Download Radioactivity from last time…

Final Exam
•
•
•
•
Physics 208 Exit survey
Mon, May 12, at 12:25-2:25 pm in Ingraham B10
2 equation sheets allowed (HAND WRITTEN!)
About 30% on new material
Rest on topics of exam1, exam2, exam3.
•
•
•
•
Study Tips:
Download blank exams and take them.
Download blank quizzes and take them.
Look through group problems.
Look through lab question sheets.
Work through new-material practice
problems on Mastering Physics
Wed, May 7 2008
Phy208 Lect29
Please take web exit survey
Link on course web site
Also will receive an email.
Helps us to understand what was effective
(and ineffective!) in the course.
Wed, May 7 2008
1
Radioactivity from last time…

Radioactive decay: alpha, beta, gamma

Decay rate r

Activity R



2
Example of α decay
Heavy nucleus spontaneously
emits alpha particle
(Units of s-1)
Prob( nucleus decays in time Δt ) = r Δt
(Units of becquerel (1 Bq=1 s-1) or
curie (1 Ci=3.7x1010 s-1)
Mean # decays / s = rN
Half-life t1/2

Phy208 Lect29
• nucleus loses 2 neutrons and 2 protons.
• It becomes a different element (Z is changed)
(Units of s)
• Example:
238
92
time for half of nuclei to decay = t1/2
t1/ 2 =
Wed, May 7 2008
ln2 0.693
=
r
r
Phy208 Lect29
Alpha particle
U " 42 He + 23490Th
92 protons
146 neutrons
2 protons
2 neutrons
Wed, May 7 2008
3
Phy208 Lect29
90 protons
144 neutrons
4
!
!
Radon
Decay sequence of 238U
Zone 1 Highest Potential (greater than 4 pCi/L)
Number of protons
Zone 2 Moderate Potential (from 2 to 4 pCi/L)
• Radon is in the
238U
decay series
• Radon is an α emitter that
presents an environmental
hazard
α decay
Wed, May 7 2008
Number of neutrons
Phy208 Lect29
5
• Inhalation of radon and its
daughters can ionize lung cells
increasing risk of lung cancer
Wed, May 7 2008
6
http://www.radonwisconsin.com/
Phy208 Lect29
1
Decay sequence of 238U
Activity of Radon
We are trying to find number of decays/sec.
So we have to know decay constant to get R=rN
r=
0.693
0.693
=
= 2.09 "10#6 s
t1/ 2
3.83days " 86,400s /day
dN
= rN = 2.09 "10#6 s " 4.0 "10 8 nuclei = 836decays /s
dt
1Ci
R = 836 decays /s "
= 0.023µCi
2.7 "1010 decays /s
R=
Wed, May 7 2008
Phy208 Lect29
But what are these?
Number of protons
• 222Rn has a half-life of 3.83 days.
• Suppose your basement has 4.0 x 108 such nuclei
in the air. What is the activity?
α decay
Number
of neutrons
Phy208 Lect29
Wed, May 7 2008
7
8
!
Beta decay
Number of protons
increases by one
Electron (beta particle)
emitted
Beta decay
• Nucleus emits an electron
(negative charge)
• Must be balanced
by a positive charge
appearing in the nucleus.
Number of protons
Number of neutrons
decreases by one
Number of neutrons
This occurs as a neutron
changing into a proton
But nucleus has only neutrons & protons.
Wed, May 7 2008
Phy208 Lect29
Wed, May 7 2008
9
Phy208 Lect29
10
beta decay example
Changing particles
14
6
Neutron made up of
quarks.
One of the down quarks
changed to an up quark.
New combination of
quarks is a proton.
C "
N + e#
7 neutrons
7 protons
8 neutrons
6 protons
!
14
7
14 nucleons
=
14 nucleons
+
6 positive
charges
=
7 positive
charges
+
1 electron
1 negative charge
Used in radioactive carbon dating.
Half-life 5,730 years.
Wed, May 7 2008
Phy208 Lect29
11
Wed, May 7 2008
Phy208 Lect29
12
2
Radiocarbon dating
•
Carbon-dating question
14C
has a half-life of ~6,000 years,
continually decaying back into 14N.
• Steady-state achieved in atmosphere,
with 14C:12C ratio ~ 1:1 trillion (1 part in 1012)
The
ratio in a fossil bone is found to be 1/8
that of the ratio in the bone of a living animal.
The half-life of 14C is 5,730 years.
What is the approximate age of the fossil?
As long as
biological
material alive,
atmospheric
carbon mix
ingested (as CO2),
ratio stays fixed.
A.
B.
C.
D.
After death, no exchange
with atmosphere. Ratio
starts to change
as 14C decays
Wed, May 7 2008
Phy208 Lect29
Other carbon
decays
13
Too few
neutrons
Too many
neutrons
– antiparticle of electron, has positive charge!
6
C
3 neutrons
6 protons
Wed, May 7 2008
9
5
4 neutrons
5 protons
Wed, May 7 2008
Since the ratio has been reduced
by a factor of 8, three half-lives
have passed.
3 x 5,730 years = 17,190 years
Phy208 Lect29
14
Antimatter
Matter and antimatter
annihilate
This is
