The Development of Nuclear Science

From 1900 - 1939

The Development of Scientific Thought in the 20th Century

Discovery & study of radioactivity 1898 Marie &.Pierre CurieIntroduction of quantum concept 1900 Max Planck hTheory of special relativity 1905 Albert Einstein E=m·c2

Quantization of light (photoelectric effect) 1905 Albert Einstein E=h·ν

Discovery of atomic nucleus 1911 Ernest Rutherford Interpretation of atom structure 1913 Nils Bohr

Particle waves 1924 Louis de BroglieWave mechanics 1925 Erwin SchrödingerUncertainty principle 1927 Werner Heisenberg

Discovery of Neutron 1932 James ChadwickArtificial Radioactivity (Reactions) 1934 Frederic Joliot & Irene CurieDiscovery of fission 1938 Otto Hahn, Fritz StrassmannInterpretation of fission 1938 Liese Meitner, Otto FrischPrediction of thermonuclear fusion 1939 C.F. v. Weizsäcker, H. Bethe

∆x·∆p=ђ

The new radiating material

Radioactive material such as Uranium- first discovered by Henri Becquerel –was studied extensively by Marie andPierre Curie. They discovered othernatural radioactive elements such as Radium and Polonium.

Nobel Prize 1903 and 1911!Unit of radioactivity:

The activity of 1g Ra = 1Ci = 3.7·1010 decays/s 1Bq = 1 decay/s

Discovery triggered a unbounded enthusiasm and led to a large number of medical and industrial applications

Applications for Radioactivity

ApplicationsPopular products included radioactive toothpaste for cleaner teeth and better digestion, face cream to lighten the skin; radioactive hair tonic, suppositories, and radium-laced chocolate bars marketed in Germany as a "rejuvenator." In the U.S, hundreds of thousands of people began drinking bottled water laced with radium, as a general elixir known popularly as "liquid sunshine." As recently as 1952 LIFE magazine wrote about the beneficial effects of inhaling radioactive radon gas in deep mines. As late as 1953, a company in Denver was promoting a radium-based contraceptive jelly.

Radium DialsRadium DialsRadium DialsIncrease in cancer (tongue – bone)due to extensive radium exposure

It was a little strange, Fryer said, that when she blew her nose, her handkerchief glowed in the dark. But everyone knew the stuffwas harmless. The women even painted their nails and their teethto surprise their boyfriends when the lights went out.

According to a Department of Commerce Information Circular from 1930, the radium paint might contain "from 0.7 to 3 and even 4 milligrams of radium”; this corresponds to a radioactivity level of 0.7 to 4 mCi or 26-150 GBq in modern units.

Explanation of natural radioactivity

Ernest Rutherford's picture of transmutation. A radium atom emits an alpha particle,turning into “Emanation” (in fact the gas radon). This atom in turn emits a particle to become “Radium A” (now known to be a form of polonium). The chain eventually ends with stable lead. Philosophical Transactions of the Royal Society of London, 1905.

Radioactivity comes in three forms α, β, γ

Nobel Prize 1908

The radioactive decay law

( )tdaughter

tmother

eAtA

eAtA

⋅−

⋅−

−⋅=

⋅=

λ

λ

1)(

)(

0

0

λ≡decay constant;a natural constant for each radioactiveelement.Half life: t1/2 = ln2/λ

exponential decay with time!

1st example: 22Na22Na has a half-life of 2.6 years, what is the decay constant?Mass number A=22; (don’t confuse with activity A(t)!)

197

77

1

2/1

105.81014.36.2

2ln

101014.31

:27.06.22ln2ln

−−

−

⋅=⋅⋅

=

⋅≈⋅=

===

ss

ssy

yyt

λ

π

λ

radioactive decay lawsActivity of radioactive substance A(t) is at any time t proportional to number of radioactive particles N(t) :

A(t) = λ·N(t)

A 22Na source has an activity of 1 µCi = 10-6 Ci, how many 22Na isotopes are contained in the source?

(1 Ci = 3.7·1010 decays/s)

1219

1106

19

6

1036.4105.8

107.310105.8

10⋅=

⋅⋅⋅

=⋅

== −−

−−

−−

−

ss

sCiAN

λ

How many grams of 22Na are in the source?

