Transcript From Last Time…

From Last Time…
Nuclear structure and isotopes
Binding energy of nuclei
Final Exam is
Mon Dec 21,
5:05 pm - 7:05 pm
2103 Chamberlin
3 equation sheets allowed
About 30% on new material
Rest on topics of exam1, exam2, exam3.
Week15HW covers material for final,
but does not count toward HW grade.
Tues. Dec 14, 2009
Phy208 Lecture 29
1
Radioactive nuclei
~ equal #
neutrons and
protons
Tues. Dec 14, 2009
Phy208 Lecture 29
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Radioactive decay
• Unstable nuclei decay by emitting particle
• Can be photon (light particle),
or matter particle.
• Emitted particle carries away energy
– Can strip electrons from atoms (ionizing radiation)
– break apart chemical bonds in living cells (radiation damage)
Geiger
counter
Tues. Dec 14, 2009
Phy208 Lecture 29
3
Biological effects of radiation
• Radiation damage depends on
– Energy deposited / tissue mass (1 Gy (gray) = 1J/kg)
– Damaging effect of particle (RBE, relative biological effectiveness)
Radiation type
RBE
X-rays
Gamma rays
Beta particles
Alpha particles
1
1
1-2
10-20
• Dose equivalent = (Energy deposited / tissue mass) x RBE
– Units of Sv (sieverts) [older unit = rem, 1 rem=0.01 Sv]
– Common units mSv (10-3Sv), mrem (10-3rem)
– Common ‘safe’ limit = 500 mrem/yr
(5 mSv/yr)
Tues. Dec 14, 2009
Phy208 Lecture 29
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Radioactive tracers
Worked on radioactivity
as student with Ernest Rutherford.
Lodged in nearby boarding home.
Suspected his landlady was serving meals later in
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.”
Tues. Dec 14, 2009
Phy208 Lecture 29
George de Hevesy
5

A random process
• Radioactive decay is a random process
– It has some probability of occurring.
• For one nucleus,
– Prob decay in t   rt
– r = decay rate
• For N nuclei,
– # decays N = N x Prob(decay) =rNt
– # decays / s = N/t =rN
r t
 N  N oe
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Radioactive half-life
• Example of random decay.
• Start with 8,000 identical radioactive nuclei
• After one half-life, half the nuclei have decayed.
Every half-life,
half the atoms decay
Undecayed
nuclei
t=0
Tues. Dec 14, 2009
t=1 yr t=2 yr t=3 yr
Phy208 Lecture 29
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Radioactive decay question
A piece of radioactive material is initially observed
to have 10,000 radioactive nuclei.
3 hours later, you measure 1,250 radiaoctive nuclei.
The half-life is
A.
B.
C.
D.
In each half-life,
the number of radioactive nuclei,
and hence the number of decays / second,
drops by a factor of two.
1/2 hour
1 hour
3 hours
After 1 half life, 5000 are left undecayed.
8 hours
After 2 half lives, 1/2 of these are left: 2,500
After 3 half lives there are 1,250 left.
Tues. Dec 14, 2009
Phy208 Lecture 29
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Radioactive decay question
A piece of radioactive material is initially observed
to have 1,000 decays/sec.
It’s half life is 2 days.
Four days later, you measure
A.
B.
C.
D.
1,000 decays / sec
500 decays / sec
250 decays / sec
125 decays / sec
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Quantifying radioactivity

Decay rate r



Prob( nucleus decays in time t ) = r t
(Units of becquerel (1 Bq=1 s-1) or
curie (1 Ci=3.7x1010 s-1)
Activity R

Mean # decays / s = rN,
Half-life t1/2

(Units of s-1)
N=# nuclei in sample
(Units of s)
time for half of nuclei to decay = t1/2
ln2 0.693


