Nuclear Physics

Six Differences Between Nuclear Reactions and Chemical Reactions

• Protons and neutrons react inside the nucleus

• Elements transmute into other elements

• Isotopes react differently• Independent of chemical

combination• Energy changes ~ 108 kJ• Mass Changes are detectable

• Electrons react outside the nucleus

• The same number of each kind of atom appear in the reactants and products

• Isotopes react the same• Depend on chemical

combination• Energy Changes ~ 103 Kj• Mass reactants = mass

products

Radioactivity

• Much of our understanding of atomic structure came from studies of radioactive elements.

• Radioactivity - The process by which atoms spontaneously emit high energy particles or rays from their nucleus.

• First observed by Henri Becquerel in 1896.

Cloud chamber

• A simple device for the detection of radiation.

• A ‘vapor trail’ is produced as radioactive particles pass through it.

Survey meter (Geiger counter)thin

window

Argon filled tube under high voltage

anode cathode

ratemeter - tells number of counts/minute

Good for area monitoring orlocating ‘hot spots’.

Radioactive elementsHe

Rn

XeI

KrBrSe

ArClS

NeFO

P

NC

H

Li

Na

Cs

Rb

K

TlHgAuHfLuBa

Fr

PtIrOsReWTa PoBiPb

Be

Mg

Sr

Ca

CdAgZrY PdRhRuTcMoNb

LrRa

ZnCuTiSc NiCoFeMnCrV

In SbSn

Ga Ge

Al

At

Te

As

Si

B

Gd TbSm EuNd

U

PmCe

Th

Pr

Pa

YbLa Er TmDy Ho

Cm BkPu AmNp NoAc Fm MdCf Es

Rf Db Sg Bh Hs Mt 110 111 112

The common types ofradioactive emissions

• The three most common forms of radioactive emission, are

• alpha particles, α , which are helium ions

• beta particles, ß , which are electrons, and

• gamma rays, γ , which are pure energy similar to x-rays

• Also should know positrons ß+, which are positive electons.

Radioactivity

• Major types of radioactive decay

• alpha emission, α, attracted to negative plate• beta emission, ß, attracted to positive plate• gamma radiation, γ , not affected

Magic numbers• Some combinations of protons and neutrons

appear to be more stable than others.

• Proton magic numbers• 2, 8, 20, 28, 40, 50, and 82

• Neutron magic numbers• 2, 8, 20, 28, 40, 50, 82, and 126.

• This indicates the existence of energy levels in the nucleus, similar to those observed for electrons outside the nucleus.

Predicting the type of decay

• The chart of the nuclides provides a convenient map of the types of isotopes.

• It shows how each type of radioisotope will decay. It does not give you the reasons why.

• There are a few rules that can be used to predict how a nuclide will decay.

Proton : neutron ratioStable isotopes run at ~ 45o slopethen slope downat Z = 20 (Ca).

A band of stability is observed.

Radioactive nuclides will attemptto find the shortestpath to ‘get back’to the band ofstability.Z - protons

N -

neut

rons

20 40 60 80

20

4

0

60

80

1

00

12

0

Proton : neutron ratio

Z - protons

N -

neut

rons

20 40 60 80

20

4

0

60

80

1

00

12

0

neutron richregion

proton richregion

1 : 1 ratio line

Decay tendencies

Z - protons

N -

neut

rons

20 40 60 80

20

4

0

60

80

1

00

12

0

ß- decay

ß+ decay orelectron capture

α decay,elements with Z > 82

Alpha Decay• Stripped helium atom 4He • Nucleii contain 2 less protons and 2 less

neutrons238U → 234Th + 4He

How many protons in uranium?How many protons in Thorium?Notice the mass numbers add up

238 = 234 + 4

Beta Decay0

-1e

• A beta particle is an electron • A neutron turns into a proton and an electron• The decay produces another proton in the

nucleus• 210Pb → 210Bi + β• How many protons in Pb, Bi?

