Nuclear Physics - Weebly
Transcript of Nuclear Physics - Weebly
![Page 2: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/2.jpg)
“Creating a new theory is not like tearing down
an old barn and erecting a skyscraper in its
place. It is rather like climbing a mountain,
gaining new and wider views, discovering
unexpected connections between our starting
point and its rich environment. But the point
from which we started out still exists and can
be seen, although it appears smaller and forms
a tiny part of our broad view gained by the
mastery of the obstacles on our adventurous
way up.”
![Page 3: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/3.jpg)
Uncuttable?
![Page 4: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/4.jpg)
The Atom
• Thompson proved in 1897 that cathode rays
were particles from inside the “a-tomos” or
“un-cuttable” atom
• Nagaoka pictured a planetary
model for the atom, with
electrons around a central mass
![Page 5: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/5.jpg)
Plum Pudding
• Thompson instead supported Lord Kelvin’s
suggestion that electrons were embedded in
a positively charged “pudding”
• Rutherford showed Nagaoka was
correct by probing the atom with
alpha particles
![Page 6: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/6.jpg)
Geiger-Marsden experiment
• Rutherford’s results
showed the atom is
mostly empty space,
with a very dense
nucleus
• To see why, try firing
pennies at water “pudding”
then 50g “nuclei” spaced out
on your table
![Page 7: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/7.jpg)
Data table for 50 “shots”
Model
# alpha
particles
Straight
Through
Slight
Deflection
Bounce
Back
Plum
pudding IIII II
Solar
system
![Page 8: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/8.jpg)
Ex 1: Use the closest approach for
8.2 MeV alpha particles to a gold
nucleus (to estimate outer limit of
radius of nuclei)
kQq
r
kQqEp
mmr 1414 10108.2
)196.1(62.8
196.12)196.179(99
EE
EEEr
E
kQqr
![Page 9: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/9.jpg)
Compare to theoretical radius R:
31
0 ARR
Where R0 is the fermi radius, and A is
the atomic mass number:
3
115 1102.1 mR m15102.1
Ex: find the radius of a U-238 nucleus
3
115 238102.1 mR m15104.7
![Page 10: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/10.jpg)
We can also use diffraction to find D
Ex: A beam of 80.0 MeV neutrons are diffracted upon passing
through a thin lead foil. The first minimum in the diffraction pattern
is measured at 12.6. Estimate the diameter of the lead nucleus.
SOLUTION: Use = h / p and m = 1.6710 -27 kg.
EK = (80.0106 eV)(1.6010 -19 J / eV) = 1.2810 -11 J.
Since EK = p2/ (2m) we see that
p2 = 2mEK = 21.6710 -271.2810 -11 = 4.27510-38.
Then p = 2.06810-19 Ns so that
= h / p = 6.6310-34 / 2.06810 -19 = 3.20710-15 m.
D = / sin = 3.20710-15/ sin 12.6
= 1.4710 -14 m.
D
sin
![Page 11: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/11.jpg)
The Bohr Atom
• Nils Bohr demonstrated the electrons in an
atom are confined to particular energy
levels.
• He called these levels “orbitals”
• Absorbing or emitting energy (a photon)
causes the electron to jump between levels
![Page 12: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/12.jpg)
Bohr’s postulates
• Radiation is only emitted when the atom
(electron) makes a transition
from a higher to a lower energy state
• The difference in energy between the two
states, ΔE = hf
• The angular momentum of the electron is
quantized in units of h/2π (mvr=h/2π)
![Page 13: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/13.jpg)
Physics Dog Ponders:
“What’s in the box?”
![Page 14: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/14.jpg)
Electron in a box
• For energy level n in a hydrogen atom, where L
is the length of the box, aka orbital
circumference, me is the mass of the electron
2
22
8 Lm
hnE
e
k
![Page 15: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/15.jpg)
Limitations?
• This model
gives confusing
spacing of
energy levels.
