1T. Norah Ali Al moneef 30.1 Radioactivity 2T. Norah Ali Al moneef Radioactive Decay: the...

T. Norah Ali Al moneef 1

CHAPTER (30)NUCLEAR PHYSICS


30.1 Radioactivity

Radioactive Decay: the spontaneous disintegration of a nucleus into a slightly lighter nucleus, accompanied by emission of particles, electromagnetic radiation, or both.

Radioactivity is a natural and spontaneous process by which the unstable atoms of an element emit or radiate excess energy in the form of particles or waves. These emissions are collectively called ionizing radiations. Depending on how the nucleus loses this excess energy either a lower energy atom of the same form will result, or a completely different nucleus and atom can be formed.


Atomic Structure


Complete Symbols

• Contain the symbol of the element, the mass number and the atomic number.

X Massnumber

Atomicnumber

Subscript →

Superscript →


XA

Z

A = number of protons + number of neutrons

Z = number of protons

A – Z = number of neutrons

Number of neutrons = Mass Number – Atomic Number


Subatomic Particles in Some Atoms

16 31 65 O P Zn

8 15 30

8 p+

8 n0

8 e-

15 p+ 30 p+

16 n0 35 n

15 e- 30 e-0


Find each of these:

a) number of protons

b) number of neutrons

c) number of electrons

d) Atomic number

e) Mass Number

Br80

35

If an element has an atomic number of 34 and a mass number of 78, what is the:

a) number of protons

b) number of neutrons


d) complete symbol


If an element has 78 electrons and 117 neutrons what is the

a) Atomic number

b) Mass number

c) number of protons

d) complete symbol

If an element has 91 protons and 140 neutrons what is the

a) Atomic number

b) Mass number


d) complete symbol


Isotopes• Atoms of the same element can have different

numbers of neutrons.• Thus, different mass numbers.• These are called isotopes.

Isotopes: elements with the same number of protons, but a different number of neutrons.

126C 13

6C 14

6C

•Chemically identical


Isotopes

• Frederick Soddy (1877-1956) proposed the idea of isotopes in 1912

• Isotopes are atoms of the same element having different masses, due to varying numbers of neutrons.

• Soddy won the Nobel Prize in Chemistry in 1921 for his work with isotopes and radioactive materials.


U235

92U

238

92

There are many types of uranium:

A

Z

Number of protons

Number of neutrons

A

Z

Number of protons

Number of neutrons


U235

92U

238

92

There are many types of uranium:

Isotopes of any particular element contain the same number of protons, but different numbers of neutrons.

A 235

Z 92

Number of protons 92

Number of neutrons

143

A 238

Z 92

Number of protons 92

Number of neutrons

146


Most of the isotopes which occur naturally are stable.

A few naturally occurring isotopes and all of the man-made isotopes are unstable.

Unstable isotopes can become stable by releasing different types of particles.

This process is called radioactive decay and the elements which undergo this process are called radioisotopes/radio nuclides.


CHARACTERISTICS OF RADIOACTIVE DECAY• It is a natural process in our universe• It is spontaneous – we cannot predict when an atom will undergo decay

Alpha radiation -

Helium nuclei

Description:

2 neutrons, 2 protons (helium nuclei)

Electric Charge:

+2

Relative Atomic Mass:

4

Penetration power:

Stopped by paper or a few cm of air

Ionisation effect:

Strongly ionising

Effects of Magnetic/Electric Field:

Weakly deflected


Alpha, Beta, and Gamma• Historically, the products of radioactivity were called

alpha, beta, and gamma when it was found that they could be analyzed into three distinct species by either a magnetic field or an electric field:


Radioactive decay results in the emission of either:• an alpha particle (a),• a beta particle (b),• or a gamma ray( ).g

Radioactive DecayIt is not uncommon for some nuclides of an element to be unstable, or radioactive.We refer to these as radionuclides.There are several ways radionuclides can decay into a different nuclide.Unstable nuclei decay releasing energy and radiation.Three types of radiationalpha (α) particles - 42He nuclei(+2 chargebeta (β) particles - electrons(- charge) positrons (+ charge)

gamma (γ) particles - high frequency electromagnetic radiation.Increasing penetration(uncharged)


• Alpha Emission: – Alpha Particle: Two protons and two neutrons

bound together and emitted from the nucleus during some kinds of radioactive decay.

