Nuclear Reactions

PHY 3101D. Acosta

4/13/2001 PHY 3101 -- D. Acosta 2

Nuclear Alchemyn First nuclear reaction performed by

Rutherford in 1919 using α-particles:

n Reaction Energy:

n Exothermic: energy released in reactionn Endothermic: energy absorbed in reaction

– Goes into mass

n Nuclear reactions take place in atmosphere:

– Carbon binds to form CO2 which is absorbed by plants and animals

n Carbon-14 dating:– 14C is continually replenished until the

plant or animal dies– 14C decays, and amount left gives age– t1/2 = 5730 years

24

714

11

817He N H O+ → +

01

714

11

614n+ → +N H C

Q M M c= − ×initial products final productsa f a f 2

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Nuclear Fission

n Enrico Fermi and Italian groups bombard nuclei with neutrons to produce new isotopes:

n In 1938, Hahn and Strassman in Germany split uranium

n Frisch and Lise Meitner call it fission(like cell division) and observe that excess energy is shed (exothermic)

n Excess neutrons are released which may catalyze more reactions

n Niels Bohr points out that 235U (0.7% natural abundance) is more likely than 238U (99.3%) to fission because of odd number of neutrons– Need to use enriched uranium

n Many possible fission fragments are possiblen For example:

n Energy released is:1.0087u + 235.04u – 98.92u –133.91u –3(1.0087u) = 0.2u ⇒ 185 MeV

n Average number of neutrons released is 2.3

01 1n X XZ

AZ

A+ → +

n n+ → + +92235

4099

52134 3U Zr Te

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Nuclear Fission

n Uranium is on the downward slope of the binding energy per nucleon curve

n More energetically favorable for Uranium to split into smaller nuclei

n More neutrons are released than incidentn If the released neutrons are absorbed, this

starts a chain reactionn Critical Mass:

– Larger mass sustains chain reaction– Smaller mass implies neutrons escape– Critical mass is a few kg for uranium

n Controlled fission: moderators slow and absorb neutrons

n More efficient fission from plutonium, which can be produced by bombarding 238U with neutrons to get 239Pu– Average of 2.7 neutrons per Pu fission– t1/2 = 24,000 years

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Atomic Bomb

n Suppose 1 kg of enriched 235U fissions:

n Large as this is, it is still small compared to the total rest mass energy:

n Only 1/1000 of energy released in fission

Q

Q

= × ××

= ×

= ×

×

185 1 14 7 1032 MeV

fission kg

235 u u

1.66 10 kg eV

7.6 10 J = 18 kT

(1 kT of TNT = 4.2 10 J = 10 calories)

-27

13

12 12

.

E mc

E

= = ×

= ×

2 8 2

16

1 3 10

9 10

kg m / s

J = 21400 kT = 21.4 MT

a fd i

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Nuclear Fusion

n Dividing high Z elements librates energy, but so does fusing low Z elements (upward part of binding energy per nucleon curve)

n Consider the fusion of deuterium and hydrogen (powers the Sun and H-bomb)

12

11

23

2

2

2 0141

0 0059 5 5

H H He

u +1.00783u - 3.01603u

u MeV

+ → +

= ×

= =

γ

Q c

Q c

.

. .

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Solar Reactions

n The “burning” of hydrogen into helium and higher Z materials in stars:

n PPI cycle:

n PPII cycle:

n PPIII cycle:

11

11

12

11

23

23

23

24

11

11

144

55

12 9

H H H MeV

H+ H He + MeV

He+ He He+ H+ H MeV

12+ → + + =

→ =

→ =

+β ν

γe Q

Q

Q

.

.

.

23

24

47

47

37

11

37

24

24

He+ He Be +

Be Li +

H+ Li He+ He

-e

→

+ →

→

γ

β ν

11

47

48

48

24

24

H Be B +

B Be

Be He He

58

58

+ →

→ + +

→ +

+

γ

β ν e

H.A.Bethe

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Stars

n Fusion of higher Z elements occurs when lower Z fuel is exhausted

n Continues until 56Fe is produced, which is at the peak of the binding energy vs. Z curve– Not energetically favorable to fuse

higher Z nuclei

n Without energy source, star collapses and may explode as a supernova

n All elements in the periodic table besides H and He are produced (and released) by stars in the universe

n Direct evidence for solar fusion is available because we have detected the neutrinos released in the solar reactions