![Page 16: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/16.jpg)
• The Bohr does provide an explanation
for the spectrum of EM radiation
emitted from an excited atom
• It doesn’t explain the relative intensity
of spectral lines
![Page 17: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/17.jpg)
• Ex: find the wavelength of a photon absorbed
for an n=1 to n=2 jump
12 EEE
)6.13(4.3 eVeVE
eVE 2.10
![Page 18: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/18.jpg)
• Ex: find the wavelength of a photon absorbed
for an n=1 to n=2 jump
hfCeVE 19106.12.10
E
hc
f
c
J
smsJ18
1834
106.1
1000.31063.6
m7102.1
![Page 19: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/19.jpg)
![Page 20: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/20.jpg)
Spectrum activity
• Sketch the spectrum for:
• Incandescent light
• Fluorescent light
• LED light
• Nitrogen
• Neon
• Water
![Page 21: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/21.jpg)
![Page 22: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/22.jpg)
Use these wavelengths to find n=3
given n=2 corresponds to -3.4 eV
hcE
m
smsJE
9
1834
10656
1000.31063.6
JE 191003.3 eV9.1 eVE 5.19.14.33
![Page 23: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/23.jpg)
Einstein Einstein described light as a stream of particles called
“photons,” each with an energy defined by their
frequency. Photoelectric effect shows:
hfE
• Ex 1: Find the energy of a radio photon
from NL 610 AM (610 kHz)
HzJshfE 534 101.61063.6
JE 28100.4 neV5.2
![Page 24: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/24.jpg)
• Physics Dog wants you to
find the energy of an
Ultraviolet ray photon with
frequency 5 x 1017 Hz
HzJshfE 1734 100.51063.6
JE 16103.3 keV1.2
![Page 25: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/25.jpg)
Find the minimum frequency
for pair production
Creation of matter?
hfE hfmc 2
h
mcf
2
Hz20105.2
![Page 26: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/26.jpg)
Photoelectric effect
• Photons above
threshold frequency
cause electrons to be
emitted from metal
plate
• Stopping potential
allows us to measure
kinetic energy of
electrons
![Page 27: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/27.jpg)
Work Function
hfEmax
• Maximum kinetic energy of photoelectron
depends on the work function of the metal ϕ
![Page 28: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/28.jpg)
![Page 29: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/29.jpg)
Ex: #1 p. 231
eVE 6.0max
JE 20
max 106.9
fc
cf
9
8
10422
1000.3
Hzf 141011.7
![Page 30: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/30.jpg)
Ex: #1 p. 231
hfEmax maxEhf
201434 106.91011.71063.6
J191075.3
hfJs
J34
19
1063.6
1075.3
hf
Hzf 14107.5
![Page 31: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/31.jpg)
Stopping Potential
eVhfhf 0
• Ex: The quantum nature of radiation
![Page 32: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/32.jpg)
![Page 33: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/33.jpg)
de Broglie
• de Broglie explained Bohr’s model by
describing the electron as a standing wave
• Only waves that have an even number of
wavelengths are allowed
• Schroedinger took this further to describe
the electron’s location as a wave equation
![Page 34: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/34.jpg)
de Broglie
• Ex: find your wavelength!
p
h
smkg
Js
10105
1063.6 34
mm 3637 10103.6
hp
![Page 35: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/35.jpg)
de Broglie
• Ex: find the wavelength of an electron
moving at 0.5c
p
h
smkg
Js831
34
105.11011.9
1063.6
m12109.4
hp
![Page 36: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/36.jpg)
P. 232 #5-8
P. 235 #9-10
![Page 37: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/37.jpg)
Davisson-Germer Experiment
![Page 39: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/39.jpg)
Davisson-Germer
• Experiment to find which of the following
affect electron diffraction angles:
– Velocity
– Atom Separation
– Atom Radius
When you are finished, do #19 p. 244
Davison Germer Example
![Page 40: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/40.jpg)
What part of
Don’t you understand?
![Page 41: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/41.jpg)
Schrodinger’s model
• Electrons are like a wave with
only certain wavelengths
allowed
• The position is undefined, but a
wave function ψ determines the
probability of locating it
![Page 42: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/42.jpg)
![Page 44: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/44.jpg)
![Page 45: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/45.jpg)
![Page 46: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/46.jpg)
Ok, but what does an atom “really”
look like?
