Download Topic 7.1-Discrete energy and radioactivity

2/6/17
The Atom
The earliest references to the concept of
atoms date back to ancient India in the 6th
century BCE.
7. Atomic and
Nuclear Physics
Chapter 7.1 The Atom
The Atom
A replica of Lavoisier's laboratory at
the Deutsches Museum in Munich,
Germany. The large lens in the center
of the picture was used to focus
sunlight in order to ignite samples
during combustion studies.
•  In 1803, English instructor and natural philosopher John
Dalton proposed that each element consists of atoms of a
single, unique type, and that these atoms can join together to
form chemical compounds.
Robert Boyle (1627-1691)
• Dalton used the concept of atoms to
explain why elements always react in a
ratio of small whole numbers - the law of
multiple proportions - and why certain
gases dissolve better in water than others.
Antoine Lavoisier
(1743-1794)
The Atom
John Dalton (1627-1691)
The Atom-*KNOW THIS EXPERIMENT*
•  In 1897, he physicist J. J. Thomson, through
his work on cathode rays, discovered the
electron and its subatomic nature, which
destroyed the concept of atoms as being
indivisible units.
•  Thomson believed that the electrons were
distributed throughout the atom, with their
charge balanced by the presence of a uniform
sea of positive charge (the plum pudding
model).
Although the term initially referred not only to
matter but also to spiritual elements, it was
later adopted in when modern Science started
to develop.
The Atom
•  In 1661, natural philosopher Robert Boyle
suggested that matter was composed of various
combinations of different "corpuscles" or atoms,
rather than the classical elements of air, earth,
fire and water.
•  In 1789 the term element was defined by the
French nobleman and scientific researcher
Antoine Lavoisier to mean basic substances
that could not be further broken down by the
methods of chemistry.
In approximately 450 BCE, Democritus coined
the term átomos (Greek: ἄτοµος), which
means "uncuttable" or "the smallest indivisible
particle of matter", i.e., something that cannot
be divided further.
J. J. Thomson
•  However, in 1909, Geiger and Marsden, two
researchers under the direction of physicist
Ernest Rutherford, bombarded a sheet of gold
foil with helium ions and discovered that a small
percentage were deflected through much larger
angles than was predicted using Thomson's
proposal.
Ernest Rutherford
(1856-1940)
(1871-1937)
Hans Geiger
Ernest Marsden
(1882-1945)
(1889-1970)
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The Atom-*KNOW THIS EXPERIMENT*
•  Rutherford interpreted the gold
foil experiment as suggesting
that the positive charge of an
atom and most of its mass was
concentrated in a nucleus at the
centre of the atom (the
Rutherford model), with the
electrons orbiting it like planets
around a sun.
Rutherford s (or Geiger-Marsden) gold foil experiment
à Expected results:
alpha particles passing
through the plum
pudding model of the
atom undisturbed.
à Observed results: a
small portion of the
particles were
deflected, indicating a
small, concentrated
positive charge.
• Positively charged helium ions
passing close to this dense
nucleus would then be deflected
away at much sharper angles
The Atom
•  Most of the α-particles passed straight through the foil, but to
Rutherford s surprise a few were scattered back towards the
source.
•  Rutherford said that this was rather like firing a gun at tissue
paper and finding that some bullets bounce back towards you!
Consequences of the Rutherford s experiment
•  All of an atom's positive charge and most of its mass is
concentrated in a tiny core. Rutherford called this the nucleus.
•  The electrons surround the nucleus, but they are at relatively
large distances from it.
•  The atom is mainly empty space!
Relative size of the nucleus and electric cloud
Rutherford s model of the atom
•  Can we use Rutherford s model of the atom to explain the
α-particle scattering?
•  The concentrated positive charge produces an electric field
which is very strong close to the nucleus.
•  The closer the path of the α-particle to the nucleus, the
greater the electrostatic repulsion and the greater the
deflection.
•  Most α-particles are hardly deflected because they are far
away from the nucleus and the field is too weak to repel them
much.
•  The electrons do not deflect the α-particles because the effect
of their negative charge is spread thinly throughout the atom.
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Rutherford s model of the atom
Rutherford s model of the atom
•  Using this model Rutherford calculated that the diameter of
the gold nucleus could not be larger than 10-15 m.
•  Other experiments confirmed the existence of a nucleus
inside the atom – a small, massive object carrying the
positive charge of the atom.
•  The force that would keep the electrons in orbit was the
electrical force between electrons and the positive nuclear
charge – Coulomb s force.
•  According to the electromagnetic theory an accelerated
charge would radiate electromagnetic waves and thus lose
energy.
•  The electrons move in circular paths around the nucleus.
But if they radiate and lose energy, then they would fall
towards the nucleus.
•  because of this, Rutherford s model cannot explain way
matter is stable, i.e., why atoms exist.
