radioactive

Chapter 17

Radioactivity

17.1 Radioactive decay

(1 hour)

Radioactivity

Half-lifeT1/2 = ln2/λ

Radioactive decay α,βand γ

ActivityAt=-dN/N = λN

Decay constantλ= -(dN/N)/N

The use of radioisotopes as a

tracers

The biological effect of radiation

1. Absorbed dose2. Dose equivalent

Conceptual map

Chapter 17

OBJECTIVES17.1 Radioactive decay

1. Explain radioactive decay as a spontaneous and random processes

2. Understand α, β+,β-, λ decay processes

17.1 Radioactive decay

• Radioactivity is the process where a nucleus is spontaneously breakdown and emits particles and rays.

• Radioactive decay is a process where a unstable nucleus splits and transmutes into less massive daughter nuclei and energetic particles

1.Radioactivity decay – spontaneous and random

• There are three types of radioactive emission from the nuclei of the radioactive atoms:

• Alpha (α) – Alpha particles are helium nuclei with two neutrons and two protons. Each alpha particle is double charged. They are good ionizers, do not have high penetrating power.

• Beta ( β) – the beta particles have the same mass and charge as an electron. Their velocity are high and they process high penetrating power.

• Gamma (γ) – Gamma rays are high-energy electromagnetic radiations of very short wavelengths. They are not particle and do not have charge, but have high penetrating power.

• The decay is independent of physical conditions and chemical bonding, but it depends only on the type of atom and the number of these atoms.

• Cannot predict which nucleus will decay• Can predict the number of nuclei that will

decay in a given time• Every nucleus has the same chance of

decaying per unit time

2. α, β+, β-, and γ decay processes

• Alpha decay : is the emission of a helium nucleus from the nucleus of heavy radioactive element (Z > 82)

• General equation: • Alpha particles: Symbol He @ , Charged

+2e and the penetrating power in air is 5 cm• Example :

QHeYX AZ

AZ

42

42

2

4

HeThU 42

23490

23892

3.Beta decay

• Negatron decay (β-)• It happen when the number of neutrons more

then protons in a nucleus and it caused unstable condition. The transformation of a neutron to proton is can give the ratio of N/Z for stable nucleus.

• A neutron inside the nucleus changes to an electron

• General equations :• Example :

011YX A

ZAZ

01

147

146 NC

)()(01

11

10 noantineutrielectronpn

• positron decay (β+)• It will happen when the number of protons

more then neutrons in a nucleus and it caused unstable condition. The transformation of a proton to neutron is can give the ratio of N/Z for stable nucleus.

• General equations :

• Note: Neutrino have a same characteristic with antineutrino

• Example:

)()(01

10

11 neutrinopositronnp

011YX A

ZAZ

01

157

152 NO

4.Gamma decay (γ)

• Gamma rays are emitted when an excited nucleus jumps to lower energy levels. This will happen when the nucleus decays into alpha or beta particles. Thus gamma-ray emission often associates with other type of decays.

• General equation: YX AZ

AZ

• Example 1:

A radioactive isotope decay and emits one alpha and two beta particles consecutively. Write the formula for the nuclides produced

Answer

XAZ

XeHeX AZ

AZ

401

42 2

Summary

• Radioactivity decay – spontaneous and random

• Alpha decay

• Negatron decay (β-)

• positron decay (β+)

• Gamma decay (γ)

QHeYX AZ

AZ

42

42

011YX A

ZAZ

011YX A

ZAZ

YX AZ

AZ

Chapter 17Radioactivity

17.2 Decay constant and half-life

(1 hour)

Radioactivity






tracers



Conceptual map

Chapter 17

OBJECTIVES17.2 Decay constant and half-life

1. State and use the decay law dN/dt=-λN

2. Define activity and decay constant

3. Derive and use N = Noe-λt or A=AOe-λt.

4. Define and use the half-life (T1/2)

17.2 Decay constant and half-life

• The basic of decay law is decay rate is directly proportional to the number of atoms, N present at that instant.

• where: • At, activity is defined as the disintegrations per

second by the radioactive nucleus. It is measured in Becquerel. 1 Bq = 1 disintegration per second

dt

dN

Ndt

dNAt

• Another unit is curie. 1 Ci =3.7 x 1010 disintegrations per second = 3.7x1010 Bq

• is decay rate• N is number of nuclei remain at time t from initial• λ is decay constant• Decay constant ,

• λ for radioactive nucleus is the probability of 1 radioactive nucleus will decay in 1 second.

Ndt

dN

• From,

• by integrating this equation from t =0 when N = N0 to t = t when N = N

dtN

dN

Ndt

dN

tN

N

tN

NN

dN

o

tNN

N

N

o

o

ln

][ln 0

tot

to

t

o

eAA

or

eNN

eN

N

The decreasing of the radioactive nuclues number is exponen to the time and this changing is direct proportional to remaining activity.