![Page 47: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/47.jpg)
Quantum Mechanics
• Quantum theory restricts predictions about
the atomic world to probabilities
• Einstein and Bohr had many debates about
this limitation “God does not play dice
with the universe” “Stop telling God
what to do”
![Page 48: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/48.jpg)
P. 239 #11a
Given E=1000N/C find v
qvBqE
B
Ev
1.0
1000
110 skm
#11b find m (in unified amu)
r
vmqvB
2
v
rqBm
u
kg26106.9
um 5.57
![Page 50: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/50.jpg)
Uncertainty principle
• Where Δx is the uncertainty in the
position and Δp is the uncertainty
in the momentum
4
hpx
![Page 51: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/51.jpg)
Ex 1a: find the uncertainty in momentum
• An electron passes through a thin
slit of width Δx = 23μm
4
hpx
x
hp
4
m
sJp
6
34
10234
1063.6
1301029.2 smkgp
![Page 52: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/52.jpg)
Ex 1b: what direction is the uncertainty in
momentum, relative to the original
direction of the electron beam?
• Perpendicular to beam direction
![Page 53: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/53.jpg)
Uncertainty principle
• Where ΔE is the uncertainty in the
change in energy and Δt is the
uncertainty in the time that energy
change occured
4
htE
![Page 55: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/55.jpg)
![Page 56: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/56.jpg)
Isotopes
• Elements have a characteristic number of
protons,
– e.g. Hydrogen always has one proton
• They may have different numbers of
neutrons
• Neutrons help to glue together the nucleus
of mutually repulsive protons
![Page 57: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/57.jpg)
Radioactivity
• Marie and Pierre Curie discovered that
some isotopes are unstable: they
spontaneously decay and give off radiation
![Page 58: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/58.jpg)
What are the effects of radiation?
![Page 59: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/59.jpg)
Up and
Atom!
![Page 60: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/60.jpg)
You wouldn’t like me when I’m
angry...
![Page 61: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/61.jpg)
Radiation
• Radiation from the nucleus comes in three flavors:
– (Alpha): massive, “slow”, blocked by paper. He2+
– (Beta): fast, low mass, blocked by >10 sheets of Al
foil. e-
– (Gamma): high energy E-M radiation AKA “light”.
Gamma ray photon. Blocked by thick lead
![Page 62: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/62.jpg)
ThU
Nuclear equations
• Balance charge, then mass
• Ex: write the equation for the alpha decay of
U-238
238
92 4
2
234
90
• Nuclear energy levels are quantized, so the
alpha particles typically have a kinetic
energy of 5 or 8 MeV. Also, we often get
gamma radiation following alpha
![Page 63: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/63.jpg)
![Page 64: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/64.jpg)
NC
• Ex: write the equation for the beta decay of
C-14
14
6
0
-1 14
7
• Beta energy levels are also quantized, but we
don’t see discrete beta energies, since the
antineutrino carries away some of the energy
![Page 65: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/65.jpg)
eNeNa
• Ex: write the equation for the beta+ decay of
Na-22
22
11 0
1
22
10
![Page 66: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/66.jpg)
ePaTh
• Ex: write the equation for the beta decay of
Th-231
231
90 0
-1
231
91
![Page 67: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/67.jpg)
UPu
• Ex: write the equation for the alpha decay of
Pu-239 and find the energy released in MeV
239
94 4
2
235
92
• Pu-239=239.052156
• U-235=235.043923
• Alpha particle = 4.002602
• Mass defect = 239.052156-235.043923-4.002602
• = 0.005631*931.5MeV
• =5.24MeV
![Page 68: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/68.jpg)
Up to P. 250 #23
![Page 69: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/69.jpg)
Ex: #18 p. 235
• U-233 has 92 protons, 141 neutrons
• 92(1.007276u)+141(1.008665u)=234.9u
• 234.9u-233.0=1.9u
• 1.9u(931.5MeV)=1.77GeV
• 1.77 GeV/233 nucleons=7.6MeV per nucleon
![Page 70: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/70.jpg)
How many particles?
![Page 71: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/71.jpg)
Why so many particles?
• Could there be another underlying
fundamental structure?
![Page 72: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/72.jpg)
Standard Model. *flavor?