– Helium nuclei with charge of 2+– Symbol: 4

2He• Net effect is loss of 4 in mass number and loss of 2 in

atomic number.


An alpha particle is identical to that of a helium nucleus.

It contains two protons and two neutrons.

Alpha Decay

XA

Z YA - 4

Z - 2 + He4

2

unstable atommore stable atom

alpha particle


XAZ Y

A - 4Z - 2 + He

42

Ra226

88 Rn222

86 + He42

Alpha Decay

Rn222

86 +Y A

Z He4

2

Rn222

86 He42+Po

21884 He

42


Alpha Particle(Helium Nucleus)

Alpha DecayAlpha Decay

Parent NucleusAm-241U-238Th-232Ra-226

Daughter NucleusNp-237Th-234Ra-228Rn-222


Beta Radioactivity

• Beta particles are just electrons from the nucleus, the term "beta particle" being an historical term used in the early description of radioactivity. The high energy electrons have greater range of penetration than alpha particles, but still much less than gamma rays.

The emission of the electron's antiparticle, the positron, is also called beta decay.


Beta Decay

A beta particle is a fast moving electron which is emitted from the nucleus of an atom undergoing radioactive decay.

Beta decay occurs when a neutron changes into a proton and an electron.


Beta DecayBeta Decay

Parent NucleusRhenium-187Potassium-40

Daughter NucleusOsmium-187Calcium-40

Beta Particle(electron)

Antineutrino


b-particle production

eXeI

ePaTh01

13154

13153

01

23491

23490

The common modes of decay

(a)The net effect of b-particle production is to change a neutron to a proton.

(b)The nuclides lie above the zone of stability.(c)The ratios of neutron/proton are too high.


Beta radiation -

high energy electron

Description:

High energy electron

Electric Charge:

-1


1/1860th

Penetration power:

Stopped by few mm of aluminium

Ionisation effect:

Weakly ionising


Strongly deflected


Gamma radiation -

Electromagnetic radiation

Description:

High energy electromagnetic radiation

Electric Charge:

0


0

Penetration power:

Reduced by several cm’s of lead or several metres of concrete

Ionisation effect:

Very weakly ionising


NO deflection


γ-radiation• γ radiation is high frequency electromagnetic

radiation. When they are emitted from the nucleus the nuclear structure stays the same, it simply represents a loss of energy


1. Proton H11 or p1

1 2. Neutron n1

0 3. Electron e0

1 or 0 1

4. Positron e0 1 or

0 1

5. Gamma ray 00

Thin mica Thin aluminiumstops BETA

Thick leadreduces GAMMA

Skin or paper stops ALPHA

The penetration power of the three types of radiation.

The effects of a field on radiation

Gamma radiation has no mass or

charge so it is not deflected.

Beta radiation has a –1 charge and a small mass so is strongly

deflected

Alpha radiation has a +2 charge but a

RAM of 4 so is only weakly deflected.

The effect of a magnetic or electric field on radiation depends upon the nature of the radiation.

Radioactive EmissionsEmission What? Penetration

Alpha 2 protons 2 neutrons

few cm in air. Stopped by paper

Beta electron 1 metre in air. Stopped by thin aluminium

Gamma electromagnetic wave

few metres of concrete will reduce their energy. Difficult to stop

1. Proton H11 or p1

1 2. Neutron n1

0 3. Electron e0

1 or 0 1

4. Positron e0 1 or

0 1

5. Gamma ray 00


Physical Half-Life• Useful parameter related to the decay constant;

defined as the time required for the number of radioactive atoms in a sample to decrease by one half

• Physical half-life and decay constant are inversely related and unique for each radionuclide

If the particle’s lifetime is very short, the particles decay away very quickly.

When we get to subatomic particles, the lifetimes are typically only a small fraction of a second!

If the lifetime is long (like 238U) it will hang around for a very long time!


