Questions

1. Radioactive material emits radiation dangerous for your health. What is the half life of a radioactive source?

2. How do decay constant and half life correspond to each other?

3. You increase the decay constant for a radioactive nucleus. What is the effect of the half life?

Terminology of nuclear energy

Mass number: number of protons and neutrons in nucleusE=mc2: energy corresponds to massBinding energy: mass difference between mass of nucleus and mass of the single nucleons (protons and neutrons)Isotopes: nuclei with identical number of protons ZIsobares: nuclei with identical atomic number AIsotones: nuclei with identical number of neutrons

The first step: E=m·c2

"It followed from the special theory ofrelativity that mass and energy are bothbut different manifestations of the samething - a somewhat unfamiliarconceptionn for the average mind.Furthermore, the equation E is equal tom c-squared, in which energy is putequal to mass, multiplied by the squareof the velocity of light, showed that verysmall amounts of mass may be convertedinto a very large amount of energy andvice versa. The mass and energy were infact equivalent, according to the formulamentioned before. This wasdemonstrated by Cockcroft & Walton in1932, experimentally."

Nobel Prize 1921

Albert Einstein

Example: Mass-Energy

smc

smkgJmcE 8

22 10311

JsmkgsmkgE 16

21628 1091091031

Definition: 1 ton of TNT = 4.184 x 109 joule (J).

1 kg (2.2 lb) of matter converted completely into energy would be equivalent to the energy released by exploding 22 megatons of TNT.

1kg of matter corresponds to an energy of:

Nuclear physics units: JeV 19106.11 1 electron-volt is the energy one electron picks up if accelerated in an electrical potential of one Volt.

+1V

By 1932 a nucleus was thought to consist of protons and electrons, which were emitted in the β-decay. Chadwick’s experiment revealed a third particle, the neutron

Strong Polonium source emitted α particles which bombarded Be;radiation was emitted which – based on energy and momentumtransfer arguments - could only be neutral particles with similar mass as protons neutrons: BEGIN OF NUCLEAR PHYSICS!

The discovery of the neutron

Nobel Prize 1935

np

011 H

011 H

The model of the nucleus

Nucleus with Z protons (p) and N neutrons (n) with a total mass number A=Z+N

Hydrogen: 1 p, 0,1 n

Helium: 2 p, 1,2 n

Lithium: 3 p, 3,4 n

Carbon: 6 p, 6,7 n

Sodium: 11 p, 11,12 n …

Uranium: 92 p, 143,146 n

242 He

011 H

6126C

363 Li

7136C

14623892U

121 D

132 He

473 Li

14323592U

112211 Na 12

2311 Na

N

Z

hydrogen isotopes: Z=1Isotopes: Z=constant, N varies!Isotones: N=constant, Z varies!Isobars: A=constant, Z,N varies!

Modern Picturenuclide chart

Z=8, Oisotopes

A=20isobars

N=12 isotones

Impact of Z and NAdding a proton (electron)

Carbon to Nitrogen

Gold to Mercury

Subtracting or adding neutrons

nucleus becomes unstable anddecays by internally convertingneutrons to protons (beta-decay)!

- decayn p+e-+

+ decayp n+e++

_

Energy in NucleiAccording to Einstein’s formula, each nucleus with a certain mass m stores energy: E=mc2

Proton mp = 1.007596 · 1.66·10-24 g = 1.672·10-24 gNeutron mn = 1.008486 · 1.66·10-24 g = 1.674·10-24 gCarbon m12C = 12.00000 · 1.66·10-24 g = 1.992·10-23 gLead m208Pb = 207.797665 · 1.66·10-24 g = 3.449·10-22 gUranium m238U = 238.050783 · 1.66·10-24 g = 3.952·10-22 g