![Page 73: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/73.jpg)
![Page 74: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/74.jpg)
![Page 75: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/75.jpg)
![Page 76: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/76.jpg)
![Page 77: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/77.jpg)
![Page 78: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/78.jpg)
Activate the Radioactivity Activity
• Team alpha, beta and gamma
• Design a procedure to test the penetrating
power of alpha, beta, and gamma radiation
• Record your results
![Page 79: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/79.jpg)
![Page 80: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/80.jpg)
TOK connection: which is the
best model?
![Page 81: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/81.jpg)
Radioactivity
• When a radioactive isotope decays, the
amount remaining can be described by an
exponential relation:
teNN 0
• Where λ is the decay constant (s-1)
• Ex: use this to find λ from half life
![Page 82: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/82.jpg)
teN
N 0
21
2
1 T
e
2
1
ln2
1ln
T
e
2
1
12ln T
21
2ln
T
21
2ln
T
![Page 83: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/83.jpg)
• Activity: start with a petri dish full of
popcorn kernels. Shake and decay once
every 10 s. A kernel has decayed if it is
pointing down after the shake. Compare %
remaining after “40s” with theoretical:
21
2ln
T
s10
2ln 069.0
teNN 0)40(069.0%100 e %3.6
![Page 84: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/84.jpg)
Decay rate λ
• Show that decay rate
21
2ln
T
teNN 0
𝑁
𝑁0= 𝑒−λ𝑡
ln𝑁
𝑁0= ln 𝑒−λ𝑡
ln1
2= ln 𝑒−λ𝑇
-ln 2 = −λT
21
2ln
T
![Page 85: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/85.jpg)
![Page 86: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/86.jpg)
Half Life T1/2
• When a radioactive isotope decays, the
amount remaining can be described by a
half life relation:
2ln
2
1 T
• Ex 1: find the decay constant for Po-211, if
it has a half life of 0.51s
21
2ln
T 136.1 s
![Page 87: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/87.jpg)
Activity Level
• Ex: find the activity
level after 2.0s if
we start with 99
atoms of Po-211
teNA 0
BqsdecaysA 9.8/9.8
![Page 88: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/88.jpg)
Instantaneous Activity Level
• Ex: find the activity
level for 2350
atoms of Po-211 NeNA t
0
)2350(36.1A
BqA 3200
![Page 89: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/89.jpg)
• Ex 1: find the amount remaining of 55kg of
plutonium in the year 3018, if it has a half
life of 8x107a
kg9995.54
teNN 0
2
1
2ln
T
77 1016.3108
2ln
1016 1016.31074.255
e
![Page 90: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/90.jpg)
Try Exercises p. 253 #24-26
![Page 91: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/91.jpg)
f(x)=100(0.5)^x
-0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
20
40
60
80
100
x
y
% Remaining vs. Half-lives elapsed
![Page 92: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/92.jpg)
• Ex 2: Exponential decay
– Cesium 137 has a half life
of 30 years. If 2.5 kg is left
for 20 years, what mass will
be left?
![Page 93: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/93.jpg)
• Ex 2: Exponential decay
– Cesium 137 has a half life of 30 years. If
2.5 kg is left for 20 years, what mass will be
left?
kgA 57.1
teNN 0
2
1
2ln
T
71016.330
2ln
![Page 94: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/94.jpg)
• Ex 3: Radioactive dating
– Cesium 137 has a half life of 30 years. If
we start with 2.5 kg how much time passes
until 0.32 kg remain?
at 89
2
1
2ln
T
71016.330
2ln
teNN 0 101031.7
5.2
32.0ln
t
![Page 95: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/95.jpg)
Try Exercises p. 255 #27-31
![Page 96: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/96.jpg)
Nuclear reactions
• Atoms can be broken up (fission) or
combined (fusion)
energynHeHH 14
2
3
1
2
1
![Page 97: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/97.jpg)
Fission and Fusion
• We can release nuclear
energy by fusing together
lighter nuclei
• Or by breaking apart
heavier elements
![Page 98: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/98.jpg)
• Ex: find the energy released by the fission
reaction of U-235
![Page 99: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/99.jpg)
• Ex: find the energy
released by the fission
reaction of U-235
)(3 1
0
141
56
92
36
235
92
1
0 nBaKrUn
![Page 100: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/100.jpg)
![Page 101: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/101.jpg)
)0(33.86.86.70 nucleon
MeV
nucleon
MeV
nucleon
MeV
MeV180)3.11702.791(1786
• Ex: find the energy
released by the
fission reaction of
U-235
)141(3.8)92(6.8)235(6.7
![Page 102: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/102.jpg)
![Page 103: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/103.jpg)
Where does the energy come from?