r
r
N  N oer t
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Phy208 Lecture 29
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Different types of radioactivity
• Three different types of decay observed:
Alpha decay
Beta decay
Gamma decay
(First three letters of Greek alphabet).
Ernest Rutherford (1899): "These experiments show that the uranium
radiation is complex and that there are present at least two distinct types
of radiation - one that is very readily absorbed, which will be termed for
convenience the alpha-radiation, and the other of more penetrative
character which will be termed the beta-radiation."
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Phy208 Lecture 29
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Example of  decay
Heavy nucleus spontaneously
emits alpha particle
• nucleus loses 2 neutrons and 2 protons.
• It becomes a different element (Z is changed)
• Example:
238
92
U  He 
92 protons
146 neutrons
Tues. Dec 14, 2009
4
2
2 protons
2 neutrons
Phy208 Lecture 29
Alpha particle
Th
234
90
90 protons
144 neutrons
12
Number of protons
Decay sequence of 238U
 decay
Number of neutrons
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Radon
Zone 1 Highest Potential (greater than 4 pCi/L)
Zone 2 Moderate Potential (from 2 to 4 pCi/L)
•
Radon is in the 238U decay series
•
Radon is an  emitter that presents
an environmental hazard
•
Inhalation of radon and its
daughters can ionize lung cells
increasing risk of lung cancer
Tues. Dec 14, 2009
14
http://www.radonwisconsin.com/
Phy208 Lecture 29
Activity of Radon
• 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?
We are trying to find number of decays/sec.
So we have to know decay constant to get R=rN
0.693
0.693
r

 2.09 106 s
t1/ 2
3.83days 86,400s /day
dN
R
 rN  2.09 106 s  4.0 108 nuclei 836decays/s
dt
1Ci
R  836 decays/s 
 0.023Ci
10
2.7 10 decays/s
Tues. Dec 14, 2009
Phy208 Lecture 29
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Decay sequence of
238U
Number of protons
But what are these?
 decay
Tues. Dec 14, 2009
Number
of neutrons
Phy208 Lecture 29
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Number of neutrons
decreases by one
Number of protons
increases by one
Electron (beta particle)
emitted
Number of protons
Beta decay
Number of neutrons
But nucleus has only neutrons & protons.
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Beta decay
• Nucleus emits an electron
(negative charge)
• Must be balanced
by a positive charge
appearing in the nucleus.
This occurs as a neutron
changing into a proton
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Changing particles
Neutron made up of
quarks.
One of the down quarks
changed to an up quark.
New combination of
quarks is a proton.
Tues. Dec 14, 2009
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
beta decay example
14
6
CÊÊÊ

14
7

NÊÊ
 e
7 neutrons
7 protons
8 neutrons
6 protons
14 nucleons
=
14 nucleons
+
1 electron
6 positive
charges
=
7 positive
charges
+
1 negative charge
Used in radioactive carbon dating.
Half-life 5,730 years.
Tues. Dec 14, 2009
Phy208 Lecture 29
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Radiocarbon dating
•
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)
As long as
biological
material alive,
atmospheric
carbon mix
ingested (as CO2),
ratio stays fixed.
Tues. Dec 14, 2009
After death, no exchange
with atmosphere. Ratio
starts to change
as 14C decays
Phy208 Lecture 29
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Carbon-dating question
The 14C:12C 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?
A.
B.
C.
D.
7,640 years
17,200 years
22,900 years
45,800 years
Tues. Dec 14, 2009
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 Lecture 29
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Other carbon
decays
Too few
neutrons
Too many
neutrons
• Lightest isotopes of carbon emit positron
– antiparticle of electron, has positive charge!
9
6
C
3 neutrons
6 protons
Tues. Dec 14, 2009
9
5
This is
antimatter
B
4 neutrons
5 protons
+ e+
Phy208 Lecture 29
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Gamma decay
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.
Nucleus also emits photon as
it drops to ground state
This is gamma radiation
Extremely high energy
photons.
Tues. Dec 14, 2009
60
28
Phy208 Lecture 29
Ni
60
28
Ni
24
Decay summary
• 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
Tues. Dec 14, 2009
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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
Tues. Dec 14, 2009
20Na
has 11 protons, 9 neutrons
20Ne 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.
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Radiation Therapy
• 50-60% of cancer patients treated with radiation
• Goal: disable cancerous cells without hurting healthy cells
• X-rays or -rays (60Co) from 20 KV to 25 MV
Tues. Dec 14, 2009
Phy208 Lecture 29
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Exposure from laboratory source
Co source has an activity of 1 µCurie3.7 10 decays/s
4
• 60
• Each decay: 1.3 MeV photon emitted
• Assume all absorbed by a 1 kg section of your body
for 1 hour

• Energy absorbed in 1 kg =
1.310 eV1.6 10
6
19
J /eV 3.7 104 decays/s1hr3600s/hr  2.8 105 J
What dose do you receive? A. 0.5 rem
5
2.8
10
J /kg1rad /0.01J /kg

B. 0.3 rem
C. 0.1 rem
D. 0.05 rem
 0.003 rad = 0.003 rem
E. 0.003 rem
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