Nuclear Reactions

Thornton and Rex, Ch. 13

Otto Hahn and Lise Meitner

Reaction KinematicsConsider a general reaction, A (x , y) B or A + x Æ y + Bwith target A at rest.

Ex. 9Be4 + 4a2 Æ 1n0 + 12C6or equivalently,

9Be4 (a,n) 12C6

Conservation of energy gives:

MAc2 + mxc2 + Kx = myc2 + Ky + MBc2 + KB

The difference between final and initialkinetic energies is called the Q-value.

Q = Ky + KB - Kx

= MAc2 + mxc2 - (myc2 + MBc2 )

If Energy is released, Q > 0

fi Exothermic

If Energy is converted to mass, Q < 0

fi Endothermic

Two of the most important exothermicreactions are Fission and Fusion.

Quickuiz

How many α particles and β particles areproduced in the decay chain

232Th90 --> 224Ra88?

(A) 1 α and 1 β

(B) 2 α and 2 β

(C) 3 α and 3 β

(D) 2 α and 1 β

(E) 1 α and 2 β

Quickuiz

How many α particles and β particles areproduced in the decay chain

232Th90 --> 224Ra88?

(A) 1 α and 1 β

(B) 2 α and 2 β

(C) 3 α and 3 β

(D) 2 α and 1 β

(E) 1 α and 2 β

α decays reduce A by 4 and Z by 2

β decays don’t change A and increase Z by 1

==> Nα = (232-224)/4 = 2

==> 2Nα - Nβ = 90 - 88 = 2

==> Nβ = 4 - 2 = 2

Neutron ActivationNeutrons - uncharged, can penetrate close

to the nucleus, can induce reactions(Neutron Activation).

1930’s - Enrico Fermi bombarded elementsfrom Hydrogen to Uranium withneutrons. On Uranium, Fermi wasunable to identify the final products ofthe reactions. He expected elementsheavier than Uranium, such as in theexpected process:

238U92 + 1n0 Æ 239U92 Æ 239Np93 + 0e-1 + n

Fission

nU

U

U

Ba Kr

n

n

n

Comments on Fission• The observed reaction is one of manypossible reactions:

235U92 + 1n0 Æ 141Ba56 + 92Kr36 + 3 1n0

• 235U92 undergoes fission. 238U92 doesnot. Uranium ore contains 99.3% U-238and only 0.7% U-235.

• Fission occurs more easily if theneutron is slow (allowing more time for thereaction to occur.)

• Q > 0, so energy released (~200 MeV).(Cf. Binding Energy vs. Atomic Weight)

• Since heavier nuclei are more neutronrich, the fission process results in therelease of extra neutrons.(Cf. plot of N vs. Z)

• Under the right conditions, the extraneutrons could cause more U-235 tofission. This would release even moreneutrons, etc., resulting in achain reaction.

(The idea of chain reaction was patentedby Leo Szilard in 1933, before he had anyidea what nuclei might participate!)

nU

U

U

U

UU

UU

U

U

U

UU

After his and Meitner’s realization of the process ofnuclear fission, Frisch returned to Copenhagen andcommunicated the news to Niels Bohr, who wasleaving for the U.S. on the next day.

In New York, in mid-January 1939, Bohr told EnricoFermi who had arrived in exile on January 2. Soongroups all over the world were investigating thefission of Uranium and its potential to cause a chainreaction.

The worsening international situation in the monthsbefore the start of World War II resulted in majorprojects being set up in several countries (U.S.,Britain, France, Germany and Japan) in order toproduce the first nuclear weapons.

The largest effort was the Manhattan Project in theUnited States. This was started at ColumbiaUniversity by Fermi in 1940. Under the leadershipof J. Robert Oppenheimer at a secret lab in LosAlamos, NM, the project produced the “atomic”bombs that exploded in the Alamogordo desert inNew Mexico (July 16 1945) and over Hiroshima(August 6 1945) and Nagasaki (August 9 1945).

Two technical problems that had to besolved in order to achieve a chainreaction in Uranium:

1) Fission occurs if U-235 captures a slowneutron, but the neutrons emitted infission are fast.

The device must contain a substancewhich slows the neutrons down. A“moderator” is an element whose nucleidon’t absorb neutrons and which arerelatively light so that in collisions withneutrons they will absorb energy andthus slow the neutrons down. Typicalmoderators are water, heavy water(D2O), or Carbon (graphite).

2) The sample must be enriched withenough U-235 relative to U-238.

An additional technical problem must beovercome to achieve controlled nuclearfission, as for power generation.

A variable amount of an additionalmaterial that is highly efficient incapturing neutrons must be inserted inthe Uranium. => Cadmium rods

The first self-sustaining nuclear reactor,using graphite as moderator, was builtunder the stands of the football stadiumat the University of Chicago by EnricoFermi on December 2, 1942.