The half-life of the nuclide is the time taken for half of initial number of unstable nuclei to decay

Half-life, T1/2

Time, t

• From equation of:

• When t =T1/2 , N =N/2

• So,

toeNN

2ln

1ln2ln

2ln1ln

ln2

1ln

2

12

2/1

2/1

2/1

2/1

2/1

2/1

T

T

T

e

e

eNN

T

T

To

o

Mean life, τ = 1/λ

So, half-life

T1/2 = τln2

T1/2 = 0.693 τ

• Example 2: The number of radioactive nuclides from a radioactive

source has reduced to 1/6 from its original value in 60 seconds. Find the decay constant for this source

Answer :

Cross multiple, e-λt=6 λt = ln6

in both sides: λ = ln 6 / t p = ln6 / 60 = 2.786 x 10-2 s-1

tt

t

o

to

ee

eN

NeNN

1

2

1

• Example 3:

An with half-life 24 days decay into

how long it will take 80 % of the sample isotope to change to ?

Answer

From the equation of

Th23490

Pa23491

Pa23491

2/1

1

)2

1( T

oN

N

2/1

1

)2

1(

100

20 T

2.05.0 2/1

1

T

Take log to both sides:

73.55

3219.224

5.0log

2.0log

2.0log5.0log

2/1

2/1

t

t

T

t

T

t

days

summary

• At, activity• Decay constant

Ndt

dNAt

Ndt

dN

•The half-life of the nuclide is the time taken for half of initial number of unstable nuclei to decay

2ln2/1 T

Chapter 17Radioactivity

17.3 The use of radioisotopes

17.4 The biological effect of ionization radiation

(1 hour )

Radioactivity






tracers



Conceptual map

Chapter 17

OBJECTIVES

17.3 The use of radioisotopes

Explain the use of radioisotopes as tracers


Define and use the absorbed dose and equivalent dose formula

17.3 The use of radioisotope

• The process is not unchanged though the radioactive nuclides become part of the compound.

• The stable atoms are replaced with radioactive nuclides in a chemical and thus the path of the chemical through the system can be traced.

1.Use of radioisotopes as tracers

• Examples:

Oil leakage: A gamma emitter is added to the oil. If there is a leak there will be an unusually high count rate close to the crack.

To investigate metabolic pathways or blood flow: A small quantities of iodine-131 ( a beta and gamma emitter) with a half-life of 8 days in injected into a patient’s bloodstream and later build up in the kidneys. The process of the iodine is measured with Geiger counter outside the body around the kidney region. If there is a blockage, the count rate will rise . To investigate metabolic pathways or blood flow: A small quantities of iodine-131 ( a beta and gamma emitter) with a half-life of 8 days in injected into a patient’s bloodstream and later build up in the kidneys. The process of the iodine is measured with Geiger counter outside the body around the kidney region. If there is a blockage, the count rate will rise .

Technectium-99 : The Technectium-99, a gamma emitter, is used to label compound which is absorbed by tissues to be studied. The gamma radiations can be recorded by detectors with outputs are combine to form an image. This technique can be study the kidney function.


• This is a measure of the radiation dose (as energy per unit mass) actually absorbed by by a specific object such as patients hand or chest.

• Its SI unit is the Gray (Gy) and the older unit is rad (from radiation absorbed dose)

• 1 Gy = 1 J/kg = Rad

1. Dose absorbed

2. Dose Equivalent

• Although different types of radiation (gamma rays and neutrons,say) may deliver the same amount energy to the body, they do not the same biological effect.

• The dose equivalent allow us to express the biological effect by multiplying the absorbed dose ( in Grays or rads) by numerical RBE factor (from relative biological effectiveness).

• For X-rays and electrons, for example, RBE = 1; for slow neutrons RBE = 5;for Alpha particles RBE = 10; and so on.

• Personnel-monitoring such as film badges register the dose equivalent.

• Dose equivalent (in rems) = dose (in rads ) x RBE

• Or

• Dose equivalent (in Sivert, Sv) = dose (in Grays) x RBE

• Its unit SI is (Sievert,Sv), 1 Sv = 100 Rem

• The recommendation of National Council on Radiation Protection is that no individual who is (nonocupationally) exposed to radiation should receive a does equivalent greater than 5 m Sv = (0.5 rem) in any year.

• ExampleWe have seen that a gamma-ray dose of 3 Gy lethal to half the people exposed to it. If the equivalent were absorbed as heat, what rise in body temperature would result? (Assume that the specific heat of the human body is 4180 J/Kg.K

Answer:From the equation of Q = mc ΔT

, , where Q/m = absorbed dose

= =7.2 x 10-4 K ≈ 700 μK

c

mQT

/

4180

3

summary1.Use of radioisotopes as tracers

2.The biological effect of ionization radiation-

-

Dose absorbed

Dose Equivalent

radioactive

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