The Bohr model
Can you see any problems here?
Bohr s model of the atom
Bohr s postulates
•  The first attempt to solve the problem
with Rutherford s model came from
Niels Bohr, a Danish physicist, in
1911.
•  By examining the H atom, Bohr realized that the electron
could exist in certain specific states of definite energy (energy
levels) without radiating energy, if a certain condition was met
by the orbit radius.
•  Bohr revised Rutherford's model by
suggesting that the electrons were
confined into clearly defined orbits,
and could jump between these, but
could not freely spiral inward or
outward in intermediate states.
•  The electron energy is thus discrete and not continuous.
Niels Bohr (1885-1962)
•  An electron must absorb or emit
specific amounts of energy to
transition between these fixed orbits.
Energy levels - evidence
•  Thomas Melvill 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.
•  An electron can only lose energy when
it makes a transition from one state to
another of lower energy. The emitted
energy is then the difference of energy
between the initial and final states.
•  The evidence for this is the absorption
and emission spectra.
Emission spectra
Individual atoms, free of the strong interactions that are present
in a solid, emit only certain specific wavelengths that are unique
to those atoms.
•  Melvill 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.
•  The new type of spectrum consisted of a series of bright
lines separated by dark gaps.
Emission spectrum of iron
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Energy levels - evidence
•  This spectrum became known as a line spectrum.
•  Melvill also noted the line spectrum produced by a particular
gas was always the same.
Emission and absorption spectra
n 
n 
• In other words, the spectrum was characteristic of the type
of gas, a kind of "fingerprint" of the element or compound.
n 
•  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.
n 
n 
Emission and absorption spectra for the same gas
Spectra can be categorized 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.
An absorption spectrum is just the opposite, consisting of a
bright, continuous spectrum covering the full range of visible
colors, 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.
Line spectra
What causes line spectra?
n 
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Line spectra
n 
Planck and Einstein's quantum theory of light gives us the
key to understanding the regular patterns in line spectra.
n 
The photons in these line spectra have certain energy
values only, so the electrons in those atoms can only have
certain energy values.
n This
energy level
diagram shows a very
simple case. It is for an
atom in which there are
only two possible energy
levels:
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.
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.
Line spectra
n 
The electron, shown by the blue
dot, has the most potential energy
when it is on the upper level, or
excited state.
n 
When the electron is on the lower
level, or ground state, it has the
least potential energy.
n The
diagram shows an electron in an excited atom dropping
from the excited state to the ground state.
n This
energy jump, or transition, has to be done as one jump.
It cannot be done in stages.
n This
transition is the smallest amount of energy that this atom
can lose, and is called a quantum (plural = quanta).
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Line spectra
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n 
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The potential energy that the electron has lost is given out as
a photon (particle of light).
This energy jump corresponds to a specific frequency (or
wavelength) giving a specific line in the line spectrum.
This outlines the evidence for the existence of atomic energy
levels.
Calculating Energy
n  Energy
= Planck’s Constant x frequency
E = hf
n  h=6.63
x 10-34 Js
Hydrogen atom energy
levels
Quantum
physics provides the tools to compute the values of
Rearranged…
E1, E2, E3, etc…The results are:
5
4
n  The
databook also gives this equation
solving for λ:
c
c
à f =
à E = h c à λ = h
λ
E
λ
c = fλ
λ =h
c
E
3
2
1
En = -13.6 / n2
Energy Level
Energy En (eV)
1
-13.6
2
-3.4
3
-1.51
4
-0.85
5
-0.54
These results DO DEPEND ON THE TYPE OF ATOM OR MOLECULE
So, the difference in energy between the 3rd and 1st quantum state is:
Ediff = E3 – E1 = -1.51 – (-13.6) = 12.09 (eV)
When this 3à 1 atomic transition occurs, this energy is released
in the form of electromagnetic energy.
Example 4
In the preceding example, what is the frequency, wavelength of the
emitted photon, and in what part of the EM spectrum is it in?
E = 12.1 [eV]. First convert this to [J].
⎛ 1.6x10-19 [J] ⎞
−18
12.1 [eV] ⎜
⎟ = 1.94 x10 [J]
⎝ 1 [eV] ⎠
λ =h
Nuclear Structure
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c
3.00x10
= (6.63x10−34 )
= 1.0x10−7 m
E
1.94x10−18
= 100nm
This corresponds to UV rays!