• Einstein showed that in a nuclear reaction,
some of the mass is converted into pure
energy according to:
2mcE • Ex 1: how much energy is generated from
0.5g of Uranium?
• Ex2: how much energy is generated when
1kg of matter meets 1kg of antimatter?
![Page 104: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/104.jpg)
2mcE
• Ex 1: how much energy is generated from
0.5g of Uranium?
• Ex2: how much energy is generated when
1kg of matter meets 1kg of antimatter?
28100.30005.0s
mkgE
JE 13105.4
2mcE 28100.30.2
smkgE
JE 17108.1
![Page 105: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/105.jpg)
Harnessing Nuclear Power
• WWII arms race
• Oppenheimer: Manhattan Project
• Gadjet: test bomb July 16th
• Little Boy: Enriched U-235 bomb: detonated
over Hiroshima Aug. 6, 1945.
– Eq: 18 kT TNT (4.2x109 J per ton)
– cf May 1945 Germany
• Fat Man: Plutonium: detonated over Nagasaki
Aug. 9, 1945
![Page 106: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/106.jpg)
Modern thermonuclear weapons
• Thermonuclear weapons use a fission
reaction to trigger a fusion bomb at the core
• This briefly reproduces the temperature and
pressure conditions at the sun’s core
• The highest yield is for hydrogen isotopes
fusing to make helium, hence “H bomb”
• Soviets 1953 test bomb
• US 1954: 15 MT
![Page 107: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/107.jpg)
![Page 108: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/108.jpg)
Nuclear Fission Reactors
• To get safe, useful energy, we need:
– A chain reaction
• nb critical mass (50 kg Uranium, 16 kg Plutonium)
– A moderator to slow the neutrons down
– Control rods to control the rate of the chain
reaction, or stop it if necessary
• The CANDU reactor uses:
– Natural uranium instead of enriched (more U-235)
– Heavy water D2O as a moderator
– Cadmium control rods
![Page 109: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/109.jpg)
![Page 110: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/110.jpg)
![Page 111: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/111.jpg)
Fusion Reactor?
• Nuclear fusion is more powerful, and cleaner:
no radioactive fuel or waste!
• The Tokamak reactor
uses magnetic fields to
contain a plasma and
generate fusion reactions
• Still not a stable
energy producer
• Fusion reactions are difficult to contain
![Page 112: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/112.jpg)
ITER: International Thermonuclear
Experimental Reactor
![Page 113: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/113.jpg)
Another option?
• We can use a "LASER" to heat up the
hydrogen and ignite the fusion reaction
![Page 114: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/114.jpg)
![Page 115: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/115.jpg)
Proton-proton chain
2x0.42MeV
2x1.02MeV
2x5.49MeV
12.86MeV
Total
26.72MeV
=4.3x10-12J
![Page 116: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/116.jpg)
What should our neutrino flux be?
2 neutrinos for every 4.3x10-12J
3.85x1026J/s total output
112
126
)2(103.4
1085.3
J
sJ
138108.1 s
![Page 117: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/117.jpg)
What should our neutrino flux be?
2 neutrinos for every 4.3x10-12J
3.85x1026J/s total output
24 d
Lb
211
38
)105.1(4
108.1
b 1214103.6 sm
![Page 118: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/118.jpg)
![Page 119: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/119.jpg)
Where are the missing neutrinos?
• When measuring solar
neutrino flux, we only
observe ~1/3 the predicted
amount
![Page 120: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/120.jpg)
![Page 121: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/121.jpg)
What’s your flavorite?
• McDonald found that neutrinos are like
Timbits that change flavour on the way here
from the Sun.
