© JP1

RADIOACTIVE RADIOACTIVE DECAYDECAY

© JP2

• It is impossible to say when a particular nucleus will decay .

• It is only possible to predict what fraction of the radioactive nuclei will decay in a certain time.

RADIOACTIVE DECAY OF ATOMS (TRANSMUTATION OF ATOMS) IS A RANDOM PROCESS

RADIOACTIVE DECAY OF ATOMS

(TRANSMUTATION OF ATOMS)

IS A RANDOM PROCESSRANDOMRANDOM

© JP3

Radioactive Decay is not affected by:

1. Physical Conditions - like temperature or pressure.

2. Chemical Changes – it does not matter if the radioactive isotope is part of a

compound.

The half-life of a radioactive isotope is the average time it takes for half of its

atoms to decay.

© JP4

Number of atoms, N

time, t

Initial numb of atoms, N0

20N

HALF LIFE t1/2

t1/2

40N

t1/2

80N

t1/2

THE RATE OF DECAY DEPENDS UPON THE

AMOUNT OF MATERIAL REMAINING, SO THE

DECAY IS EXPONENTIAL

© JP5

N0

N

t

teNN 0

λ = the decay constant – measures the probability of an atom decaying

λ has units of seconds-1

When N = ½ No, t = t1/2 2

1

002

1 t

eNN

22/1 te

2ln

2/1 t

© JP6

A0

A

t

teAA 0

As the Activity, A, depends upon the number of atoms in the source, the Activity also decays exponentially

N.B. Active isotopes have short half lives

© JP7

teNN 0

differentiating teNdt

dN 0

Ndt

dN

orN

t

Nactivity

i.e. The activity = the number of atoms in

the source times the decay constant

© JP8

UNITS OF ACTIVITY

1 Bq = one disintegration per second

Gray (Gy) – the amount of radiation causing 1 kg of tissue to absorb 1 joule (J) of energy

Other units

Sievert (Sv) – Arbitrary unit, based on the Gray , but adjusted to account for damage to living tissue.

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Example 1

A radioactive source contains 1 x 10-6 g of plutonium – 239. The source is found to emit 2300 alpha particles per second in all directions. Find the half life of plutonium.

1. Finding the number of atoms present in 1 x 10-6 g of plutonium – 239

2. 239 g contain 6.02 x 1023 atoms

3. Hence 1 x 10-6 g contain 2.52 x 1015 atoms = NN

t

N

4. 2300 = λ x 2.52 x 1015

5. λ = 9.13 x 10-13 s-1

132

1 1013.9

693.02ln

t

6. t1/2 = 7.59 x 1011 s = 24 060 years

© JP10

Example 2A compartment on a Geiger Müller tube is filled with a solution containing 1.00g of carbon extracted from one of the Dead Sea scrolls. This gives a count rate of 1000 per hour. When a similar solution containing 1.00 g of carbon extracted from a living plant is used instead, the count rate is 1200 per hour. With no solution in the compartment, the count rate is 300 per hour.

Estimate the age of the scroll if the half life of carbon -14 is 5600 years.

The original count rate corrected for background radiation is A0 = 1200 – 300 = 900 counts per hour

The corrected count rate after the sample has decayed for t years is A = 1000 – 300 = 700 counts per hour

t = 2027 years

teAA 014

2

1

1024.15600

693.02ln yeart

900

70041024.1 te

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MEASUREMENT OF HALF LIFE

1. SIMPLY MEASURE AND PLOT HOW THE ACTIVITY VARIES WITH TIME

MEASUREMENT OF SHORT HALF LIVES

2. READ OFF

20N

t1/2

REPEAT AND AVERAGE !! OR PLOT A LOG GRAPH

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MEASUREMENT OF HALF LIFEMEASUREMENT OF SHORT HALF LIVES

LOG GRAPHS

tAA 0lnlnmxcy

teAA 0

lnA

t

gradient = - λ

2ln

2/1 t

© JP13

MEASUREMENT OF HALF LIFE

MEASUREMENT OF LONG HALF LIVES

1. RECORD ACTIVITY

2. BY WEIGHING / CHEMICAL ANALYSIS FIND THE NUMBER OF MOLES OF MATERIAL PRESENT

t

N

3. USING AVOGADRO’S NUMBER, FIND THE NUMBER OF ATOMS PRESENT

4. APPLY TO FIND λNt

Nactivity

2ln

2/1 t