5.3.3 Radioactivity

(a) describe the spontaneous and random nature of radioactive decay of unstable nuclei

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cs Radioactive decay

Stable Unstable: Will emit radiation randomly once

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cs Radioactive decayNuclear decay is spontaneous because: the decay of a particular nucleus is not affected by the

presence of other nuclei the decay of nuclei cannot be affected by chemical

reactions or external factors such as temperature and pressure

and is random because: it is impossible to predict when a particular nucleus in

the sample is going to decay each nucleus in a sample has the same chance of

decaying per unit time

(b) describe the nature, penetration and range of α- particles, β-particles and γ-rays

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cs Radiation penetration

PAP

ER

ALU

MIN

IUM

LEA

D

ALPHA

BETA

GAMMA

2 Protons2 Neutrons

High EnergyElectron

High Frequency Wave

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cs Radiation penetration

Alpha decayType of decay:

What is emitted?

Description of decay:

Example of decay:

Effect on A and Z:

Alpha particle (helium nuclei)

238 234 4

U Th + + energy 92 90 2

2 neutrons and 2 protons are emitted from the nucleus.

A decreases by 4, Z decreases by 2

(A-4, Z-2)

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cs Radiation penetration

Beta decayType of decay:

What is emitted?

Description of decay:

Example of decay:

Effect on A and Z:

High energy electron

A neutron in the nucleus decays into a proton and a high energy electron which is emitted with an anti-neutrino.

A stays the same, Z increases by 1

(A=, Z+1)

14 14 0

C N + + ν 6 7 -1

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cs Radiation penetration

Gamma decayType of decay:

What is emitted?

Description of decay:

Effect on A and Z:

High energy electromagnetic radiation

Nucleus loses energy and becomes more stable. Gamma radiation is the

energy it loses.

A stays the same, Z stays the same

(A=, Z=)

(c) define and use the quantities activity and decay constant

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cs Activity

The activity of a source is defined as follows:

Activity is measured in decays per second (or h-1 or day-1, etc)

An activity of one decay per second is one becquerel (1 Bq)

1 Bq = 1 s-1

The activity A of a radioactive sample is the rate at which nuclei decay or disintegrate

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cs Decay constant

The decay constant of a source is defined as follows:

For example, in a sample of one million nuclei, if 200 000 in one hour, then the decay constant is

Decay constant λ = 0.20 h-1

The decay constant λ is the probability that an individual nucleus will decay per unit time interval

(d) select and apply the equation for activity A = λN

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Activity of a sample depends on the decay constant λ The greater the decay constant, the greater the activity Activity also depends on the number of undecayed

nuclei in the sample N

A = λN

Activity equation

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cs Questions

1. A sample of carbon-15 initially contains 500 000 undecayed nuclei. The decay constant for this isotope of carbon is 0.30 s-1. Determine the initial activity of the sample

2. A small sample of radium gives a received count rate of 20 counts per minute in a detector. It is known that the counter detects only 10% of the decays from the sample. The sample contains 1.5 x 109 undecayed nuclei. Determine the decay constant of this form of radium

A = λN= 0.30 s-1 x 500 000= 150 000 s-1 or 150 000 Bq

Count rate = 20 m-1 therefore 0.33 s-1

Activity = 3.3 s-1

Decay Constant = 3.3 s-1 / 1.5 x 109

= 2.0 x 10-9 s-1

(e) select and apply the equations A = Aoe-λt and N = Noe-λt where A is the activity and N is the number of undecayed nuclei

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cs Decay equations

100

50

0

0 14

Undecayed Atoms [N]orActivity [A] (s-1)

Time [t] (s)

28

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cs Decay equations

The decay in the graph can be expressed as an equation

If N0 is the number of undecayed nuclei, then N that remain undecayed after time t is given by:

N = Noe-λt

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cs Decay equations

The activity A of a sample is proportional to the number of undecayed nuclei N. Hence the activity of the sample decreases exponentially:

A = Aoe-λt

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cs Questions

Now attempt SAQ 13, 14 and 15

Use Worked Example 5 & 6 for help

(e) define and apply the term half-life

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cs Half-life

100

50

0

0 14 28Time (s)

Und

ecay

ed A

tom

s

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cs Half-life

The half-life t½ of a radioisotope is the mean time taken for half of the active nuclei in a

sample to decay

(g) select and use the equation λt1/2 = 0.693

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cs Decay constant and half-life

The decay constant and half-life are connected by the formula:

λt1/2 = 0.693

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cs Assessment

Chapter 14 SAQ’s 1 to 21

End of Chapter 14 questions 1 - 5

Radioactivity worksheet questions