Radioactivity

Manos PapadopoulosNuclear Medicine DepartmentCastle Hill HospitalHull & East Yorkshire Hospitals NHS Trust

RADIOACTIVE DECAY

Only certain combinations of nucleons form a stable nucleus

Unstable nuclei

spontaneous nuclear transformation

formation of new elements

emission of radiation

These unstable isotopes are called

radioactive isotopes

The spontaneous nuclear transformation is called

radioactivity or radioactive decay / disintegration

RADIOACTIVE DECAY

An unstable “parent” (P) nuclide is transformed into a more

stable daughter (D) nuclide through various processes

where d1 + d2 + … signify the emitted particles

The process is usually accompanied by the emission of

gamma radiation

...21 ddDP

RADIOACTIVITY

ACTIVITY

Activity (A) is defined as:

the number of radioactive atoms (N) undergoing nuclear

transformations per unit time (t)

dt

dNA

UNITS OF ACTIVITY

Traditionally, expressed in units of curies (Ci)

1 Ci = 3.7 × 1010 disintegrations/second

Typical activities for imaging: 0.1 to 30 mCi

for therapy: up to 300 mCi

The Système International (SI) unit is the becquerel

(Bq)

1 Bq = 1 disintegration/second

DECAY CONSTANT

Radioactive decay is a random process

The number of atoms decaying per unit time (dN/dt)

is proportional to the number of unstable atoms (N)

where λ is the transformation constant (or decay constant)

being characteristic of each radionuclide

ANdt

dN N

dt

dN

HALF-LIFE

The half-life (τ1/2) is defined as:

the time required for the number of radioactive atoms in a

sample to decrease by one half

λ and τ1/2 are related as follows:

where ln2 denotes the natural logarithm of 2

Both λ and τ1/2 are

unique for each radionuclide

2/12/1

693.02ln

RADIOACTIVE DECAY LAW

The rate at which a radioactive isotope disintegrates is defined by the following DECAY LAW:

Where N(t): number of radioactive atoms at time t

N0: initial number of radioactive atoms (at time zero)

τ1/2: half-life

e: base of natural logarithm ( ≈ 2.718) λ: decay constant

t

t eNeNtN

2/1

2ln

00

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

0 10000 20000 30000 40000 50000

Years

Nu

mb

er o

f 14

C a

tom

s

τ1/2 = 5730y

5730

1/ 2 1/ 2 1/ 20 0 0 0/ 2 / 4 / 8t t tN N N N

N0

RADIOACTIVE DECAY LAW

PROBLEM

A nuclear medicine technologist injects a patient with

800 MBq of [99Tcm]-SestaMIBI (τ1/2=6.02 hours). One

hour later the patient is imaged. Assuming that none of

the activity is excreted, how much activity remains at

the time of imaging?

SOLUTION

A0 = 800 MBq

λ = 0.693/6.02 hours = 0.115 hours-1

t = 1 hour

MBqA

MBqA

eMBqA

eMBqA

eAAhourhours

t

713

891.0800

800

800115.0

1)115.0(

0

1

RADIOACTIVE DECAY TYPES

Radioactive decays are classified by the types of particles that are

emitted during the decay:

Alpha decay (α)

Beta decay (β)

Gamma decay (γ)

Isomeric transition (ΙΤ)

Electron capture (ε or ec)

Internal conversion (IC)

Spontaneous fission (SF)

Neutron emission (n)

ALPHA DECAY

Spontaneous emission of an alpha (α) particle

from the nucleus

An α particle is a Helium nucleus

containing two protons and two neutrons

42particle He

ALPHA DECAY

Typically occurs Heavy nuclides (A>150)

