11/29/2010

1

Nuclear Binding, Radioactivity

• Sections 32-1 – 32-9

Physics 1161: Lecture 25

RadioactivitySpontaneous emission of radiation from the nucleus of an unstable isotope.

Marie Curie1867 - 1934

Wilhelm Roentgen1845 - 1923

Antoine Henri Becquerel1852 - 1908

Nucleus = Protons+ Neutrons

nucleons

A = nucleon number (atomic mass number)

Gives you mass density of element

Z =

N =

A=N+Z

Nuclear Physics

Li6

3

A

Z

Periodic_Table

A material is known to be an isotope of lead.

Which of the following can be specified?

1. The atomic mass

number

2. The neutron

number

3. The number of

protons

But protons repel one

another (Coulomb

Force) and when Z is

large it becomes

harder to put more

protons into a nucleus

without adding even

more neutrons to

provide more of the

Strong Force. For this

reason, in heavier

nuclei N>Z.

# neutrons vs # protons Where does the energy released in the nuclear

reactions of the sun come from?

1. covalent bonds

between atoms

2. binding energy of

electrons to the

nucleus

3. binding energy of

nucleons

11/29/2010

2

Strong Nuclear Force

• Acts on Protons and Neutrons

• Strong enough to overcome Coulomb

repulsion

• Acts over very short distances

Two atoms don’t feel force

Hydrogen atom: Binding energy =13.6eV

Binding energy of deuteron = or

2.2Mev!

2.2 × 10 6 eV

Simplest Nucleus: Deuteron=neutron+proton

neutron proton

Very strong force

Coulomb force

electron

proton

Strong Nuclear Force

(of electron to nucleus)

Binding Energy

Einstein’s famous equation E = m c2

Proton: mc2 = 938.3MeV

Neutron: mc2= 939.5MeV

Deuteron: mc2 =1875.6MeV

Adding these, gives

1877.8MeV

Difference is

Binding energy,

2.2MeV

MDeuteron = MProton + MNeutron – |Binding Energy|

Iron (Fe) has the most binding energy/nucleon. Lighter have

too few nucleons, heavier have too many.

BIN

DIN

G E

NE

RG

Y i

n M

eV

/nu

cle

on

92238U

10

Binding Energy Plot

Mass/Nucleon vs Atomic Number

Fusion

Fission

E = mc2

E: energy

m: mass

c: speed of light

c = 3 x 108 m/s

11/29/2010

3

E = mc2

• Mass can be converted to energy

• Energy can be converted to mass

• Mass and energy are the same

thing

Mass Defect in Fission

• When a heavy element (one

beyond Fe) fissions, the resulting

products have a combined mass

which is less than that of the

original nucleus.

Mass Defect of Alpha ParticleMass Defect of Alpha Particle

Mass difference = 0.0304 u

Binding energy = 28.3 MeV

Fusion product has less mass than the sum of the parts.

Which of the following is most correct for the

total binding energy of an Iron atom (Z=26)?

1 2 3 4

0% 0%0%0%

1. 9 MeV

2. 234 MeV

3. 270 MeV

4. 504 Mev

BIN

DIN

G E

NE

RG

Y i

n M

eV

/nu

cle

on

αααα particles: nucleii 24He

ββββ−−−− particles: electrons

γγγγ : photons (more energetic than x-rays)

3 Types of Radioactivity

Radioactive

sources

B field into

screen

detector

Alpha Decay

• Alpha decay occurs when there are too many protons in the nucleus which cause excessive electrostatic repulsion.

• An alpha particle is ejected from the nucleus.

• An alpha particle is 2 protons and 2 neutrons.

• An alpha particle is also a helium nucleus.

• Alpha particle symbol: 42He

11/29/2010

4

Beta Decay• Beta decay occurs when neutron to proton ratio is

too big• A neutron is turned into a proton and electron and

an antineutrino• The electron and the antineutrino are emitted

Gamma Decay

• Gamma decay occurs when the nucleus is at too high

an energy

• Nucleus falls down to a lower energy level

• High energy photon – gamma ray - is emitted

92238U→ 90

234 Th + αα: example 24He = αrecall

β: example

Decay Rules

1) Nucleon Number is conserved.

2) Atomic Number (charge) is conserved.

3) Energy and momentum are conserved.