A gram of isotope with mass number A contains NA isotopes

NA ≡ Avogadro’s Number = 6.023·1023

➱ 22g of 22Na contains 6.023·1023 isotopes

ggN

particlesg

particlesN

1023

12

23

12

1059.110023.6

1036.422

2210023.61

1036.4

−⋅=⋅⋅⋅

=

⋅=

⋅=

teNtN ⋅−⋅= λ0)(

How many particles are in the source after 1 y, 2 y, 20 y?

CisyAeyN

CisyAeyN

CisyAeyN

tNstNtAetN

yy

yy

yy

ty

µ

µ

µ

λ

067.05.2490)10(1093.21036.4)10(

58.021590)2(1054.21036.4)2(

765.028305)1(1033.31036.4)1(

)(105.8)()(1036.4)(

1111027.012

112227.012

112127.012

1927.012

1

1

1

1

==⋅=⋅⋅=

==⋅=⋅⋅=

==⋅=⋅⋅=

⋅⋅=⋅=⋅⋅=

−⋅−

−⋅−

−⋅−

−−⋅−

−

−

−

−

Decay in particle number and corresponding activity!

2nd example: Radioactive DecayPlutonium 239Pu, has a half life of 24,360 years.1. What is the decay constant?2. How much of 1kg 239Pu is left after 100 years?

kgyN

kgyN

kgyN

kgyN

kgyN

ekgyNeNtN

yyt

Pu

Pu

Pu

Pu

Pu

yyPu

tPu

0578.0)000,100(

5.0)360,24(

7520.0)000,10(

9719.0)000,1(

9972.0)100(

1)100()(

1085.224360

2ln2ln

239

239

239

239

239

15

2392391001085.2

0

15

2/1

=

=

=

=

=

⋅=⇒⋅=

⋅===

⋅⋅−⋅−

−−

−−λ

λ

The first step: E=m·c2"It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing - a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned before. This was demonstratedby Cockcroft and Walton in 1932, experimentally."

Nobel Prize 1921

Albert Einstein

Example: Mass-Energy

smc

smkgJmcE 8

22 10311 ⋅=

==

1kg of matter corresponds to an energy of:

( ) 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.

JeV 19106.11 −⋅=Nuclear physics units:+1V

1 electron-volt is the energy one electron picks up if accelerated in an electrical potential of one Volt.

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

The discovery of the neutron

Nobel Prize 1935

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!

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……

Uranium: 92 p, 143,146 n

242 He

011 H

6126C

363 Li

7136C

14623892U

121 D

132 He

473 Li

14323592U

N

ZModern Picturenuclide chart

Z=8, Oisotopes

A=20isobars

N=12 isotones

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

Energy in NucleiAccording to Einstein’s formula each nucleus with 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 gUranium m238U= 238.050783 · 1.66·10-24 g = 3.952·10-22 g

B = (Z · mp+ N · mn- M) · c2

B(12C) = 1.47 · 10-11 J; B/A=1.23 · 10-12 JB(238U) = 2.64 · 10-10 J; B/A=1.21 · 10-12 J

Binding energy B of nucleus

Breaking up nuclei into their constituents requires energy

1 amu=1/12(M12C)=1.66 · 10-24 g

Nuclear Potential

( ) ( )

MeVaMeVaMeVaMeVaMeVa

oddNZAoddNZAaevenNZAaA

ZAaAZZaAaAaB

psymcsv

pp

symcsv

34;23;72.0;8.16;5.15

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

21

3/43/4

23/13/2

=====

+==⋅−=⋅+=

+−

⋅−⋅−⋅⋅−⋅−⋅=

−−

−

δδδ

δ

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

1 MeV = 1.602·10-13 J

Nuclear Binding EnergyB

/A

in u

nits

MeV

1 MeV = 1.602·10-13 J

Binding energy normalized to mass number B/A

A

Example: Nuclear Binding EnergyConversion of nuclei through fusion or fission leads to release of energy!

( )

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)(

−−−

−−−

⋅=⋅⋅−⋅=

−+=

+⇒

⋅=⋅−⋅⋅=

+⋅−=

+⇒+

2.88631·10-10238U1.59643·10-10119Pd1.47643·10-1112C4.53297·10-124He3.34131·10-132H

B (J)isotope

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