Radioactive Decay• The number of atoms in a sample that decay depends on

the total number of atoms in the sample!!• This fact yields a rate of decay called an exponential decayThe Decay Constant, λ• The rate of decay is called the decay constant. It determines the half-life of a radioactive element.• The decay constant is unique for each radioactive element.• Number of atoms decaying per unit time is

proportional to the number of unstable atoms• The decay constant of radioactive decay is equal to

the reciprocal value of the half life time • Constant of proportionality is the decay constant ()

dN/dt =- N

http://www.euronuclear.org/info/encyclopedia/l/lifetimemean.htm


Radioactive Half-LifeRadioactive Half-Life

The time it takes for one-half of a radioactive sample to decay

The time it takes for one-half of a radioactive sample to decay

Look at factors of 2 One half-life (1/2)

Two half-lives (1/4)Three half-lives (1/8)

Look at factors of 2 One half-life (1/2)

Two half-lives (1/4)Three half-lives (1/8)

For Example: A material has decreased by ¼ of its original amount it has

gone through two half-lives For Example: A material has decreased by ¼ of its original amount it has

gone through two half-lives


• Number of atoms decaying per unit time is proportional to the number of unstable atoms

• Constant of proportionality is the decay constant ()∆N/ ∆ t =- N dN/dt =- N0

= - t Nt

N0

ln

Half-Life

where: Nt = number of radioactive atoms at time tN0 = initial number of radioactive atomse = base of natural logarithm = 2.71828…t = time

Nt = N0e-t

Note when t = 0, N = N0

(this is a decrease, since sign is - )


Physical Half-Life• Useful parameter related to the decay constant;

defined as the time required for the number of radioactive atoms in a sample to decrease by one half

= ln 2/T1/2 = 0.693/T1/2

• Physical half-life and decay constant are inversely related and unique for each radionuclide

• The half-life of such a process is:

= t1/2 0.693


Half-life is the time it required for half the atoms of a radioactive nuclide to decay. It can be measured in seconds, minutes, days, or years.

decay curve

8 mg 4 mg 2 mg 1 mg

initial

1 half-life

23


Half-Life ProblemRa-223 has a half-life of 12 days. If today, you

had 100 grams of this isotope, how much would remain after 36 days?

1. How many half-life periods has it undergone in 36 days?

36 days = 3 half life periods 12 days/half-life

100 g 50g 25g 12.5 g 12.5 g


Physical Half Life• Longer the half life, the longer the isotope will continue to emit radiation• Half Life REMAINS the same, no matter how many atoms present• The Half Life and Decay Constant of a material are related!

Physical Half-Life

• 238U (Uranium) : 4.47 x 109 years

• 226Ra (Radium) : 1600 years

• 99mTc (technetium) : 6.4 hours

• 140Xe (Xenon) : 13.6 seconds

• 212Po (Polonium) : 299 x 10-9 secs

• Wait a minute…….. A negatively charge particle from the nucleus?• A neutron decomposes into a proton and an electron. The proton stays in the nucleus and the electron is released.

• Beta Particles can pass through paper, but are stopped by metals

epath 01

23491

23490


• Physical Half-LifeTime (in minutes, hours, days, or years) required for the activity of a radioactive material to decrease by one half due to radioactive decay

• Biological Half-LifeTime required for the body to eliminate half of the radioactive material (depends on the chemical form)

• Effective Half-LifeThe net effect of the combination of the physical and biological half-lives in removing the radioactive material from the body

• 1 HL = 50% 2 HL = 25% 3 HL = 12.5%


Half-life, effective The period during which the quantity of a radionuclide in a biological system is reduced by half by interaction of radioactive decay and excretion due to biological processes.

Tbiol: biological half-life

Tphys:physical half-life

1. Tphysical the time taken for half of the atoms in a radioactive material to undergo decay. 2. T biological the time required for half of a quantity of radioactive material absorbed by a living tissue or organism to be naturally eliminated (biological half-life) or removed by both elimination and decay (effective half-life)

http://www.euronuclear.org/info/encyclopedia/h/half-life-biological.htm


The half life of radium Ra is 1.6x103 yr. If the sample contains 3.00x1016 nuclei find the decay constant


The half life of I-123 is 13 hr. How much of a 64 mg sample of I-123 is left after 26 hours?

t1/2 = 13 hrs

26 hours = 2 x t1/2

Amount initial = 64mg

Amount remaining = 64 mg x ½ x ½

= 16 mg


The half-life of a radioactive substance is 2.5 minutes. What fraction of the original radioactive substance remains after 10 minutes?