γ: example γ00* +→ PP A

Z

A

Z

1) 238 = 234 + 4 Nucleon number conserved

2) 92 = 90 + 2 Charge conserved

−−+→ e01

1

1

1

0 pn

Needed to conserve

energy and momentum.

ν00+

A nucleus undergoes α decay. Which of the

following is FALSE?

1. Nucleon number decreases by 4

2. Neutron number decreases by 2

3. Charge on nucleus increases by 2

The nucleus undergoes decay. Which

of the following is true?β− 90

234 Th

1. The number of protons in the

daughter nucleus increases by one.

2. The number of neutrons in the

daughter nucleus increases by one.

Radioactive Decay

238

92U →

234

90Th→234

91Pa →

11/29/2010

5

U 238 Decay

• Decay Series

Nuclear Decay Links

• http://physics.bu.edu/cc104/uudecay.html

• http://www.physics.umd.edu/lecdem/honr22

8q/notes/U238scheme.gif

• http://www.physics.umd.edu/lecdem/honr22

8q/notes/fourdecschemes.gif

Which of the following decays is NOT allowed?

92238U→ 90

234 Th + α

HePbPo 4

2

210

82

214

84 +→

ν000

1

40

20

40

19 pK ++→ −− e

γ+→ NC 14

7

14

6

1.

2.

3.

4.

Decays per second, or “activity”:

If the number of radioactive

nuclei present is cut in half, how

does the activity change?

∆N∆t

= −λNNo. of nuclei

present

decay constant

1. It remains the same

2. It is cut in half

3. It doubles

Decays per second, or “activity”

Start with 16 14C atoms.

After 6000 years, there are only 8 left.

How many will be left after another 6000 years?

∆N∆t

= −λN No. of nuclei

present

decay constant

Every 6000 years ½ of atoms decay

1. 0

2. 4

3. 6

time

N(t ) =N0e−λt =N0 ⋅2

−t

T1/2

Decay Function

11/29/2010

6

Instead of base e we can use base 2:

N(t ) =N0e−λtSurvival:

No. of nuclei present

at time t

No. we started with

at t=0

e−λt = 2

−t

T1/2

T1/2 =

0.693

λwhere

Then we can write N(t ) =N0e−λt =N0 ⋅2

−t

T1/2

Half life

Radioactivity Quantitatively

∆N∆t

= −λN

No. of nuclei

present

decay constant

Decays per second, or

“activity”

Carbon Dating

• Cosmic rays cause transmutation of Nitrogen to Carbon-14

• C-14 is radioactive with a half-life of 5730 years

– It decays back to Nitrogen by beta decay

• The ratio of C-12 (stable) atoms to C-14 atoms in our

atmosphere is fairly constant – about 1012/1

• This ratio is the same in living things that obtain their carbon

from the atmosphere

1 14 1 14

0 7 1 6n N H C+ → +

14 0 14

6 1 7C e N−→ +

You are radioactive!

One in 8.3x1011 carbon atoms is 14C which β− decays with a ½

life of 5730 years. Determine # of decays/gram of Carbon.

∆N∆t

= −λN

( )

××

=

11

23

14103.8

11002.6

mole

12

0.1

gN

2/1

693.

T=λ

g

atoms 106

10×=

Carbon Dating

We just determined that living organisms

should have a decay rate of about 0.23

decays/ gram of carbon.

The bones of an ice man are found to have a

decay rate of 0.115 decays/gram. We can

estimate he died about 6000 years ago.

Summary• Nuclear Reactions

– Nucleon number conserved

– Charge conserved

– Energy/Momentum conserved

– αααα particles = nuclei

– ββββ---- particles = electrons

– γγγγ particles = high-energy photons

• Decays

– Half-Life is time for ½ of atoms to decay

N(t ) =N0e−λtSurvival:

T1/2 =

0.693

λ

24He

Mass/Nucleon vs Atomic Number

Fusion

Fission

Fusion

Fission

11/29/2010

7

U-235 -- Fissile Abundance of U-235

U-235 Fission

by

Neutron Bombardment

Possible U-235 Fission

Chain Reaction Breeder ReactionBreeder Reaction

11/29/2010

8

Breeder Reactor

• Small amounts of Pu-239 combined with U-

238

• Fission of Pu frees neutrons

• These neutrons bombard U-238 and

produce more Pu-239 in addition to energy