector This eliminates or reduces the
  92. 92. EXAMPLE 1 (a) Radium-226 has a half-life of 1622 years. A sample contains 25g of this radium isotope. How much will be left after 3244 years? (b) How many half-lives will it take before the activity of the sample falls to below 1% of its initial activity? How many years is this?
  93. 93. EXAMPLE 1 SOLUTION (a) 3244 years is 2 half lives (2 x 1622) N= No(1/2)n = 25 x (1/2)2 = 25 x (1/4) =6.25
  94. 94. EXAMPLE 1 SOLUTION (b)The activity of a radioactive sample is directly proportional to the number of remaining atoms of the isotope. After t1/2, the activity falls to ½ the initial activity. After 2 t1/2, the activity is ¼. It is not till 7 half-lives have elapsed that the activity is 1/128th of the initial activity. So, 7 x 1622 = 11354 years
  95. 95. EXAMPLE 2 A Geiger counter is placed near a source of short lifetime radioactive atoms, and the detection count for 30-second intervals is determined. Plot the data on a graph, and use it to find the half-life of the isotope.
  96. 96. EXAMPLE 2 • Interval Count • 1. 12456 • 2. 7804 • 3. 5150 • 4. 3034 • 5. 2193 • 6. 1278 • 7. 730
  97. 97. EXAMPLE 2 SOLUTION The data are plotted on a graph with the point placed at the end of the time interval since the count
  98. 98. EXAMPLE 2 SOLUTION A line of best fit is drawn through the points, and the time is determined for a count rate of 12 000 in 30 seconds. Then the time is determined for a count rate of 6000, and 3000.
  99. 99. EXAMPLE 2 SOLUTION t(12 000) = 30s t( 6000) = 72s, so t1/2 (1) = 42s t( 3000) = 120s, so t1/2 (2) = 48s  The time difference should have be the half-life of the sample.
  100. 100. EXAMPLE 2 SOLUTION Since we have two values, an average is taken. t s1 2 42 48 2 45/ = + =
  101. 101. Background radiation • Can you overdose on radiation?
  102. 102. https://www.flickr.com/photos/oregonstateuniversity/8528630449
  103. 103. • The Four Forces in Nature by relative strength Fundamental Interactions Type Relative Strength (2 p in nucleus) Field Particle Strong nuclear 1 Gluons (was mesons) Electromagnetic 10-2 Photon Weak nuclear 10-6 W± and Zo Gravitational 10-38 Graviton (?)
  104. 104. An analogy is used to help understand how a force can be experienced due to exchange of a particle…. Imagine Harry & Julius throwing pillows at each other Each catch results in the child being thrown backwards A repulsive force Fundamental Interactions
  105. 105. Fundamental Interactions
  106. 106. If they grab the pillow out of the other’s hand to exchange pillows They are pulled towards each other An attractive force Fundamental Interactions

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