1 amu=1/12(m12C)=1.66 · 10-24 gBreaking up nuclei into their constituents requires energy

http://ie.lbl.gov/toimass.htmlhttp://www.nndc.bnl.gov/masses/mass.mas03

Binding energy of a nucleusB = (Z · mp+ N · mn- M) · c2Binding energy B

of nucleus

nucleon

JA

CB

Jsmkg

smgsmg

smggg

cmmmCBCnp

1212

112

112

821625

28232424

212

1017.1

10404.110404.110404.1/1091056.1

/10310992.110674.1610672.16

66 12

nucleon

JA

UB

Jsmkg

smgsmg

smggg

cmmmUBUnp

12238

102

102

721624

28222424

2238

10145.1

10725.210725.210725.2/1091003.3

/10310952.310674.114610672.192

14692 238

Nuclear Potential

MeVaMeVaMeVaMeVaMeVa

oddNZAoddNZAaevenNZAaA

ZAaAZZaAaAaB

psymcsv

pp

symcsv

34;23;72.0;8.16;5.15

);(0);,();,(

21

3/43/4

23/13/2

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2

1 MeV = 1.602·10-13 J

Nuclear Binding Energy

Mass number A

1 MeV = 1.602·10-13 J

Binding energy normalized to mass number B/A

Nuclear Decay Processes

A B+bA(b)B14C(-)14N234U(α)230Th

Decay energy is released in kinetic energy of emittedparticles or in electromagnetic gamma radiation energy

JeVMeVQ

MeVMeVMeVMeVQ

BBBQBBBQcmcmmQ

U

U

ThHeUUAbBd

AbBd

127

22

104.81025.55.52

5.52128.12755296.28325.1779

234

234

2304234234

JeV 19106.11

Political developments in Europe

Economic instabilities, and theeconomic downturn worldwidetriggered by Black Fridaystrengthened the radical rightwing National Socialist PartyNSDAP party in Germany,which ran on a social andnational platform.

Democratic partiesRight wing partiesLeft wing parties

In January 1933 the party leader Adolf Hitler was appointed by

President Hindenburg asnew German Chancellor

-Reichstagsbrand-27 February 1933

The Reichstag building, seat of the German parliament, burns after being seton fire. This enabled Adolf Hitler to seize power under the pretext of protectingthe nation from threats to its security. (Photo credit: U.S. National Archives)

This Decree of the Reich President for the Protection of the People and State abrogates the following constitutional protections: • Free expression of opinion • Freedom of the press • Right of assembly and association • Right to privacy of postal communications • Protection against unlawful searches & seizures • Individual property rights • States' right of self-government

A supplemental decree creates the SA (Storm Troops) and SS (Special Security) Federal police agencies.

Consequences for Science and Academia

Minister of Education tookmore flexible stand. Jewishscientists were allowed to holdtemporary assistant posts, butthey were facing increasingadministrative difficulties.

KWI under Planck tried firstto remain independent but gotmore involved in war relatedresearch during WW-II.

KWI for Physics in Berlin with van de Graaff Accelerator tower in front

Removal from all Jewish faculty members from their posts(Law of restoration of Career Civil Service 1933). Many ofthe leading figures emigrated. Bernhard Rust became the new

Nuclear Reactions and Energy Release

a

A

Frederic Joliot and Irene Curie at Parishad observed the first nuclear reaction.Enrico Fermi showed the existence ofneutron induced reactions, whichproduce artificial radioactivity.Nuclear reactions can produce energyQ > 0 exothermicor need energy Q < 0 endothermic

A(a,b)B Q = (mA+ ma- mB- mb)·c2

Q = BB+ Bb- BA-BB

Nobel Prize 1938

difference of masses in entranceand exit channel determines Q

Q value of nuclear reaction process

a

A

b

B

A+a B+bA(a,b)B

projectile

target

product

recoil

reactioncendothermi0reactionexothermic0

22

QQ

BBBBQcmmcmmQ

aAbB

aAbB

Example: Nuclear Binding Energy

isotope B (J)

2H 3.34131·10-13

4He 4.53297·10-12

12C 1.47643·10-11

119Pd 1.59643·10-10

238U 2.88631·10-10

JJJQ

UBPdBPdBQ

QPdU

JJJQHBHBHeBQ

QHeHH

111010146

2389273

1194673

11946

7311946146

23892

121213

2242

421

211

21

1006542.31059633.121088631.2

)()()(

2

108647.31053295.41034131.32)()(2)(

Conversion of nuclei through fusion or fission leads to release of energy!

http://ie.lbl.gov/toimass.htmlhttp://nucleardata.nuclear.lu.se/database/masses/http://www.nndc.bnl.gov/masses/mass.mas03

Nuclear Energy possible through fission and fusion

The most stable nucleus is 56Fe