Transcript ModernPhys.Nuclear

Modern Physics
Thanks to:
Dr. P. Bertrand
Oak Ridge HS
1
Quantum Physics




Physics on a very small (atomic) scale is
“quantized”.
Quantized phenomena are discontinuous and
discrete, and generally very small.
Quantized energy can be throught of an
existing in packets of energy of specific size.
Atoms can absorb and emit quanta of energy,
but the energy intervals are very tiny, and
not all energy levels are “allowed” for a given
atom.
2
Electromagnetic Spectrum
3
Light is a ray


We know from geometric optics that
light behaves as a ray; it travels in a
straight line.
When we study ray optics, we ignore
the nature light, and focus on how it
behaves when it hits a boundary and
reflects or refracts at that boundary.
4
But light is also a wave!


We studied this earlier in the year and
we will use this equation again here.
C=fl



C: 3 x 108 m/s (speed of light in a vacuum)
f: frequency (Hz or s-1)
l: wavelength (m) (distance from crest to
crest)
5
In quantum physics, we focus on
how light behaves as a particle!



Light has a dual nature. In addition to
behaving as a wave, it also behaves as
a particle.
It has energy and momentum, just like
particles do. Particle behavior is
pronounced on a very small level, or at
very high light energies.
A particle of light is called a “photon”.
6
Calculating photon energy



The energy of a photon is calculated
from the frequency of the light.
E = hf = hc / l
because c = f l
E = nhf (for multiple n # of photons)


E: energy (J or eV)
h: Planck’s constant



6.625 x 10-34 J s (SI system)
4.14 x 10-15 eV s (convenient)
f: frequency of light (s-1, Hz)
7
Checkpoint

Which has more energy in its photons,
a very bright, powerful red laser or a
small key-ring red laser?


Neither! They both have the same energy
per photon; the big one has more power.
Which has more energy in its photons,
a red laser of a green laser?

The green one has shorter wavelength and
higher frequency. It has more energy per
photon.
8
Quantum Double-Slit Experiment


https://www.youtube.com/watch?v=fw
XQjRBLwsQ Dr. Quantum
https://www.youtube.com/watch?v=h0
hwuyOmd4k Einstein – History
Channel
9
The “electron volt” (eV)



The electron volt is the most useful unit
on the atomic level.
If a moving electron is stopped by 1 V
of electric potential, we say it has 1
electron volt (or 1 eV) of kinetic energy.
1 eV = 1.602 x 10-19 J
10
Sample Problem
What is the frequency and wavelength of
a photon whose energy is
4.0 x 10-19 J?
E = hf
f = E/h =
c=fl
l = c/f =
11
Sample Problem






The bonding energy of H2 is 104.2 kcal/mol.
Determine the frequency and wavelength of a
photon that could split one atom of H2 into two
separate atoms. (1 kcal = 4l86 J).
E = (104.2 kcal)(4186 J)(
1 mol
)
mol
kcal 6.02x10 23mol’cls
E = 7.24 x 10-19 J = hf
f = 7.24 x 10-19 J/ 6.625 x 10-34Js
f = 1.09 x 1015 Hz
***
12
Atomic Transitions
How many photons are emitted per second
by a He-Ne laser that emits 3.0 mW of
power at a wavelength of 632.8 nm?
P = Etot /t
E = hf  P = n(hf)/t

c=fl
f = c/ l
P = nh(c/ l)
n = (P)(t)( l )
t
(c)(h)
13
Solution
Find total energy in one second from power
P = W/t = E tot / t
E tot = Pt = 3.0 x 10 -3 J
Now see how many photons, n, will produce this energy
E = hf (one photon)
E tot = nhf (for n photons)
E = nhc/ l (since wavelength is given and not
frequency)
3.0x10-3 = n (6.625x10-34Js)(3.0x108m/s)/632.8x10-9m
n = 9.55 x 1016
14
General Info re the Atom