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Atomic structure
Mass number and atomic number
Electrons (negative particles) - e
A – Mass number
Protons (positive particles) - p
Neutrons (uncharged particles) - n
Z – Atomic number
A
Z
X
Element X
Mass number = no. of protons + no. neutrons
Particle
Relative Mass
Charge
Location
Proton
1
+1
Nucleus
Neutron
1
0
Nucleus
Electron
1/1800
-1
Electric cloud
= no. of nucleons
A=p+n
Atomic number = no. of protons
Z=p
Atoms have no charge. So, no. electrons = no. protons
e=p
Elements
n 
All materials are made from about 100 basic
substances called elements.
n 
An atom is the smallest piece of an element
you can have.
n 
Each element has a different number of protons
in its atoms:
¨  it
has a different atomic number (sometimes called
the proton number).
atomic number also tells you the number of
electrons in the atom.
¨  The
Isotopes
Isotopes
Isotopes are atoms that have the same number of protons but
different number of neutrons.
Hydrogen
1
1
H
1 proton
0 neutrons
Deuterium
2
1
H
1 proton
1 neutron
Hydrogen
1
1
Tritium
3
1
H
n 
1 proton
2 neutrons
n 
H
Deuterium
2
1
H
Tritium
3
1
H
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.
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Evidence for neutrons
Interactions in the nucleus
n 
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.
n 
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.
n 
Therefore, there must be some other particle that
accounts for the difference in mass, and that particle is the
neutron.
n 
Electrons are held in orbit by the force of attraction between
opposite charges.
n 
Protons and neutrons (nucleons) are bound tightly together
in the nucleus by a different kind of force, called the
strong, short-range nuclear force.
n 
It is this force that prevents the protons from repelling each
other and breaking the nucleus apart.
n 
There are also Coulomb interaction between protons due
to the fact that they are charged particles.
Radioactivity
7. Atomic and
Nuclear Physics
n 
In 1896, Henri Becquerel discovered, almost by accident, that
uranium can blacken a photographic plate, even in the dark.
n 
Uranium emits very energetic radiation - it is radioactive.
Chapter 7.2 Radioactivity
Henri Becquerel (1852-1908)
In 1903, he shared the Nobel Prize in Physics with
Pierre and Marie Curie "in recognition of the
extraordinary services he has rendered by his
discovery of spontaneous radioactivity".
Radioactivity
n 
Then Marie and Pierre Curie
discovered more radioactive
elements including polonium and
radium.
n 
Scientists soon realized that there
were three different types of
radiation.
n 
Image of Becquerel's photographic plate
which has been fogged by exposure to
radiation from a uranium salt.
Properties of Alpha, Beta and Gamma Radiation
Marie Curie (1867-1934)
These were called alpha (α), beta
(β), and gamma (γ) rays from the
first three letters of the Greek
alphabet.
Pierre Curie (1859-1906)
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Properties of Alpha, Beta and Gamma Radiation
The diagram shows how the different types are affected by a
magnetic field.
n 
n 
The alpha beam is a flow of
positively (+) charged
particles, so it is equivalent
to an electric current.
n 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.
n 
n 
It is deflected in a direction
given by the Right Hand
Rule. (you know…from
earlier)
Ionizing Properties
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.
Ionising Properties
n 
α -particles, β -particles and γ -ray photons are all very
energetic particles.
n 
We often measure their energy in electron-volts (eV)
rather than joules. (1 Joule = 6.24 x 1018 eV)
n 
Typically the kinetic energy of an α -particle is about 6
million eV (6 MeV).
n 
We know that radiation ionizes molecules by `knocking'
electrons off them.
n 
As it does so, energy is transferred from the radiation to
the material.
n 
The next diagrams show what happens to an α-particle
Penetrating power of alpha radiation.
n 
Properties of Alpha, Beta and Gamma Radiation
Since the α-particle is a heavy, relatively
slow-moving particle with a charge of +2e, it
interacts strongly with matter.
105
n 
It produces about 1 x
path in air.
n 
After passing through just a few cm of air it has lost
its energy.
Penetrating power of beta radiation.
n 
The β-particle is a much lighter particle than
the α -particle and it travels much faster.
n 
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 ionization than the α
-particle.
n 
The β -particle produces about 1 x 103 ion pairs
per cm in air, and so it travels about 1 m before
it is absorbed.
ion pairs per cm of its
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Penetrating power of gamma radiation.
n 
A γ-ray photon interacts weakly with matter because it
is uncharged and therefore it is difficult to stop.
n 
A γ -ray photon often loses all its energy in one event.
n 
However, the chance of such an event is small and on
average a γ -photon travels a long way before it is
absorbed.
Alpha, Beta and Gamma Radiation
Detection of alpha radiation.
Geiger-Muller (GM) tube
n  This can be used to detect alpha, beta, and gamma
radiation.
Geiger-Muller (GM) tube
The `window' at the end is thin enough for alpha particles to
pass through.
If an alpha particle enters the tube, it ionizes the gas inside.
This sets off a high-voltage spark across the gas and a
pulse of current in the circuit.
A beta particle or burst of gamma radiation has the same
effect.
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Ionisation Chamber
n 
n 
The ionization chamber is another detector which uses the
ionizing power of radiation.