(1) ½ (2) 1/8 (3) ¼ (4) 1/16

Nt = N0e-t

Nt /N0= e-t

= e-0.693x10/2.5

=1/16


What is the half-life of an isotope if it decays to 12.5% of its radioactivity in 18 minutes?(a) 9 minutes(b) 8 minutes(c) 12 minutes(d) 6 minutes(e) 0.17 minutes

utes

Te

TeNN

TeN

N

T

Tmin6

5.12100

ln

180.693

180.693

5.12

100ln

5.12

100

2/1

2/1

18693.0

18693.0

0

18693.0

0

2/1

2/1

2/1


The half life of radium Ra is 1.6x103 yr. If the sample contains 3.00x1016 nuclei. Find the number of nuclei after 4.8x103 yr.


30.9 radioactive decaysIn all nuclear processes , the following quantities must be conserved1- energy (including mass energy)2- momentum ( both linear and angular)3- electric charge the number of elementary positive and negative charges must be equal before and after NT4- number of nucleons , - A is the same before and after NT

• Einstein - mass IS energy• E = mc2

• m is the mass difference between the parent nuclei and the daughters. The equation gives the energy released. Mass is converted into energy!


BASIC TYPES OF RADIOACTIVE DECAY

Alpha () decay• Occurs when atomic nuclei have too many protons and neutrons

(i.e., Are heavy) (A > 150) and is often followed by gamma and characteristic x-ray emission

• Consist of 2 protons and 2 neutrons• Mass of an alpha particle is ~8000 me

• Charge = +2 charge• Are highly ionizing• Have low penetrating abilities (only cm in air and mm in water)• Easily shielded; common types of shielding are paper, cardboard, air,

clothing; will not penetrate skin

• Changes both the mass and identity of the nucleus of the parent radionuclide• This means that the decay results in the formation of a new element as the

daughter product


Alpha Decay

A

Z XA4Z2 Y 4

2Healpha particles are very heavy and very energetic compared to other common types of radiation. These characteristics allow alpha particles to interact readily with materials they encounter, including air, causing many ionizations in a very short distance.

Are deflected by electric and magnetic fields (i.e. are charged

α-particles are relatively large particles, thus they have lots of collisions with atoms of the materials through which they pass. During these collisions the α-particles energy can cause ionisation of the materials. α- particles cause lots of ionisation


Alpha Radiation Only a hazard when inside your body

(internal hazard)

can’t penetrate skin

internal hazard

stopped by paper

found in soil, radon and other radioactive materials


Converting protons and neutrons• There are certain combinations of protons and neutrons that

are more stable than others• If the number of protons :neutrons is not correct the nucleus is

unstable.• The solution is to release certain types of radioactivity. Note:

proton (11p), neutron (1

0n)1

0n 11p + 0

–1e (– emission)1

1p 10n + 0

1e (+ emission)1

1p + 0–1e 1

0n (EC – electron capture)

What makes unstable nuclei unstable?-

If a nucleus is allowed to decrease its energy by transforming “excessive” protons (neutrons) into neutrons (protons), it will do it!

The potential experienced by nucleons is a 3D potential well. The ground-state configuration of the carbon-16 nucleus : 12

6 C

protons neutrons

energy. Each nuclear energy level can contain four particles: two protons (s=½) and two neutrons (s=½).

The processes responsible for these transformations are driven by weak interaction (the fourth fundamental interaction):

Some important transformation processes driven by weak interaction:

n e p

p n e

p e n

0r

Why N Z for light nuclei

If the electrostatic repulsion of protons can be neglected (this is the case of light nuclei: recall that the positive electrostatic energy Z2), the nucleus tends to keep approximately equal numbers of protons and neutrons.

protons neutrons

energy138 O

1/2 8.9t ms

protons neutrons

energy137 N

1/2 5730t y

protons neutrons

energy147 N

protons neutrons

energy146 C

Even in this case, the nucleus can still lower its total energy: the rest energy of neutron is slightly more than the rest energy of a proton and an electron.