Atoms are composed of


When an atom encounters a photon


Nuclei (protons and neutrons) and
electrons
It usually ignores the photon, but
sometimes absorbs the photon
If an atom absorbs a photon

The photon disappears and gives all its
energy to the atom’s electrons
15
Quantized atomic energy levels
*This graph shows
allowed quantized
energy levels in a
hypothetical atom.
*The more stable states
are those in which the
atom has lower energy.
*The more negative the
state, the more stable
16
the atom.
Quantized atomic energy
levels
The highest allowed
energy is 0.0 eV. Above
this level, the atom loses
its electron, This level is
called the ionization or
dissociation level.
 The lowest allowed energy
is called the ground state.
This is where the atom is
most stable.

States between the highest
and lowest state are called
excited states.

17
Transitions of the
electron within the
atom must occur from
one allowed energy
level to another.
 The atom CANNOT
EXIST between
energy levels.

18
Absorption of photon by atom




When a photon of light is absorbed by
an atom, it causes an increase in the
energy of the atom.
The photon disappears.
The energy of the atom increases by
exactly the amount of energy contained
in the photon.
The photon can be absorbed ONLY if it
can produce an “allowed” energy increase
in the atom.
19
Absorption of photon by atom
When a photon is
absorbed, it
excites the atom
to higher quantum
energy state.
 The increase in
energy of the atom
is given by DE = hf.

Ground state
20
Absorption Spectrum
• When an atom absorbs photons, it removes the
photons from the white light striking the atom,
resulting in dark bands in the spectrum.
• Therefore, a spectrum with dark bands in it is
called an absorption spectrum.
Absorption spectrum
seen through hand
held spectroscope
21
Absorption Spectrum
Absorption
spectra
always involve
atoms going
up in energy
level.
22
Emission of photon by atom




When a photon of light is emitted by an
atom, it causes a decrease in the energy
of the atom.
A photon of light is created.
The energy of the atom decreases by
exactly the amount of energy contained
in the photon that is emitted.
The photon can be emitted ONLY if it
can produce an “allowed” energy
decrease in an excited atom.
23
Emission of photon by atom
• When a photon
Is emitted from
An atom, the
Atom drops to
A Lower
Quantum
Energy state.
• The drop in
energy can be
computed by
DE = -hf.
D E = -hf
24
Emission Spectrum
• When an atom emits photons, it glows! The
photons cause bright lines of light in a spectrum.
• Therefore, a spectrum with bright bands in it is
called an emission spectrum.
25
Emission of photon by atom
26
Sample Problem
27
Solution
28
Photoelectric Effect #1
• Sample Problem
29
Solution
30
Sample Problem
31
Solution
32
Atoms absorbing photons
increase in energy
33
Question
Now, suppose a photon with TOO
MUCH ENERGY encounters an atom?
 If the atom is “photo-active”, a very
interesting and useful phenomenon can
occur…
 This phenomenon is called the
Photoelectric Effect.