Emission of gamma and characteristic X-Rays

DP A

ZAZ

42

ALPHA DECAY

Alpha particle emitted from the atomic nucleus Alpha particle and daughter nucleus have equal and

opposite momentums

241 237 495 93 2Am Np He

ΑLPHA PARTICLES

Not used in medical imaging

range in solids and liquids

few micrometres

range in air

few centimetres

Alpha particles cannot penetrate the dead layer of the

skin

Health hazard only when enter the body

ΒETA DECAY

Beta positive (β+) decay:Proton (p+) → neutron + positron (β+) + neutrino

Beta negative (β-) decay:Neutron → proton (p+) + electron (β-) + antineutrino

_1

1 vDP AZ

AZ

vDP AZ

AZ

1

converts one neutron into a proton and an electron no change of A, but different element occurs with nuclides with an excess number of neutrons

3 31 2 eH He e

β- DECAY

β+ DECAY

11 116 5 eC B e

converts one proton into a neutron and a positron no change of A, but different element occurs with nuclides with an excess number of protons

ΒΕΤΑ PARTICLES Electron (β-) Positron (β+) As beta particles traverse lose energy Positron interacts with an electron Annihilation radiation

two opposite directed 511 keV photons threshold for positron decay 2×511 keV = 1.02 MeV

Used in Medical Imaging Positron emitting radiopharmaceuticals Positron Emission Tomography (PET)

Anti-particles

ΒΕΤΑ PARTICLES

Positron Emission and Annihilation

GAMMA DECAY

Nucleus in excited state (surplus of energy)

Release of excess energy emission of γ-rays

nucleus returns to its ground state

XX AZ

AZ

*

GAMMA DECAY

3 * 32 2He He

no change of A or Z – same element release of photon usually occurs in conjunction with other decay

GAMMA DECAY

Decay scheme of Cs13755

ISOMERIC TRANSITION

Half-lives from 10-12 sec – 600 years

These excited states are called

metastable or isomeric states

No change in

atomic number

mass number

neutron number

ISOMERIC TRANSITION

Isomeric transition is a radioactive decay process

excited nucleus decays to lower energy state

gamma radiation emitted

no emission of corpuscular radiation (i.e. particles)

no capture of particle by the nucleus

XX AZ

mAZ

Mo-99 DECAY SCHEME

Mo-99 DECAY SCHEME

99Mo decays by β- decay

into 99Tcm (i.e. 99Tcm metastable state of 99Tc)

half-life = 66 hours

99Tcm decays by isomeric transition

into 99Tc ground state with 6 hr half-life

half-life = 6.01 hours

ELECTRON CAPTURE

Nucleus captures orbital electron (usually a K- or L-shell)

conversion of a proton into a neutron

simultaneous ejection of a neutrino

Emission of

characteristic X-rays

Auger electrons

energyvYeX AZ

AZ

1

7 74 3

ECeBe e B

ELECTRON CAPTURE

converts one proton into a neutron no change of A – but different element occurs with nuclides with an excess number of protons

Tl-201 DECAY SCHEME

201Tl decays by electron capture

into 201Hg

half-life = 73.1 hours

201Hg-characteristic X-Rays

68.9-80.3 keV

Emission of characteristic X-Rays used in myocardial perfusion

INTERNAL CONVERSION

Nucleus in excited state (surplus of energy)

De-excitation through

ejection of a tightly bound electron (K- or L-shell)

alternative mechanism to electron capture

No change of Z – same element

SPONTANEOUS FISSION

Heavy nuclei decay by splitting into two daughter

nuclei

release of neutrons

release of energy

SUMMARY I

Half-Life (τ1/2)

the time required for radioactivity to decay to half its initial value

Decay Constant (λ) the probability that an atom will decay/transform per

unit time

Activity rate of decay/transformation

At = A0 e-λt

SUMMARY II

Radioactive Decay Modes depending on the emitted radiation

Alpha particles Helium nuclei – used in radionuclide therapies

Beta particles used in imaging (e.g. positrons - PET)

used in therapy (e.g. 131I, 32P)

Gamma ray photons used in imaging (e.g. 99Tcm, 201Tl)

THE END

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