β- radiation

• β – particles are high speed electrons ejected from the nuclei of radioactive atoms

• It occurs when a neutron in the nucleus splits to become a proton and an electron. The proton remains in the nucleus and the electron (β- particle) is emitted at high speeds

• Β – particles are more penetrating than α – particles (since they are smaller particles they have less collisions and so penetrate further).

• The fact that they have less collisions means that they cause less ionisation.

• They are deflected by electric and magnetic fields (i.e. they are charged particles)


• When a β particle is emitted the mass no. stays the same (since the mass of an electron is very small) and the atomic no. increases by one (as an extra proton is created with the β particle.

Beta Particles: Electrons or positrons having small mass and variable energy. Electrons form when a neutron transforms into a proton and an electron or:

neutron decay (-, lowers the N/Z ratio


Beta Radiation Hazards skin, eye and internal hazard

stopped by plastic

found in natural food, air and water


Beta decay ( b-• is a stream of negatively charged electrons.• has a very light mass of an electron• has a -1 charge• can be stopped by a piece of aluminum• has a speed that is 90% of the speed of light.• can ionize air and other particles.

)

AZ X

AZ1 Y 0

1e 00

- release of anti-neutrino (no charge, no mass) )

•Beta-minus (-) decay characteristically occurs with radionuclide's that have an excess number of neutrons compared with the number of protons (i.e., high N/Z ratio)

•Any excess energy in the nucleus after beta decay is emitted as gamma rays, internal conversion electrons or other associated radiations

Po218

84 Rn218

85 + b0-1

Th234

90 Pa23491 + b0

-1

Tl21081 Pb

21082 + b0

-1

•Beta-plus (+) decay characteristically occurs with radionuclides that are “neutron poor” (i.e., low N/Z ratio)

- release of neutrino ( )


proton decay (+, raises the N/Z ratio):


A

Z XA

Z1 Y 0+1e 0

0


Beta Particles: Electrons or positrons having small mass and variable energy. Electrons form when a neutron transforms into a proton and an electron or:


NEGATIVE BETA (ß-) DECAYOccurs when atoms have too many neutrons (i.e., Are “neutron-rich”) and decay by emitting a negative beta particle (ß-)

17

During negative beta decay, excess neutrons are converted into protons, electrons, and antineutrinos. The protons remain in the nucleus but the new electrons are emitted as negative beta particles (ß-) or negatrons.

Less ionizing than alphas due to decreased mass of negatrons Changes the identity of the nucleus but not the mass The z number is increased due to onversion of neutrons into protons


POSITRON (ß+) EMISSIONOccurs when the nucleus of the atom has too many protons (i.e., is proton-rich). It is also known as positive beta decay.

Results in a positive electron emitted from the nucleus of the proton rich atom. This positive electron is known as a positron. An additional particle, a neutrino, is also emitted from the nucleus. Neutrinos are very small particles with no electric charge. They have little or no mass and participate in weak interactions.Positrons have same mass as electronsPositrons have charge +1Positrons are less ionizing than alphasPositrons are more penetrating than alpha decay

but less than gammaThe best shielding is lead with thickness of 1 inch or more


Electron Capture

• Electron capture is one form of radioactivity. A parent nucleus may capture one of its orbital electrons and emit a neutrino. This is a process which competes with positron emission and has the same effect on the atomic number. Most commonly, it is a K-shell electron which is captured, and this is referred to as K-capture.

electron capture: (inner-orbital electron is captured by the nucleus)

Addition of an electron to a proton in the nucleus– As a result, a proton is transformed into a neutron.

p11 + e

0−1 n

10

electron capture (raises the N/Z ratio):


decay - three types

- converts one neutron into a proton and electron- no change in mass number, but different element- release of anti-neutrino (no charge, no mass)

1) - decay

2) + decay

3) Electron capture

3 31 2 eH He e

11 116 5 eC B e

- converts one proton into a neutron and electron- no change in mass number, but different element- release of neutrino

7 74 3

ECeBe e B


Gamma Radioactivity• Gamma radioactivity is composed of electromagnetic

rays. It is distinguished from x-rays only by the fact that it comes from the nucleus. Most gamma rays are higher

in energy than x-rays and therefore are very penetrating.