34
Photoelectric Effect
E = work function + K
35
Photoelectric Effect
36
Sample Problem
37
Solution
38
Photoelectric Effect #2
• Sample Problem
39
Sample Problem
40
Solution
41
Review of Photoelectric Effect
42
Question
43
The Photoelectric Effect
Experiment
44
Photoelectric Effect
45
Strange results in the
Photoelectric Effect experiment
46
Voltage versus current for different
intensities of light
47
Voltage versus current for
different frequencies of light
48
Experimental determination of the
Kinetic Energy of a photoelectron
49
Graph of Photoelectric Equation
50
Photoelectric simulations
• http://lectureonline.cl.msu.edu/~mmp/kap28/Pho
toEffect/photo.htm
• This is a link for a simulated photoelectric effect
experiment
• Another link:
http://zebu.uoregon.edu/%7Esoper/Light/atomspec
tra.html
•
***
51
Mass of a Photon
• Photon do not have “rest mass”. They
must travel at speed of light and nothing
can travel at the speed of light unless it
has mass = zero.
• A photon has a fixed amount of energy (E
= hf)
• We can calulate how much mass would
have to be destroyed to create a photon
(E=mc2)
52
Sample Problem
• Calculate the mass that must be destroyed
to create a photon of 340 nm light.
Emass = Ephoton
mc2 = hf = hc / l
m=h =
h
cl
cl
m = (6.625 x 10-34 kgm2/s2 x s)
=
(3x 10 8 m/s)(340 x 10 -4 m)
53
Momentum of Photon
p = mv = mc(c/c)=mc2/c = E/c = hf/c = h/l
• Photon do not have “rest mass”, yet they
have momentum! This momentum is
evident in that, given a large number of
photons, they create a pressure?
• A photon’s momentum is calculated by
p = E = hf = h
c
c
l
54
Experimental proof of the
momentum of photons
• Compton scattering
– High-energy photons collided with electrons
exhibit conservation of momentum
– Work Compton problems just like other
conservation of momentum problems - except
the momentum of a photon uses a different
equation.
55
Sample Problem
• What is the momentum of photons that
have a wavelength of 620 nm?
p = h = 6.625 x 10 -34 kgm2/s2 x s
l
620 x 10 -9 m
= __________________kgm/s
kgm/s  mass x velocity
56
Sample Problem
• What is the frequency of a photon that has the
same momentum as an electron with speed of
1200 m/s?
pe=pp
meve = h/l = h/c/f = hf/c
f = mevec/h
f = (9.11x10 -31 kg)(1200m/s)(3x108m/s)
6.625 x 10 -34 kgm2/s2 x s
f = ________________s-1
57
Wave-Particle Duality
• Waves act like particles sometimes and
particles act like waves sometimes.
• This is most easily observed for very
energetic photons (gamma or x-Ray) or
very tiny particles (electrons or nucleons)
58
Particles and Photons both
have Energy
• A moving particle has kinetic energy.
– E = K = ½ mv2
• A particle has most of its energy locked up
in its mass.
– E = mc2
• A photon’s energy is calculated using its
frequency.
– E = hf
59
Particles and Photons both
have Momentum
• For a particle that is moving
– p = mv
• For a photon
– p = h/l
– Check out the units! They are those for
momentum.
60
Particles and Photons both
have Wavelength
• For a photon
–
l = c/f
• For a particle, which has an actual mass,
this equation still works
– l = h/p where p = mv
– This is referred to as the deBroglie
wavelength
61
Experimental proof that particles
have wavelength
• Davisson-Germer Experiment
– Verified that electrons have wave properties
by proving that they diffract
– Electrons were “shone” on a nickel surface
and acted like light by diffraction and
interference
62
Problem
• What is the momentum of photons that
have a wavelength of 620 nm?
63
Sample problem
What is the wavelength of a 2,200 kg
elephant running at 1.2 m/s?
p = h/l  l = h/p = h/mv
l = 6.625 x 10-34 Js
(2200kg)(1.2m/s)
lelephant = 2.51 x 10-37 m
64
Naming a Nucleus
• Physicists
• Mass #
•
• Charge #
Chemists
Electronic Chg on
atom or molecule
# atoms in molec.
65
Most common isotope of carbon
12
Mass Number: protons
plus neutrons
C
6
Element
symbol
Atomic number:
protons
66
Isotopes
• Isotopes have the same atomic number
but different atomic mass.
• Isotopes have similar or identical
chemistry.
• Isotopes have different nuclear behavior.
67
Uranium Isotopes
238
235
U
92
U
92
Low Radioactive Fission
68
Nuclear Particles
Proton
Mass: 1 amu
Charge: +e
Neutron
Mass: 1 amu
Charge: 0
(1 amu = 1/12 mass of Carbon 12 atom)
69
Electrons
Negative
0
e
-1
Positive
0
e
+1
70
Nuclear Reactions
• Nuclear Decay - a spontaneous process in
which an unstable nucleus ejects a particle and
changes to another nucleus.
– Alpha decay
– Beta decay
• Beta Minus
• Positron
• Fission - a nucleus splits into two fragments of
roughly equal size
• Fusion - Two nuclei combine to form a heavier
nucleus.
71
Decay Reactions
• Alpha decay
– A nucleus ejects an alpha particle, which is just a helium
nucleus
• Beta decay
– A nucleus ejects a negative electron
• Positron decay
– A nucleus ejects a positive election
• Simulations: Nuclear Reactions
– https://www.youtube.com/watch?v=50RWvXmQcFk (Bozeman)
72
Nuclear Decay
Radiation and radioactive decay (Bozeman):
https://www.youtube.com/watch?v=oFdR_y
MKOCw
73
Alpha Decay
• This occurs when a helium nucleus is
released.
• This occurs only with very heavy
elements.
74
Beta (b-) Decay
• A beta particle (negative electron) is
released when a nucleus has too many
neutrons for the protons present. A
neutron converts to a proton and electron
leaving a greater number of protons. An
antineutrino is also released.
+
75
Positron (b+) Decay
• Positron decay occurs when a nucleus has
too many protons for the neutrons present.
A proton converts to a neutron. A neutrino
is also released.
76
Neutrino and Anti-Neutrino …
• Proposed to make beta and positron
decay obey conservation of energy.
• Possess energy and spin, but do not
possess mass or charge.
• Do not react easily with matter and are
extremely hard to detect.
77
Neutrino & Antineutrino
Production
Neutrinos are produced in nuclear reactions
in the Sun when:
4protons --> alpha particle + 2p+ +
2neutrinos
Antineutrinos are produced by natural
radioactivity in the Earth by the decay of
238U and 232Th
78
Gamma Radiation, h
This isotope of radium has a
small percentage of
particles that don't have their
full energy; instead the nucleus
is left excited and emits gamma
rays.
79
Complete the reaction and identify
the type of decay:
80
Complete the reaction for the alpha
decay of Thorium-232.
+
81
Fission and Fusion
82
Fission






