7/30/2019 Measures of radioactivity: a tool for understanding statistical data analysisa tool for understanding statistical data

1/1

Measures of radioactivity:Measures of radioactivity:

a tool for understanding statistical data analysisa tool for understanding statistical data analysisVera Mont albanoVera Mont albano

Phys. Department, University of Siena

References

[1] A. Porri, R. Benedetti, E.Mariotti, V. Millucci, V. Montalbano, Esperienze significative del ProgettoLauree Scientifiche di Siena, Proceeding ComunicareFisica, Trieste 1 6 ottobre 2007

[2] A. Porri, R. Benedetti, E.Mariotti, V. Millucci, V. Montalbano, La Scuolaestiva del Pigelleto e I Giocattolial Liceo, in atti del XLVI National Congress AIF, Suppl. n. 3 La Fisicanella Scuola , 130, 2008

[3] R. Benedetti, S. DiRenzone, E.Mariotti, V. Montalbano, A. Porri, Un percorso di orientamento sulla fisica moderna, Comunicare Fisica 2010, in corso di stampa

[4] R. Benedetti, E. Mariotti, V. Montalbano, A.Porri, Active and cooperative learning paths in thePigelletos Summer School of Physics, Twelfth International Symposium Frontiers of Fondamental Physics (nearby poster ID 91)

[5] P. R. Bevington Data Reduction and Errors Analysis for Physical Science, McGraw-Hill Book Company, New York 1969

[6] http://stattrek.com/Lesson3/SamplingTheory.aspx?Tutorial=Stat

An early experience

The starting point was the Pigelletos Summer School of Physics [1-4] .

Forty students from high school are selected to attend a full immersion summer school of

physics in thePigelleto Natural Reserve, on the south east side of Mount Amiata in the

province of Siena.

In the 2009 school, titled The Achievements of Modern Physics, a learning path on

radioactivity was proposed to two small groups of students.

After a brief introduction to the nuclear phenomenology, they were involved

in measures of radioactivity from a weak source ofU in order

to characterize the emitted ionizing radiation by using a educational

device provided by a school.

A teacher was impressed by students involvement and suggested

of elaborating a learning path on Nuclear Physics in which

the students are active and perform directly measures of radioactivity.

Experiment al setup

The measures are realizedby using a commercialGeiger counter usuallyused for dosimetry.It can detect alpha, betaand gamma rays and it is

possible to collect datawithout any unit

conversion (counts) anddownload them into acomputer.

The detector and the sources are aligned by means of supportson an optical bench.

The sources are shown with theirsupports (from left):

a) small sheets of Uranium inplastic holder m1 = 0.152 g

b) sheets U in plastic holderm2 = 0.888 g

c) fluorescent marble

Our target

In order to integrate this learning path in

the ordinary school program, the activities

are planned for the last year of high school

(5a

Liceo Tecnologico) after the lessons onelectromagnetism.

Teachers make few lessons in class in which

present and discuss the phenomenology of

nuclear physics.

Afterward, the experimental setup is

presented in order to perform measure of

background radioactivity in the laboratory.

The next step is to divide students in small

groups that are involved in measures of,

and emission from weak sources ofU

and a very weak source with trace of

uranium ore.

During measurements, it rises soon the

necessity of performing many measures and

the problem of valuating uncertainties.

The students are ready to recall all their

knowledge on statistics for facing this

problem.

A brief intr oduction to n uclear phenomena

The lessons give an historical sight on the discovery of radioactivity, and connectthe previous knowledge of students to these phenomena so far from theirdaily experience.

The main topics are the following:- Discovery of radioactivity- Pierre e Marie Curie- Neutron discovery and atom structure- Dimensions of atom and its constituents- Natural radioactivity phenomenology (in particular , and rays)

- I sotopes- Forces into atoms and nuclei (how strong or weak with numerical examples)- Nuclei can die- Law of radioactive decay- Natural radioactive chains- Binding energy and mass of a bound state- Equivalence mass-energy- Binding energy per nucleon- Fission and related topics- Fusion and related topics

Related topics can be very stimulating for students, specially in these times forour society

An introduct ion to stati stical data analysis

Let us start from a question:

There are limits to the precision of a measurement?

By answering to this question, we can fix the cases in which the use of statistical data analysis

make sense.

The first step is to recall all previous knowledge of students on statistics (there are many but

almost never used in physics by teachers), such as [5,6]

- Distributions

- Representation of casual phenomena

- Mean, median, variance and standard deviation

- Bernoulli, Poisson and Gauss distributions and examples

At this point, it is possible to introduce the pupils to some elements of sampling theory, such

as

- The existence of a parent distribution- What is a good statistical sample

- Mean and variance of a sample

Now we are ready to deal with the statistical data analysis of our measures.

The data are collected in the meantime by the Geiger detector and can be downloaded in a

computer. The teacher can divide the data in sets in order of giving different tasks to any

group of students.

Some examples:

- testing samples by giving 10, 20, 30, 50 data from the background and compare means

and standard deviations of these samples with the mean and standard deviation of much

more measures (e.g. more then 1000)

- Perform measures for short period in order to verify that radioactive decay follows

Poissons distributions

- Verify that for mean values greater than the Poissons distribution become

indistinguishable from the normal one

In particular, can be very interesting to show that in case of very weak source it is possible to

quantify differences from background smaller than the uncertainties related to the physics

of radioactive decay by performing many measurements and by using statistical data

analysis.

interessante stimare qual la varianza della media m

Si pu far vedere che

n

i

mmx

nn

s

1

22 )()1(

1

Quindi nel caso in cui si hanno misure i cui risultati fluttuano,

una volta verificato che non ci sono errori sistematici, il risultato

della misura si scrive:

msm

2039

4925143

597054

326

248541

275337

d1=d0 d1=d0+4.25 d3=d0+26.4

m1= 0.152 g

24821 244

2108 286

213 215

184855 714

157134 608

685 227

Fondo =18.08 0.05

Prime misure in classe

N=25