? 14 10 m Jerry Gilfoyle Radioactivity 1 / 14 Radioactivity - - PowerPoint PPT Presentation

The Structure of Matter

10 m

7

10 m

1

10 m

−6

10 m

−9

10 m

−15

10 m

−14

10 m

−10

10 m

19

?

Jerry Gilfoyle Radioactivity 1 / 14

Radioactivity and Nuclear Decay

At the end of the nineteenth cen- tury Henri Becquerel discovers the spontaneous emission of ‘rays’. The surprise was that no energy in- put was required. These rays carry off huge amounts

• f energy.

Some examples of ‘rays’.

Original Photographic Plate Developed by Henri Becquerel.

Po Bi Pb + He (α) (β) Cs + ν Po + e

55 137 83 212 84 212 82 208 84 212 137 56 56 137

Pb + He

4 2

Ba(0.0 keV) + γ Ba(0.662 keV) + e + (undetected) νe (undetected)

e

Jerry Gilfoyle Radioactivity 2 / 14

Why Should You Care?

1 Massive release of energy from a small amount of material.

Weapons Energy source

2 How can we explain it? −

→ Why does the Sun shine?

3 Gobs of current uses. 1

Food treatments.

2

Smoke detectors.

3

Medical applications (PET scans).

4

Environmental, medical, and biological monitoring.

Jerry Gilfoyle Radioactivity 3 / 14

The 4He − 234

90Th Potential

α-Th Potential Blue - known Red - a guess 10 20 30 40 50 60 70

• 40
• 20

20 40 r(fm) V(MeV)

Jerry Gilfoyle Radioactivity 4 / 14

Rutherford Scattering

Alpha source

84 210

Microscope Alpha beam Collimator ZnS Scattered helium Thorium target

2 4 82

Po He + Pb

206

Jerry Gilfoyle Radioactivity 5 / 14

The 4He − 234

90Th Potential

α-Th Potential Blue - known Red - a guess 10 20 30 40 50 60 70

• 40
• 20

20 40 r(fm) V(MeV)

Jerry Gilfoyle Radioactivity 6 / 14

Milking the Cow

This ‘clock’ ticks by producing a short-lived, radioactive material. Start with a liquid containing the ra- dioactive isotope 137Cs that decays very slowly.

137Cs→e−+137Ba(0.662 MeV)

The number “0.662 MeV” means there is still energy (0.662 MeV) stored in the Ba-137 nucleus. The excited Ba-137 then emits a high-energy photon or gamma ray to reach the stable ground state of

137Ba.

137Ba(0.662)→137Ba(0.0)+γ

137 137

γ

−

e

56Ba

Cs

55

excited state ground state (0.662 MeV)

Decay scheme of cesium-137.

Jerry Gilfoyle Radioactivity 7 / 14

Geiger-Muller Tube

A Geiger-Muller tube (or GM tube) is the sensing element of a Geiger counter instrument that can detect a single particle of ionizing radiation. It is a type of gaseous ionization detector with an operating voltage in the Geiger plateau.

Jerry Gilfoyle Radioactivity 8 / 14

Using the Reduced χ2

The χ2 and reduced χ2 are defined as χ2 =

N

• i=1

((yi − f (xi))2 σ2

i

and reduced χ2 = χ2 N − d.o.f where N is the number of data points. In Mathematica the esti- mated variance is equal to the re- duced χ2 if the proper weighting is used.

• R. Muto, et al., Phys. Rev. Lett., 98, 042501

(2007).

Jerry Gilfoyle Radioactivity 9 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function?

Jerry Gilfoyle Radioactivity 10 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function? When variations in a measurement are

Jerry Gilfoyle Radioactivity 10 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function? When variations in a measurement are

1 random Jerry Gilfoyle Radioactivity 10 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function? When variations in a measurement are

1 random 2 independent of each other Jerry Gilfoyle Radioactivity 10 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function? When variations in a measurement are

1 random 2 independent of each other 3 continuous Jerry Gilfoyle Radioactivity 10 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function? When variations in a measurement are

1 random 2 independent of each other 3 continuous 4 can be positive or negative Jerry Gilfoyle Radioactivity 10 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function? When variations in a measurement are

1 random 2 independent of each other 3 continuous 4 can be positive or negative

Do these conditions apply for radioactive decay?

Jerry Gilfoyle Radioactivity 10 / 14

Probability Distribution Functions

When Do You Use a Gaussian Probability Distribution Function? When variations in a measurement are

1 random 2 independent of each other 3 continuous 4 can be positive or negative

Do these conditions apply for radioactive decay? NO!

Jerry Gilfoyle Radioactivity 10 / 14

Poisson Statistics

P(m : n, p) = 1 m!µme−µ µ = np m - no. of events µ - average n - no. of trials p - probability of an event Probability of a discrete event occurring m times in a particular time period.

Jerry Gilfoyle Radioactivity 11 / 14

Poisson Statistics

P(m : n, p) = 1 m!µme−µ µ = np m - no. of events µ - average n - no. of trials p - probability of an event Probability of a discrete event occurring m times in a particular time period. Number of soldiers killed by horse-kicks each year in Prussian cavalry corp (famous example in by a book of Ladislaus Josephovich Bortkiewicz (1868-1931)). Number of yeast cells for brewing Guinness (William Sealy Gosset (1876-1937)). The number of phone calls arriving at a call center per minute. The number of deaths per year in a given age group. The number of jumps in a stock price in a given time interval. The number of mutations in a given stretch of DNA after a certain amount

• f radiation.

The proportion of cells infected at a given multiplicity of infection.

Jerry Gilfoyle Radioactivity 11 / 14

Probability Distributions

Binomial distribution: P(m; n, p) = n! m!(n − m)!pmqn−m q = 1 − p n - total number of events; m - number of events of probability p For p << 1 one obtains the Poisson distribution P(m; n, p) = 1 m!µme−µ µ = np What is the difference between a Gaussian distribution and a Poisson? Gaussian - random, independent, continuous variations. Poisson - discrete, random, positive variations.

Jerry Gilfoyle Radioactivity 12 / 14

Semi-log Plots

Time dependence

• f

the

137Ba(0.662)

decay

• n

a lin- ear scale. Semi-log plot reveals the back- ground is significant.

137Ba (0.662) decay

χ2/ν =2.6 t1/2=2.65 ±0.02 min 10 20 30 40 50 60 1000 2000 3000 4000 5000 t (min) N Radioactive Decay

No background?

137Ba (0.662) decay

χ2/ν =2.6 t1/2=2.65 ±0.02 min 10 20 30 40 50 60 1 10 100 1000 t (min) N Radioactive Decay

Background!

Jerry Gilfoyle Radioactivity 13 / 14

Semi-log Plots

Time dependence

• f

the

137Ba(0.662)

decay

• n

a lin- ear scale. Semi-log plot reveals the back- ground is significant.

137Ba (0.662) decay

χ2/ν =2.6 t1/2=2.65 ±0.02 min 10 20 30 40 50 60 1000 2000 3000 4000 5000 t (min) N Radioactive Decay

No background?

137Ba (0.662) decay

χ2/ν =2.6, χ2/ν =8.7 t1/2=2.65 ±0.02 min (red) t1/2=2.90 ±0.03 min (green) 10 20 30 40 50 60 1 10 100 1000 t (min) N Radioactive Decay

Background!

Jerry Gilfoyle Radioactivity 14 / 14