antimatter
B
7,640 years
17,200 years
22,900 years
45,800 years
• Every particle
has an antiparticle.
• Antimatter (anti-atoms)
has been formed.
• Lightest isotopes of carbon emit positron
9
14C:12C
Photons are created,
conserving energy,
momentum.
+ e+
Phy208 Lect29
15
Wed, May 7 2008
Positron Emission Tomography - PET
Phy208 Lect29
16
Emission Detection
Ring of detectors
Gamma Photon #2
Short-lived radioactive tracer isotope emits positron
Positron annihilates with nearby electron
–
e+ + e- → 2γ
• Two 511 keV gamma rays are produced
Lect29
• They fly in opposite directions (toPhy208
conserve
momentum)
Wed, May 7 2008
Isotope
Max. Positron
Range (mm)
18F
2.6
11C
3.8
68Ga
9.0
82Rb
16.5
• If detectors receive gamma rays at the approx. same time, we have a
detection
• Nuclear physics sensor and electronics
17
Wed, May 7 2008
Phy208 Lect29
18
3
Detect ionizing
radiation
Radioactive tracers
Worked on radioactivity
as student with Ernest Rutherford.
Lodged in nearby boarding home.
Geiger counter
Suspected his landlady was serving meals
later in the week ‘recycled’ from the Sunday meat pie.
His landlady denied this!
deHevesy described his first foray
into nuclear medicine:
“The coming Sunday in an unguarded moment I
added some radioactive deposit [lead-212] to the
freshly prepared pie and on the following Wednesday,
with the aid of an electroscope, I demonstrated to the
landlady the presence of the active deposit in the soufflé.”
Wed, May 7 2008
Decay of
• Electroscope
George de Hevesy
Phy208 Lect29
19
Wed, May 7 2008
Phy208 Lect29
20
Gamma decay
60Co
Alpha decay (alpha particle emitted),
Beta decay (electron or positron emitted),
can leave nucleus in excited state
– Nucleus has excited states just like hydrogen atom
– Emits photon as it drops to lower state.
• This is one of sources used in
the lab.
• Decays by electron emission, as
predicted.
• But decays to an excited state.
• Photons emitted as excited
state drops to its ground state.
Wed, May 7 2008
Phy208 Lect29
Nucleus also emits photon as
it drops to ground state
This is gamma radiation
Extremely high energy
photons.
21
Ni
Phy208 Lect29
• rad (radiation absorbed dose)
• amount of radiation to deposit 0.01 J
of energy in 1 kg of absorbing material
• 50-60% of cancer patients treated with radiation
• Goal: disable cancerous cells without hurting healthy cells
• RBE (relative biological effectiveness =
# rads of x-rays that produces same
biological damage as 1 rad of radiation
being used
• rem (roentgen equivalent in man) =
dose in rem = dose in rad x RBE
• X-rays or γ-rays ( 60Co) from 20 KV to 25 MV
Phy208 Lect29
28
60
28
Ni
22
Radiation Levels
Radiation Therapy
Wed, May 7 2008
Wed, May 7 2008
60
23
Radiation type
RBE
X-rays
Gamma rays
Beta particles
Alpha particles
1
1
1-2
10-20
Wed, May 7 2008
Ground
0.30 rem/yr
Mercury 9 60.6 rem/yr
Apollo 14 146.2 rem/yr
MIR Station 34.9 rem/yr
Space Station 36.5 rem/yr
Safe limit ( US gov )
0.50 rem/yr
Phy208 Lect29
24
4
Your exposure in the lab
Decay summary
• Your
has an activity of 1 µCurie ( 3.7 "10 4 decays /s)
• Each decay: 1.3 MeV photon emitted
• Assume all are absorbed by a 1 kg section of your
body for 1 hour
!
• Energy absorbed in 1 kg =
60Co
(1.3 "10 eV )(1.6 "10
6
#19
J /eV )( 3.7 "10 4 decays /s)(1hr)( 3600s /hr) = 2.8 "10#5 J
What dose do you receive? A. 0.5 rem
B. 0.3 rem
!
C. 0.1 rem
(2.8 "10
#5
J /kg)(1rad /(0.01J /kg))
= 0.003 rad = 0.003 rem
Wed, May 7 2008
D. 0.05 rem
E. 0.003 rem
Phy208 Lect29
!
25
• Alpha decay
– Nucleus emits He nucleus (2 protons, 2 neutrons)
– Nucleus loses 2 protons, 2 neutrons
• Beta- decay
– Nucleus emits electron
– Neutron changes to proton in nucleus
• Beta+ decay
– Nucleus emits positron
– Proton changes to neutron in nucleus
• Gamma decay
– Nucleus emits photon
as it drops from excited state
Wed, May 7 2008
Phy208 Lect29
26
Decay question
20Na
decays in to 20Ne, a particle is emitted?
What particle is it?
Na atomic number = 11
Ne atomic number = 10
A.
B.
C.
D.
Alpha
Electron beta
Positron beta
Gamma
Wed, May 7 2008
20Na
has 11 protons, 9 neutrons
has 10 protons, 10 neutrons
So one a proton (+ charge ) changed to a
neutron (0 charge) in this decay.
A positive particle had to be emitted.
20Ne
Phy208 Lect29
27
5