Gamma emission• All nuclear decays release gamma radiation. • The nucleus is unstable and oscillates until it

releases the particle, but it is left in a high energy state that requires the release of excess electromagnetic radiation in the form of gamma radiation.

• Alpha, beta, and positron emitters give off alpha particles with little gamma radiation.

• Gamma emitters give off lots of gamma rays with each particle emitted.

Electron Capture

• Addition of an electron to a proton in the nucleus is known as electron capture or K-capture.– The result of this process is that a proton is transformed into a

neutron.

p11 + e0

-1 n10

Decay Series• Most radioactive elements are too far from

the zone of stability to reach it in one decay.• Multiple decays must occur.• This is called a decay series.• Uranium’s can be 13 to 15 steps long.• Can take different paths because there is a

probability of the nucleus undergoing certain decays, sometimes the probability of alpha vs. beta are close that either are likely.

Radioactive decay• Although we can predict the methods by which an

isotope may undergo radioactive decay to become more stable, we can not predict how quickly these changes will occur.

• The rate of decay is dependent on the stability of the specific radioactive species.

• Half Life is defined as the time required for 50% of a specific radioactive species to decay.

• We commonly use the symbol - t1/2

Half-life

With each half-life,50% of an isotope

will decay.

With each half-life,50% of an isotope

will decay.

100

0

80

60

40

20

0 2 4 6 8 10

%

half-lives

Half-life examples

• Name Half-life

• Carbon-14 5720 years• Sodium-24 15 hours• Iron-59 45 days• Cobalt-60 5.3 years• Nickel-63 100 years• Uranium-235 704 million years

Half-life example 1

• The t1/2 for 63Ni is 100 years. If you had 100 g of 63Ni, how much would remain after 400 years?

• ……after 250 years?

Half-life• Amount remaining for 63Ni

• (half-lives) amount (g) time(yrs)• 0 100 0

– 1 50 100– 2 25 200– 3 12.5 300– 4 6.25 400

– Decay can take a long time!

– Always take 1/2 amount and add t 1/2

– 63Ni is used in some smoke detectors.

Half-life• Amount remaining for 63Ni

• (half-lives) amount (g) time(yrs)• 0 100 0

– 1 50 100– 2 25 200– 3 12.5 300– 4 6.25 400

– At 250 years, we need to interpolate to find the # g remaining half-way between 2 and 3 half-life cycles.

– Half-way between 25 and 12.5 g is 18.75 g, but the decay rate is faster in the beginning of the cycle when more atoms are present, so the amount is a little less than 18.75 g.

250

Half-life• Amount remaining for 63Ni

• (half-lives) amount (g) ln (amount) time(yrs)• 0 100 4.61 0

– 1 50 3.91 100– 2 25 3.22 200– 3 12.5 2.53 300– 4 6.25 1.83 400– 5 3.12 1.14 500– 6 1.56 0.44 600– 7 0.78 -0.25 700– 8 0.39 -0.94 800– 9 0.20 -1.61 900– 10 0.10 -2.30 1000

A linear relationship will exist between the natural log (ln) of undecayed atoms vs. time.

Half-lifeYou can plot the

ln (amount) vs. timeto create a linear curve.

You can plot the ln (amount) vs. time

to create a linear curve.