![Page 122: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/122.jpg)
Try Exercises p. 256-9 #32-36
![Page 123: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/123.jpg)
Ex: 34a
• Find the energy released in MeV:
nHeHH 1
0
3
2
2
1
2
1
2.014101u+2.014101u=3.016029u+1.008665u+?
0.003509u x 931.5 MeV/u = 3.27 MeV
![Page 124: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/124.jpg)
Ex: 34b
• Find the energy released in MeV:
pHHH 1
1
3
1
2
1
2
1
2.014101u+2.014101u=3.016049u+1.007276u+?
0.004877 u x 931.5 MeV/u =4.543 MeV
![Page 125: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/125.jpg)
To be nuclear or not nuclear…
• Create a presentation supporting your
viewpoint
• Include pros and cons in terms of the
ethical, financial, and environmental issues
associated with nuclear energy
![Page 126: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/126.jpg)
Mass Spectrometer
• Use the electric and magnetic forces to select
a mass
![Page 127: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/127.jpg)
First: Velocity Selector
• Only particles with the correct velocity
continue to the next stage
Be FF
qvBqE
B
Ev
![Page 128: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/128.jpg)
Next: mass spectrometry
• We can use this to separate isotopes
maF
r
mvqvB
2
v
qBrm
![Page 129: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/129.jpg)
Ex: Mass spectrometry question
• An electron is accelerated from rest in a
vacuum through a potential difference of 2.1
kV. b)Deduce that the final speed of the
electron is 2.7 × 107 m s–1.c)
Path ofelectron P
2.7 × 10 m s–17
+95 V
2.2 cm
0 V
12 cm
![Page 130: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/130.jpg)
Nuclear quantization
• The excited Al-27 can release this energy as
gamma photons either 1&2 or 3. Ex: find λ
for 1
![Page 131: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/131.jpg)
MeVMeVE 19.002.183.0
JE 196 106.11019.0
hfJE 141004.3
E
ch
fc
14
348
1004.3
1063.6103
m121054.6
![Page 132: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/132.jpg)
See me putting in the hard work now,
Momma doesn't have to call work now,
I decide when I start work now,
Problems hit the gym, they all work out
![Page 133: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/133.jpg)
1. This question is about nuclear decay and
ionization.
(a) A nucleus of radium-226 (22688Ra ) undergoes
alpha particle decay to form a nucleus of radon (Rn).
Identify the proton number and nucleon number
of the nucleus of Rn.
Proton number: ..................................................
Nucleon number: ...............................................(2)
(b) Immediately after the decay of a stationary
radium nucleus, the alpha particle and the radon nucleus
move off in opposite directions and at different speeds.
(i) Outline the reasons for these observations. (3)
![Page 134: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/134.jpg)
(ii) Show that the ratio
is about 56. (3)
(c) The initial kinetic energy of the alpha particle is
4.9 MeV. As the alpha particle passes through air, it
loses all its kinetic energy by causing the ionization of
1.7 × 105 air molecules.
(i) State what is meant by ionization. (1)
(ii) Estimate, in joules, the average energy needed to
ionize an air molecule. (2)
(d) Outline why a beta particle has a longer range in
air than an alpha particle of the same energy. (3)
(Total 14 marks)
atomradon ofenergy kinetic initial
particle alpha ofenergy kinetic initial
![Page 135: Nuclear Physics - Weebly](https://reader030.fdocuments.net/reader030/viewer/2022012721/61b3dede4628d3371a154f0c/html5/thumbnails/135.jpg)
1. (a) (i) proton number: 86;nucleon number: 222
(b) (i) momentum conserved; so different speeds as
different masses; opposite directions because momentum zero
initially;
(ii) k.e.α ÷ k.e.Rn = mαvα2 ÷ mRnvRn
2 / sensible ratio formed; =
(mαvα)2mRn ÷ (mRnvRn)
2mα / cancellation of momentum terms; =
mRn ÷ mα = (= 55.5);
(c) (i) removal (addition) of electron from
atom/molecule; (ii) ;
4.6 × 10–18 J;
(d) beta have smaller mass / smaller / have greater speed than
alpha; beta have smaller charge than alpha; therefore less likely
to interact with air molecules;