Chapter 2. Radiation

Chapter 2. Radiation

1.Radioactivity

2.Radiation interaction with Matter 3.Radiation Doses and hazard Assessment

1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides

2.1 Radioactivity

1) Overview

Radioactive nuclei and their radiations have properties that are the basis of many of the ideas and techniques of atomic and nuclear physics.

40K

The uranium decay series.

222Rn is responsible for higher levels of background radiation in many parts of the world. because it is a gas and can easily seep out of the earth into unfinished basements and then into the house

Radioactivity in Nature

Radon

5

Radioactive Decaystransmutations of nuclides

Radioactivity means the emission of alpha () particles, beta () particles, or gamma photons () etc. from atomic nuclei. The term radioactivity was actually coined by Marie Curie

Radioactive decay is a process by which the nuclei of a nuclide emit , or rays etc.

In the radioactive process, the nuclide undergoes a transmutation, converting to another nuclide.

1) Overview

Conservation of charge

Conservation of the number of nucleons A

Conservation of mass/energy (total energy)

Conservation of linear momentum

Conservation of angular momentum

2) Types of Radioactive Decay

Apparatus similar to that used by Henri Becquerel to determine the magnetic deflection of radioactive decay products. The magnetic field is perpendicular to the direction of motion of the decay products.

The law of conservation of mass and energy covers all reactions. Sum of mass before reaction = Sum of mass after reaction + Q Q = Sum of mass before reaction - Sum of mass after reaction

Energy in Radioactive DecayBefore decay

Recoiling nucleus

Interesting Items:Spectrum （能谱） of particlesEnergy in gamma decayEnergy in beta decayEnergy in alpha decay

3) Energetics of Radioactive Decay

Gamma Decay Energy

Gamma, , rays are electromagnetic radiation emitted from atomic nuclei. The bundles of energy emitted are called photons.

Ei ____________

h v

Ef ____________

Eothers _________

Excited nuclei are called isomers, and de-excitation is called isomeric transition (IT). Energy for photons

h v = E i - E f

a)

Types of Isomeric Transitions and their Ranges of Half-life

Radiation Type Symbol J Partial half life t (s)

Electric dipole E1 1 Yes 5.7e-15 E–3 A–

2/3

Magnetic dipole M1 1 No 2.2e-14 E–3 Electric quadrupole E2 2 No 6.7e-9 E–5 A–

4/3

Magnetic quadrupole M2 2 Yes 2.6e-8 E–5 A–

2/3

Electric octupole E3 3 Yes 1.2e-2 E–7 A–2

Magnetic octupole M3 3 No 4.9e-2 E–7 A–

4/3

Electric 24-pole E4 4 No 3.4e4 E–9 A–8/3

Magnetic 24-pole M4 4 Yes 1.3e5 E–9 A–2

Nature of Gamma Transitions

Various Gamma Transitions in 7Li

3/ 2– ground state½ – 0.778 MeV

7/ 2+ 4.64 MeV

½+ 6.54 MeV

M1

E1

E3

M3

M2

Gamma Decay Energy and Spectrum

Gamma transition of 7Li

Gamma Ray Spectrum of O18

E

Intensity 2h+2+0+

3.27 MeV

1.981.98 MeV

3.27 MeV

5.25 MeV

a)

Intensities of the peaks are related to the population of the excited state as well as the half life of the transition.

Eγ is the energy of the gamma photon, E* is the excitation energy (above the ground state) of the initial parent nucleus, and Ep is the recoil kinetic energy of the resulting ground-state nuclide.

the kinetic energy of the recoil nucleus is negligible

=Q

15

An Ideal Alpha Spectrum

MeV

No.of

8 10

211Po particle energy: | 98.9% 10.02 MeV | 0.5% 9.45 | 0.5% 8.55 |

| 207Pb |7/2+ 0.90 MeV – 0.5%5/2+ 0.57 MeV – 0.5%1/2+ –

98.9%

b)How is alpha energy evaluated and determined? What is a typical alpha spectrum and why?

Expeimentally?

What is the initial kinetic energy of the alpha particle produced in the radioactive decay:

The Qα value in mass units

17

c) Beta Decay Spectra and Neutrino

Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying the missing energy.

A Typical Beta SpectrumIntensityor # of

Energy of

E max

A Beta Decay Scheme

PZ DZ+1 + – + v

?

c)

The mass of the neutrino is negligibly small.

19

d) Positron Decay Energy

Positron Emission

+

–

1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides

2.1 Radioactivity

4) Characteristics of Radioactive Decay

137mBa decay data,

Stochastic process

Radioactivity or decay rate A is the rate of disintegration of nuclei. Initially (at t = 0), we have No nuclei, and at time t, we have N nuclei. This rate is proportional to N, and the proportional constant is called decay constant .

dNA = – ––––– = N Integration gives

d t

ln N = ln No – t or N = No e – t

Also A = Ao e – t

activity or decay rate A decay constant

the number of decays ortransmutations per unit of time

specific activity

normalized to the mass or volume of the sample

Many safety limits and regulations are based on the specific activity concept

Radioactive Decays 24

Variation of N as a function of time t

N No

t

N = No e - t

Also A = Ao e - t

Radioactive Decay Kinetics -exponential

Number of radioactive nuclei decrease exponentially with time as indicated by the graph here.