4.61

0

2.30

-2.30

0 400 800

ln (a

mou

nt, N

t)

Time, t in yrs

y = m x + bln Nt = ∆ ln Nt t + ln N0

∆ t

Radioactive decay

• At a time equal to one half-life period

• ∆ t = half-life, t1/2 and Nt = 1/2 N0

ln Nt = ∆ ln Nt t + ln N0 ∆ t

∆ ln Nt = ln N0-ln Nt = ln N0 = ln N0

ln Nt ln 1/2 N0

∆ ln Nt = ln 2 = 0.693

ln Nt = 0.693 t + ln N0 t1/2

Radioactive decay• Upon further math manipulation ln Nt =

0.693 t + ln N0

• t1/2

• ln Nt - ln N0 = 0.693 t

• t1/2

• ln Nt = 0.693 t

• ln N0 t1/2

• = e -k tNt

N0

Radioactive decay• We can also recognize radioactive decay as a first

order rate where the radiation decreases proportionately with the amount of atoms remaining. Mathematically:

• -∆ N /∆ t = k N

• By integration, we obtain:

• ln N = - k t + a

• When t = 0, a = ln N0 so:

• ln (N /N0) = k t•

• N = N0 e - k t

Radioactive decay

• The rate constant (k) is dependent on the specific radioactive species.

• It is one significant characteristic of a radioactive isotope.

• We commonly use a modified form of this constant , t1/2

• The time required for 50% of a specific radioactive species to decay.

Activity• In practice, we can’t directly evaluate N or even

∆N /∆t.

• A useful approach is to determine activity (A).

• Activity = disintegrations / unit time

• or you can use

• Activity = counts / unit time

• If the detection method is not 100% but is proportional to the number of disintegrations.

Activity• Since activity is proportional to N, we can use the

following relationships:

• At = A0 e-k t

• or

• At = A0 1/2 t / t 1/2

• This assumes that we are only measuring a single species. Decays from multiple sources can result in counting errors

Half-life example

• The t1/2 for 63Ni is 100 years. If you had 100 g of 63Ni, how much would remain after 250 years?

• At = A0 e -0.693 t / t1/2

• = 100 g e -0.693 (250 y)/(100 y)

• = 17.7 g

Energy changesin nuclear reactions.

• Binding energy (mass defect)– Binding energy is positive (endothermic), taking apart– Mass defect is negative (exothermic), putting together– Measure of stability gained when protons and neutrons

get together to form a nucleus.– The equation that shows the relationship between mass

and energy is:

• E = mc2

– We can use this relationship to determine how much energy is produced by a decrease in mass.

Binding energy• A more useful version of the equation is:

• ∆E = ∆mc2

• where:• ∆E = the binding energy• ∆m = mass difference between the nucleus

and the separate nucleons.

What would be the binding energy for a nuclear reaction that has a mass defect of 1 amu?

Binding energy

Binding energy = ∆m(amu) x 1.49 x 10-13 kJ / amu

E = 1 amu (3.00 x 10 8 m/s)2

= 9.00 x 1016amu • m2

1 s2

E = 9.00 x 1016 amu • m 2

1 s 2

1.66 x 10-27 kg

1 amu

= 1.49 x 10 -10kg • m 2 / s 2 = 1.49 x 10-10 J

Example

• Determine the binding energy of 16O.

• We have accurate measurements of the masses for stable nuclides that can be used.

• 16O 15.9949146 amu• n 1.0086649 amu• p 1.0078250 amu

Example

• To determine the binding energy, we simply need to look at the mass of the atom and the particles if taken separately.

• 16O has 8 protons and 8 neutrons

• 8 n 8 x 1.0086649 = 8.0693192• 8 p 8 x 1.0078250 = 8.0620000

• Total 16.1319192

Example• Finally, calculate the binding energy based on the

mass difference.

• ∆m = 16.1319192 - 15.9949146• = 0.1370046 amu

• BE = 0.1370046 amu * 1.49x 10-13 kJ / amu

• = 2.05 x 10-14 kJ / amuSince 1 g = 6.02 x 1023 amu, this would be equivalent to 1.23 x 1010 kJ / gram.

Binding energy• We can calculate the binding energy per nucleon for

all of the stable isotopes to compare their relative stabilities. We end up with the following plot.

Mass number

Rela

tive

bind

ing

Ener

gype

r nuc

leon

56

Fe Most stable

Binding energy• As the total number of nucleons increases, we reach

a point where the binding energy is at a maximum.

