Tues. Dec 14, 2009Phy208 Lecture 29 1 Final Exam is Mon Dec 21, 5:05 pm - 7:05 pm 2103 Chamberlin 3 equation sheets allowed About 30% on new material Rest.

Tues. Dec 14, 2009 Phy208 Lecture 29 1

Final Exam is Mon Dec 21, 5:05 pm - 7:05 pm 2103 Chamberlin

3 equation sheets allowedAbout 30% on new materialRest on topics of exam1, exam2, exam3.

Week15HW covers material for final,but does not count toward HW grade.

From Last Time…Nuclear structure and isotopesBinding energy of nuclei


Radioactive nuclei

~ equal # neutrons and protons


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


Biological effects of radiation

Radiation type RBE

X-rays 1Gamma rays 1Beta particles 1-2Alpha particles 10-20

• Radiation damage depends on– Energy deposited / tissue mass (1 Gy (gray) = 1J/kg)– Damaging effect of particle (RBE, relative biological effectiveness)

• 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)


Radioactive tracersWorked 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:

George de HevesyGeorge de Hevesy

“The coming Sunday in an unguarded moment Iadded some radioactive deposit [lead-212] to thefreshly prepared pie and on the following Wednesday,with the aid of an electroscope, I demonstrated to thelandlady the presence of the active deposit in the soufflé.”


A random process

• Radioactive decay is a random process– It has some probability of occurring.

• For one nucleus,– – r = decay rate

• For N nuclei, – # decays N = N x Prob(decay) =rNt– # decays / s = N/t =rN

€

Probdecay in Δt( ) = rΔt

€

⇒ N = Noe−r t


Radioactive half-life• Example of random decay.• Start with 8,000 identical radioactive nuclei• After one half-life, half the nuclei have decayed.

t=0 t=1 yr

t=2 yr

t=3 yr

Every half-life, half the atoms decay

Undecayed nuclei


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. 1/2 hourB. 1 hourC. 3 hoursD. 8 hours

In each half-life, the number of radioactive nuclei, and hence the number of decays / second, drops by a factor of two.

After 1 half life, 5000 are left undecayed. After 2 half lives, 1/2 of these are left: 2,500After 3 half lives there are 1,250 left.


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. 1,000 decays / secB. 500 decays / secC. 250 decays / secD. 125 decays / sec


Decay rate r (Units of s-1) Prob( nucleus decays in time t ) = r t

Activity R (Units of becquerel (1 Bq=1 s-1) orcurie (1 Ci=3.7x1010 s-1)

Mean # decays / s = rN, N=# nuclei in sample

Half-life t1/2 (Units of s) time for half of nuclei to decay = t1/2

Quantifying radioactivity

€

=ln2

r=

0.693

r

€

N = Noe−r t


Different types of radioactivity

• Three different types of decay observed:Alpha decayBeta decayGamma 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."


Heavy nucleus spontaneously emits alpha particle

Example of a decay

• nucleus loses 2 neutrons and 2 protons.

• It becomes a different element (Z is changed)

• Example:

€

92238U→ 2

4He+ 90234Th

92 protons146 neutrons

90 protons144 neutrons

2 protons2 neutrons

Alpha particle


Decay sequence of 238U

Number of neutrons

Num

ber

of

pro

ton

s

a decay


RadonZone 1 Highest Potential (greater than 4 pCi/L)

Zone 2 Moderate Potential (from 2 to 4 pCi/L)

http://www.radonwisconsin.com/

• Radon is in the 238U decay series

• Radon is an a emitter that presents an environmental hazard

• Inhalation of radon and its daughters can ionize lung cells increasing risk of lung cancer

http://www.radonwisconsin.com/


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

€

r =0.693

t1/ 2

=0.693

3.83days× 86,400s /day= 2.09 ×10−6 s

R =dN

dt= rN = 2.09 ×10−6 s× 4.0 ×108nuclei = 836decays /s

R = 836 decays /s×1Ci

2.7 ×1010decays /s= 0.023μCi


Decay sequence of 238U

Number of neutrons

Num

ber

of

pro

ton

s

a decay

But what are these?


Beta decay

Number of neutronsN

um

ber

of

pro

ton

sNumber of neutrons decreases by one

Number of protons increases by one

Electron (beta particle) emitted

But nucleus has only neutrons & protons.


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


Changing particles

Neutron made up of quarks.

One of the down quarks changed to an up quark.

New combination of quarks is a proton.


beta decay example

Used in radioactive carbon dating. Half-life 5,730 years.

€

614 C → 7

14 N + e −

8 neutrons6 protons

7 neutrons7 protons

14 nucleons 14 nucleons

6 positive charges

7 positive charges

=

=

+ 1 electron

+ 1 negative charge


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.

After death, no exchange with

atmosphere. Ratio starts to change

as 14C decays


Carbon-dating questionThe 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. 7,640 yearsB. 17,200 yearsC. 22,900 yearsD. 45,800 years

Since the ratio has been reduced by a factor of 8, three half-lives have passed.

3 x 5,730 years = 17,190 years


Other carbon decays

• Lightest isotopes of carbon emit positron – antiparticle of electron, has positive charge!

3 neutrons6 protons

4 neutrons5 protons

+ e+

This is antimatter

Too few neutrons

Too many neutrons

B9

5C

9

6


Gamma decayAlpha 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 stateThis is gamma radiation

Extremely high energy photons. Ni

6028

Ni6028


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


Decay question20Na decays in to 20Ne, a particle is

emitted? What particle is it?Na atomic number = 11Ne atomic number = 10

A. AlphaB. Electron betaC. Positron betaD. Gamma

20Na has 11 protons, 9 neutrons20Ne has 10 protons, 10 neutronsSo one a proton (+ charge ) changed to a neutron (0 charge) in this decay.

A positive particle had to be emitted.

20Na has 11 protons, 9 neutrons20Ne has 10 protons, 10 neutronsSo one a proton (+ charge ) changed to a neutron (0 charge) in this decay.

A positive particle had to be emitted.


Radiation Therapy

• 50-60% of cancer patients treated with radiation

• Goal: disable cancerous cells without hurting healthy cells

• X-rays or γ-rays (60Co) from 20 KV to 25 MV


Exposure from laboratory source

• 60Co source has an activity of 1 µCurie • 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 =

€

3.7 ×104 decays /s( )

€

1.3×106eV( ) 1.6 ×10−19J /eV( ) 3.7 ×104 decays /s( ) 1hr( ) 3600s /hr( ) = 2.8 ×10−5J

€

2.8 ×10−5J /kg( ) 1rad / 0.01J /kg( )( )

= 0.003 rad = 0.003 rem

What dose do you receive? A. 0.5 rem

B. 0.3 rem

C. 0.1 rem

D. 0.05 rem

E. 0.003 rem

Tues. Dec 14, 2009Phy208 Lecture 29 1 Final Exam is Mon Dec 21, 5:05 pm - 7:05 pm 2103 Chamberlin 3 equation sheets allowed About 30% on new material Rest.

Documents

2009phy208 lecture

hevesyphy208 lecture

msvyrphy208 lecture

rnphy208 lecture

half of nuclei

number of radioactive

decays n

radioactive tracersworked