As a result, the radioactivity vary in the same manner.

Note N = A

No = Ao

25

Half-life and its measurementVariation of N as a function of time t

N No

t

N = No e - t

Also A = Ao e - t

Be able to apply these equations!

N = No e– t

A = Ao e – t

ln N = ln No – t ln A = ln Ao – t

Determine half life, t½

Ln(N or A)

t

ln N1 – ln N2

= ––––––––––– t1 – t2

t½ * = ln 2

Half life is not affected by chemical and physical state of matter.

Condition?Very long?

Decay Probability for a Finite Time Interval

does not decay

does decay

As the time interval becomes very small, i.e., t —>Δt « 1,

p(t)dt, probability a radionuclide, which exists at time t = 0, decays in the time interval between t and t + dt

the probability distribution function for when a radionuclide decays.

Mean Lifetime

calculate the average lifetime of a radionuclide by using the decay probability distribution

Ln A

t

Decay by competing Processes

The probability fi that the nuclide will decay by the ith mode is

λ is the overall decay constant

<-How to calculate

What is the probability 64Cu decays by positron Emission? The decay constants for the three decay modes of this radioisotope are λ β+ = 0.009497 h-1, λ β- = 0.02129 h-1, and λ EC = 0.02380 h-1.

The overall decay constant is

The probability that an atom of 64Cu eventually decays by positron emission is

1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics decay transients6) Naturally Occurring Radionuclides

2.1 Radioactivity

a) Decay with Production

Q(t) is the rate at which the radionuclide of interest is being created

N(t) -> Ne = Q0/λ t -> the equilibrium condition

the special case that Q(t) = Q0

(a constant production rate)

means?

Example How long after a sample is placed in a reactor is it before the sample activity reaches 75% of the maximum activity? Assume the production of a single radionuclide species at a constant rate of Q0 s-1 and that there initially are no radionuclides in the sample material.

A(0)=0A(t) = Qo[1-exp(-λt)] Amax = Q0

0.75Qo = Qo[1-exp(-λt)]

b) Three Component Decay Chains

Daughter Decays Faster than the Parent λI < λ2,

transient equilibrium: daughter's decay rate is limited by the decay rate of the parent.

λI << λ2,

The activity of the daughter approaches that of the parent. This extreme case is known as secular equilibrium( 久期平衡 ).

Daughter Decays Slower than the Parent

A2(t)= A2(0)e-λ2t +

A2(t)= A2(0)e-λ2t +

the daughter decays in accordance with its normal decay rate.

1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides

2.1 Radioactivity

6.1 Cosmogenic Radionuclides

The most prominent of the cosmogenic radionuclides are tritium 3H and 14C.

14N(n,T)12C and 16O(n,T)14N

14N(n,p)14C

12.3 a HTO

5730 a CO2

electron?

6.2 Singly Occurring Primordial ( 原生） Radionuclides

The solar system was formed about 5 billion years ago. These radionuclides are seen to all have half-lives greater than the age of the solar system. Of these radionuclides, the most significant are 40K and 87Rb since they are inherently part of our body tissue.

Families of Radioactive Decay Series

Radioactive Decay Series of 238U238U92 234Th90 + 42 (t1/2 4.5e9 y)

234Th90 234Pa91 + – + (t1/2 24.1 d)

234Pa91 234U92 + – + (t1/2

6.7 h) 234U92 . . . (continue)

. . .206Pb82

Only alpha decay changes the mass number by 4.

There are 4 families of decay series.4n, 4n+1?, 4n+2, 4n+3,

n being an integer.

Each naturally occurring radioactive nuclide with Z > 83 is a member of one ofthree long decay chains,

thorium (4n), uranium (4n + 2), and actinium (4n + 3)

The Decay Path of 4n + 2 or 238U Family 238U234U234Pa

234Th230Th226Ra

222Rn 218At

218Po214Po214Bi

214Pb

210Po 210Bi206Pb 210Pb 206Tl 210Tl 206Hg

Minor route

Major route

decay

decay

Radioactivity - 238U radioactive decay series

Radioactivity - 239Np radioactive decay series

The Decay Paths of the 4n + 1 or 237Np93 Family Series237Np93

233U92 (2e6 y)(1.6e5 y) 233Pa91

229Th90

225Ac89 (7300 y; minor path) (10 d) 225Ra88

221Fr87

217At85

213Po84 (1 min) 209Bi83 213Bi83

209Pb82

209Tl81

2.14 x 106 y,

1) Overview2) Types of Radioactive Decay3) Energetics of Radioactive Decay4) Characteristics of Radioactive Decay5) Decay Dynamics6) Naturally Occurring Radionuclides

2.1 Radioactivity