nuclear binding, radioactivity sections 32-1 – 32-9 physics 1161: lecture 33

51
Nuclear Binding, Radioactivity • Sections 32-1 – 32-9 Physics 1161: Lecture 33

Upload: ruby-haynes

Post on 18-Dec-2015

218 views

Category:

Documents


0 download

TRANSCRIPT

Nuclear Binding, Radioactivity• Sections 32-1 – 32-9

Physics 1161: Lecture 33

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

Marie Curie1867 - 1934

Wilhelm Roentgen1845 - 1923

X-Rays

emitted

by cathode

ray tube

Poloniu

m and

radium

Antoine Henri Becquerel1852 - 1908

Uranium

produced

X-rays

Nucleus = Protons+ Neutrons

nucleons

A = nucleon number (atomic mass number)Gives you mass density of element

Z = proton number (atomic number) Gives chemical properties (and name)

N = neutron number

A=N+Z

Nuclear Physics

Li63

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

A material is known to be an isotope of lead. Which of the following can be specified?

1 2 3

0% 0%0%

1. The atomic mass number

2. The neutron number

3. The number of protons

Lead Z=82

Chemical properties (and name) determined by number of protons (Z)

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.

# protons = # neutrons

Where does the energy released in the nuclear reactions of the sun come from?

1 2 3

0% 0%0%

1. covalent bonds between atoms

2. binding energy of electrons to the nucleus

3. binding energy of nucleons

Where does the energy released in the nuclear reactions of the sun come from?

1 2 3

0% 0%0%

1. covalent bonds between atoms

2. binding energy of electrons to the nucleus

3. binding energy of nucleons

Strong Nuclear Force

• Acts on Protons and Neutrons

• Strong enough to overcome Coulomb repulsion

• Acts over very short distancesTwo atoms don’t feel force

Hydrogen atom: Binding energy =13.6eV

Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger!

2.2106eV

Simplest Nucleus: Deuteron=neutron+protonneutron 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, get 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

NER

GY

in M

eV/n

ucle

on

92238U

10

Binding Energy Plot

Fission

Fusio

n Fusion = Combining small atoms into largeFission = Breaking large atoms into small

Mass/Nucleon vs Atomic Number

Fusion

Fission

E = mc2

E: energym: massc: speed of lightc = 3 x 108 m/s

E = mc2

• Mass can be converted to energy• Energy can be converted to mass• Mass and energy are the same thing• The total amount of mass plus energy in the universe is constant

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 MeV2. 234 MeV3. 270 MeV4. 504 Mev

BIN

DIN

G E

NER

GY

in M

eV/n

ucle

on

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 MeV2. 234 MeV3. 270 MeV4. 504 Mev

Total B.E 56x9=504 MeV

BIN

DIN

G E

NER

GY

in M

eV/n

ucle

on

For Fe, B.E./nucleon 9MeV

2656Fe has 56 nucleons

particles: nucleii 24He

particles: electrons

: photons (more energetic than x-rays) penetrate!

3 Types of Radioactivity

Easily Stopped

Stopped by metal

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

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

234Th: example 24He recall

: example

Decay Rules1) Nucleon Number is conserved.2) Atomic Number (charge) is conserved.3) Energy and momentum are conserved.

: example 00

* PP AZ

AZ

1) 238 = 234 + 4 Nucleon number conserved2) 92 = 90 + 2 Charge conserved

e01

11

10 pn

Needed to conserve energy and momentum.

00

A nucleus undergoes decay. Which of the following is FALSE?

1 2 3

0% 0%0%

1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2

A nucleus undergoes decay. Which of the following is FALSE?

1 2 3

0% 0%0%

1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2

decay is the emission of 24He

He42

23490

23892 ThU

Z decreases by 2(charge decreases!)

A decreases by 4

The nucleus undergoes decay. Which of the following is true?

1 2

0%0%

90234Th

1. The number of protons in the daughter nucleus increases by one.

2. The number of neutrons in the daughter nucleus increases by one.

decay involves emission of an electron: creation of a charge -e.

In fact, inside the nucleus, and the electron and neutrino “escape.”

n p e e

00

01

23491

23490 PaTh

e

Radioactive Decay

23892U 4

2He 23490 Th

23490Th 0

1e 23491Pa

4.5 x 109 yr half-life

24 day half-life1.17 min half-life

23491Pa

01e 234

92 U250,000 yr half-life

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?

1 2 3 4 5

0% 0% 0%0%0%

92238U 90

234Th

HePbPo 42

21082

21484

00

01

4020

4019 pK

e

NC 147

146

1. 2. 3. 4.

Which of the following decays is NOT allowed?

1 2 3 4 5

0% 0% 0%0%0%

92238U 90

234Th

HePbPo 42

21082

21484

00

01

4020

4019 pK

e

NC 147

146

1. 2. 3. 4.

238 = 234 + 492 = 90 + 2

214 = 210 + 4

84 = 82 + 2

14 = 14+0

6 <> 7+0

40 = 40+0+019 = 20-1+0

Decays per second, or “activity”:If the number of radioactive nuclei present is cut in half, how does the activity change?

1 2 3

0% 0%0%

Nt

NNo. 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?

1 2 3

0% 0%0%

Nt

N No. of nuclei present

decay constant

Every 6000 years ½ of atoms decay

1. 02. 43. 6

time

N(t)N0e t N0 2

t

T1/2

Decay Function

Instead of base e we can use base 2:

N(t)N0e tSurvival:

No. of nuclei present at time t

No. we started with at t=0

e t 2

tT1/2

T1/2

0.693

where

Then we can write N(t)N0e t N0 2

t

T1/2

Half life

Radioactivity Quantitatively

Nt

N

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 1 140 7 1 6n N H C

14 0 146 1 7C e N

You are radioactive!

One in 8.3x1011 carbon atoms is 14C which decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon.

Nt

N

11

2314 103.8

11002.6

mole12

0.1g

N

2/1

693.T

1-12s1083.36060243655730

693.

gatoms

106 10

decays/s 23.0

Carbon DatingWe 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– particles = nuclei– - particles = electrons– particles = high-energy photons

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

N(t)N0e tSurvival:

T1/2

0.693

24He

Mass/Nucleon vs Atomic Number

Fusion

Fission

Fusion

Fission

U-235 -- Fissile

Abundance of U-235

U-235 Fissionby

Neutron Bombardment

Possible U-235 Fission

How Stuff Works Site

• Visit the How Stuff Works Site to learn more details about nuclear energy

Chain Reaction

Plutonium Production

U-238 – Not Fissile

Breeder ReactionBreeder Reaction

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