Occurs when an unstable, heavy nucleus split apart
into two lighter nuclei (new elements).
Can be induced by free neutrons.
Mass is destroyed and energy produced according to
E = mc2.
http://library.thinkquest.org/17940/texts/fission/fissio
n.html
http://www.atomicarchive.com/Movies/index.shtml
www.atomicarchive.com/Movies/Movie4.shtml
83
Neutron-induced fission



Produces a chain reaction
Nuclear power plants operate by
harnessing the energy released in
fission by controlling the chain reaction
of U-235.
Nuclear weapons depend upon the
initiation of an uncontrolled fission
reaction
84

U-235 bombarded with a neutron eads to an
exponential growth of chain reactions.
85


A single U-235 fuel pellet the size of a
fingertip contains as much energy as
17,000 cubic feet of natural gas, 1,780
pounds of coal or 149 gallons of oil.
For more information:
http://www.nei.org/howitworks/nuclear
powerplantfuel/
86

Naturally occurring uranium consists of
three isotopes: uranium-234, uranium235 and uranium-238. Although all
three isotopes are radioactive, only
uranium-235 is a fissionable material
that can be used for nuclear power.
87
Uranium-238, uranium's most common
isotope, can be converted into plutonium239, a fissionable material that can also be
used as a fuel in nuclear reactors. To
produce plutonium-239, atoms of uranium-238 are
exposed to neutrons. Uranium-239 forms when
uranium-238 absorbs a neutron. Uranium-239 has a
half-life of about 23 minutes and decays into
neptunium-239 through beta decay. Neptunium-239
has a half-life of about 2.4 days and decays into
plutonium-239, also through beta decay.
88
Critical Mass