The chamber contains fixed electrodes, which attract
electrons and ions produced by the passage through the
chamber of high-speed particles or rays.
n When
the electrodes
detect ions or electrons,
a circuit is activated and
a pulse is sent to a
recording device such
as a light.
Cloud and Bubble Chamber
n 
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n 
n 
n 
n 
Have you looked at the sky and seen a cloud trail behind a high flying
aircraft?
Water vapor in the air condenses on the ionized exhaust gases from the
engine to form droplets that reveal the path of the plane.
A cloud chamber produces a similar effect using alcohol vapor.
Radiation from a radioactive source ionises the cold air inside the
chamber.
Alcohol condenses on the ions of air to form a trail of tiny white droplets
along the path of the radiation.
The diagrams below show some typical tracks
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Cloud and Bubble Chamber
Stability
n 
The α-radiation produces dense straight tracks
showing intense ionization.
n 
Notice that all the tracks are similar in length.
n 
The high-energy β-ray tracks are thinner and less
intense.
n 
The tracks vary in length and most of the tracks
are much longer than the α -particle tracks.
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The γ-rays do not produce continuous tracks.
n 
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A bubble chamber also shows the tracks of
ionizing radiation. The radiation leaves a trail of
vapor bubbles in a liquid (often liquid hydrogen).
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n 
If you plot the neutron number
N against the proton number Z
for all the known nuclides, you
get the diagram shown here
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?
A plot of neutron number versus proton
number is also called Segre plot.
Stability
n 
It is the strong nuclear force that holds the nucleons
together, but this is a very short range force.
n 
The repulsive electric force between the protons is a longer
range force.
n 
So in a large nucleus all the protons repel each other, but
each nucleon attracts only its nearest neighbors.
n 
More neutrons are needed to hold the nucleus together
(although adding too many neutrons can also cause
instability).
n 
There is an upper limit to the size of a stable nucleus,
because all the nuclides with Z > 83 are unstable.
Radioactive decay
equations
Alpha decay
Beta decay
4
2
He or 24α
n 
An alpha-particle is a helium nucleus and is written
n 
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
The nuclear equation is
n 
n 
n 
n 
A
Z
X → ZA−−42Y + 24α
n 
n 
n 
Many radioactive nuclides decay by β-emission.
This is the emission of an electron from the nucleus.
But there are no electrons in the nucleus!
n What
happens is that one of the neutrons changes into a
proton (which stays in the nucleus) and an electron (which is
emitted as a β-particle).
n This means that the proton number increases by 1, while
the total nucleon number remains the same.
n The nuclear equation is
A
Z
Note that the top numbers balance on each side of the
equation. So do the bottom numbers.
A
X→Z+1
Y+ −10e + ν
Notice again, the top numbers balance, as do the bottom ones.
€
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The (anti)neutrino
The (anti)Neutrino
n  While
n  The
a nuclear equation balances, energy
and momentum are not conserved, giving
reason for another particle – the neutrino
(or the antineutrino).
n  Basically, the momentum and energy
escape in a tiny particle.
n  Neutrino = Italian - little neutral one (oh,
cute…)
antineutrino accompanies the
electron, in beta decay. ( ν )
n  The Neutrino accompanies the positron, in
beta decay. (ν )
n  In nuclear physics, the prefix “anti-” refers
to an anti particle,
that has some opposite
€
characteristic from it’s pair.
€
Beta decay
The (anti)Neutrino
n  Neutrino
has no electric charge
n  Was thought of to have no mass, but more
recent experiments suggest there may be
a minimal mass (smaller than an electron!)
n  Interacts weakly with matter, and is
incredibly difficult to detect.
n  (I know…sounds made up, huh?)
Decay chains
n 
n 
n 
n 
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
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.
n 
n 
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.
n 
Decay chains
n 
When determining the
products of decay series, the
same rules apply as in
determining the products of
alpha and beta, or artificial
transmutation.
n 
The only difference is
several steps are involved
instead of just one.
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Half-life
n 
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n 
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n 
n 
n 
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.
Half-life
n 
Iodine-131 is a radioactive isotope of iodine.
n 
The chart illustrates the decay of a sample of iodine-131.
n 
On average, 1 nucleus disintegrates every second for every
1000 000 nuclei present.
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.
Half-life
n 
The half-life of a radioactive isotope is the time
taken for half the nuclei present in any given
sample to decay.
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.
Activity and Half-life
n 
n 
n 
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.
Activity and Half-life
n So
`half-life' has another meaning as well:
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.
n The
graph shows how,
on average, the activity
of a sample of
iodine-131 varies with
time.
n As the activity is
always proportional to
the number of
undecayed nuclei, it too
halves every 8 days.
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Exponential Decay
n 
n 
n 
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 then take an average
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