A

Z X* A

Z X0 0

Gamma rays are not charged particles like a and b particles.


• Gamma ray release

• Net effect is no change in mass number or atomic number.

• Gamma ray – high energy photon – Examples


GAMMMA () -rayIs a form of pure electromagnetic radiation emitted from nuclei that have excess energy. It is sometimes called gamma photon radiation.

25

Are photons emitted from unstable nuclei to rid themselves of excess energy. Gamma photons are subatomic packets of pure energy. They are higher in energy of ~ 1 x 10-12 J). with high frequency and more penetrating than the photons that make up visible light.When atoms decay by emitting a or b particles to form a new atom, the nuclei of the new atom formed may still have too much energy to be completely stable.

GAMMMA RAYS AND X RAYSHave the same properties except for their origin Gammas come from within the nuclei of atoms X-rays come from outside the nuclei

Both are electromagnetic energy in the form of emitte photons

27


Have the same properties except for their origin Gammas come from within the nuclei of atoms X-rays come from outside the nuclei

Both are electromagnetic energy in the form of emitted photons

27


g decay

- conversion of strong to coulombic E- no change of A or Z (element)- release of photon- usually occurs in conjunction with other decay

3 * 32 2He He


Penetration of Matter• Though the most massive and most energetic of radioactive

emissions, the alpha particle is the shortest in range because of its strong interaction with matter. The electromagnetic gamma ray is extremely penetrating, even penetrating considerable thicknesses of concrete. The electron of beta radioactivity strongly interacts with matter and has a short range.

89

Classification of Decays

Neutrons

Pro

tons

a

b-

a-decay: • emission of Helium nucleus• Z Z-2• N N-2• A A-4

e--decay (or -decay)• emission of e- and n• Z Z+1• N N-1• A = const

e+-decay • emission of e+ and n• Z Z-1• N N+1• A = const

e+EC

Electron Capture (EC)• absorbtion of e- and emiss

n• Z Z-1• N N+1• A = const


Four types of radioactive decay1) alpha (a) decay - 4He nucleus (2p + 2n) ejected2) beta () decay - change of nucleus charge, conserves mass3) gamma (g) decay - photon emission, no change in A or Z4) spontaneous fission - for Z=92 and above, generates two smaller nuclei

An Example….

Parent

U238 → 8 alpha + 6 beta = ?92 protons

146 neutrons

An Example….

ParentU238 → 8 alpha + 6 beta

8 {lose 2 protons} + 6 (add 1 proton) {lose 2 neutrons}

- 16 protons + 6 protons- 16 neutrons

An Example….



- 16 protons + 6 protons = - 10 protons- 16 neutrons- 32 atomic mass - 10 atomic

number

An Example….




number

U238 – 32 = “X” 206

An Example….




number

U238 – 32 = “X” 206

92 protons – 10 protons = 82 protons

An Example….




number

U238 – 32 = “X” 206

92 protons – 10 protons = 82 protons

“X” 206 with 82 protons

Which type of radioactive emission has a positive charge and weak penetratingpower?(1) alpha particle (3) gamma ray(2) beta particle (4) neutron

When a neutron is transformed into a proton what else is emitteda) alpha b) position c) 1H d) electron e) none of these


What is the missing particle?


A. Radioactive Decay


Which of the following statements about alpha particles (α) is correct? A. They are massless particles. B. They are electromagnetic wave. C. They are traveling at the speed of light. D. They will be deflected by electric and magnetic field.

There are two radioactive sources A and B, both of them have the same number of active nuclei at the beginning. After 10 days, the number of active nuclei in B is more than A. Which of the following statements is correct? A. The mass of A is larger than B. B. The mass of B is larger than A. C. The half-life of B is longer than A. D. The half-life of A is longer than

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