The neutrons released from an atom
that has undergone fission cannot
immediately be absorbed by other
nearby fissionable nuclei until they slow
down to “thermal” levels.
A critical mass is the smallest amount
of fissile material needed for a
sustained nuclear chain reaction.
89
Nuclear Reactors
Nuclear reactors produce electrical energy through
fission.
Advantages: a large amount of energy is produced
without burning fossil fuels or creating greenhouse
gases.
Disadvantage: produces highly radioactive waste.
Simulation:
http://video.google.com/videosearch
?q=nuclear+power+plant+operation&
hl=en&emb=1&aq=f#
http://www.howstuffworks.com/nucle
ar-power.htm
90
91
Fission



Occurs only with very heavy elements since
fissionable nuclei are too large to be stable.
A charge/mass calculation is performed to
balance the nuclear equation.
Mass is destroyed and energy is produced
according to E = mc2.
92
Problem: complete the following reaction
and determine the energy released.
?
93
Fusion





Occurs when 2 light nuclei come together to form a
new nucleus of a new element.
The most energetic of all nuclear reactions.
Produced on the sun.
Fusion of light elements can result in non-radioactive
waste.
Proton-Proton Reaction
www.chemistrydaily.com/chemistry/Nuclear_reaction
94
Fusion



The reaction that powers the sun. It
has not been reliably sustained on earth
in a controlled reaction.
Advantages: tremendous energy
produced and lack of radioactive waste
products.
Disadvantages: too much energy to
control.
95
Mass defect…



How much mass is destroyed when a nucleus
is created from its component parts.
Generally much less than the mass of a
proton or neutron, but it is still significant.
This loss of energy results in the creation of
energy according to E = mc2.
96
Calculating energy released in
nuclear reactions
1. Add up the mass (in atomic mass units, u_
of the reactants. Use your book.
2. Add up the mass ( in amu’s) of the
products.
3. Find the difference between reactant and
product mass. The missing mass has been
converted into energy.
4. Convert mass to kg (1 u = 1.66x10-27 kg)
5. Use E = mc2 to calculate energy released.
97
What is the mass defect of 12C in atomic mass
units? How does this relate to mass in kg and
energy in eV and J?
6 1n + 6 1H 
12C
1amu=1.66x10-27 kg
0
1
E =eV, e =1.6x10-19C
Mass of reactants (6 neutrons, 6 protons)
6(1.008665 amu)+6(1.0078225 amu)
=12.09894
Mass of product : 1(12.000)
=12.00000
Dm = 0.09894
-27
Dm=(0.09894u)(1.66x10 kg/u)
-11J=92MeV
E=1.476x10
-28
Dm=1.4x10 kg
1.6x10-19J/eV
E = Dmc2 = (1.4x10-28kg)(3x108m/s)2
E = 1.476 x 10-11J
98
Problem



When a free proton is fused with a free
neutron to form a deuterium nucleus,
how much energy is released?
Mass of 1 proton = 1.0078225 amu
Mass of 1 neutron = 1.008665 amu
99
Mass on the left:
1.008665 +1.0078225 = 2.0164875u
On the right:
2.000
Mass defect:
0.0164875 u
100



Radioactive Decay of Bismuth-210
(T½ = 5 days)
Translation: “The half life of Bismuth-210
is 5 days.”
The half life for bismuth
is 5 days.
At the end of 5 days
there is 50 g remaining
After 10 days 25 g
After 15 days 12.5 g
What is happening to the
radioactive bismuth?
Radioactive Decay of Bismuth-210 (T ½ = 5 days)
Half Life Problem
Tritium (H-3) has a half life of 12.3 yr.
How much of a 1.0 g sample will remain
after 24.6 yr?
24.6yr 1 h.l. = 2 h.l.
12.3 yr
Sample = 1.0 g = 0.25 g remaining
2 xh.l.
2 2h.l.
104
105