• Higher mass nucleons are less stable.

• This is why we can obtainenergy from both fissionand fusion and why alpha emission iscommon for heavierisotopes. fusion fission

Max. binding energy

Fe

Nuclear power• Power can be obtained two ways.

• Fission - Splitting atoms• Get energy if the nucleus is big.• The smaller ones are more stable.• What we do in nuclear reactors.

• Fusion - Joining atoms• Get energy if the nuclei are small.• The larger one is more stable.• This is how the sun works.

Chain reactions• Critical Reaction

• When just enough fissions occur to keep the chain reaction going.

• (neutrons formed = neutrons used)• Creates useful nuclear power.

Supercritical ReactionWhen excess neutrons are produced and the

rate of fission keeps increasing at an uncontrolled rate.

Creates nuclear bombs.

Energy from fission• Uranium-235 is used as a ‘fuel’ in a reactor.• One common reaction is

• n + U Kr + Ba + 3 n + energy

•

10

23592

9236

14156

10

One thermal neutron at room temperature is absorbed, but 3 high speed neutrons are emitted.

In order to continue the chain reaction, the emitted neutrons must be slowed down by a moderator, such as water or graphite.

Binding energyThe mass defect from splitting 1 mole of uranium-235 in a fission reactor is 0.186 grams. How many kJ of energy are released?

E = 0.186g1 kg

1000 g

3.00 x 108 m

1 s

2

= 1.67 x 1013kg • m2 / s2 = 1.67 x 1013 JThe energy produced by splitting one mole of U-235 atoms

is approximately 17 trillion kJ.

100 grams of 235U could produce as much energy as 80 trillion tons of TNT.

US Nuclear reactors

core

reactorvessel

primary coolantsecondary

coolant

turbine

heatexchangerConcrete & steel

Containment building

MOST IMPORTANT! REMOVE HEATAS FAST AS IT IS PRODUCED!

Nuclear Power Plant accidents

• Three Mile Island –oops!• Chernobyl – OMG• Fukushima – Whoa!

• Geopolitical issues?• New designs – breeder reactors, safer

traditional reactors.

Nuclear bombsA conventional explosive is used to drive two sections of U-235 together.

This creates a supercritical mass.

Energy from fusion• When you join small atoms together, you can

also get energy.

• The Sun fuses hydrogen to make helium.

4 1H12He4 + 2 1e0

+ 2 positrons4 hydrogenatoms

1 heliumatom

Energy from fusion• We’re currently trying to fuse two isotopes of

hydrogen - it’s easier.

H + H He + n + 14.6 MeV

• (1 Mev = 1.6 x 10-22 kJ)• It will be great when it works. Deuterium fuel can

be extracted from the oceans - almost free.

• But it requires a temperature of over 200 million Celsius to start the reaction.

21

31

42

10

Energy from fusion

• The Tokamac fusion reactor is like a giant electromagnetic thermos bottle that contains the fusion reaction.

Energy from fusion• This is a picture of the core of a Tokamac

fusion reactor.

Energy from fusion• This is an outside

view of a fusion reactor .

• It takes the electrical power equal to a city of 1/2 million people to maintain the fusion reaction.

Thermonuclear Weapons

• Called the Hydrogen bomb• Uses nuclear fusion but requires a huge

amount of energy to start.• Gets the energy from a fission reaction.• Two bombs for the price of one. • Not a big jump from fission to fusion bombs,

that’s why stopping countries before they get fission bombs is a good idea.

Biological effects• Somatic damage - damage to organism, acute

exposure and sickness• Genetic damage – damage to DNA which creates

long-term damage to organism and offspring.– Related to penetrating power, energy of radiation,

ionizing ability, and chemical properties.• Measured in rems = rads x RBE• Rem = roentgen equivalent for man• RBE = relative effective biological effect• Rad = radiation absorbed dose.