Nuclear Binding Energy

Nuclear Binding Energy




Nuclear Energy 1 cont..

Atomic Number = number of protons

Atomic Mass = number of protons + number of neutrons

What is Atomic Weight?

Calcium and Neon examples

Chart of Nuclides

Discovery of 40 Mg, 42,43 Al, and 44 Si in 2007

Enhanced selectivity from two-stage separator:!

1.5×10 17 48 Ca nuclei ( nat W target, E/A = 141 MeV)!

→ three 40 Mg nuclei!

Transport Beam Line!

S800 Analysis Line!








A1900 Fragment


Timing Detectors!

Production Target!

Achromatic Degrader!



Baumann et al., Phys. Rev. C75 (2007) 064613; Nature (2007)!

Where is the Energy coming from??????

Splitting the Uranium Atom:

Uranium is the principle element used in nuclear reactors

and in certain types of atomic bombs. The specific isotope

used is 235 U. When a stray neutron strikes a 235 U nucleus,

it is at first absorbed into it. This creates 236 U. 236 U is

unstable and this causes the atom to fission.

• 235 U + 1 neutron

• 235 U + 1 neutron

2 neutrons + 92 Kr + 142 Ba + ENERGY

2 neutrons + 92 Sr + 140 Xe + ENERGY

Radioactivity: Examples

Americium -­‐241: Used in many smoke detectors for homes and business...

Cadmium -­‐109: Used to analyze metal alloys for checking stock, sorCng scrap.

Calcium -­‐ 47: Important aid to biomedical researchers studying the cell funcCon and

bone formaCon of mammals.

Californium -­‐ 252: Used to inspect airline luggage for hidden gauge the

moisture content of soil in the road construcCon and building industries...and to measure

the moisture of materials stored in silos.

Carbon -­‐ 14: Helps in research to ensure that potenCal new drugs are metabolized withou

forming harmful by-­‐products.

Cesium -­‐ 137: Used to treat cancers...

Chromium -­‐ 51: Used in research in red blood cell survival studies.

Cobalt -­‐ 57: Used in nuclear medicine to help physicians interpret diagnosis scans of

paCents' organs, and to diagnose pernicious anemia.

Cobalt -­‐ 60 : Used to sterilize surgical instruments...spices/fruits

Copper -­‐ 67: cancer


Alpha decay

Beta decay

Electron capture

Gamma Decay


very short

very long- longer than age of earth….billions of yrs


C 5730 yrs

Alpha Decay



Beta Decay

Gamma Decay

Half-lives are very often used to describe quantities undergoing

exponential decay—for example radioactive decay—where the half-life is

constant over the whole life of the decay.

Number of





0 1

/ 1 100

1 1

/ 2 50

2 1

/ 4 25



3 1

/ 8 12 .5

4 1

/ 16 6 .25

5 1

/ 32 3 .125

6 1

/ 64 1 .563

7 1

/ 128 0 .781

... ... ...

n 1/2 n 100(1/2 n )

A quantity is said to be subject to exponential decay

if it decreases at a rate proportional to its value. Symbolically,

this can be expressed as the following differential equation,

where N is the quantity and λ is a positive number called the

decay constant.

The solution to this equation is:

Here N(t) is the quantity at time t, and N 0

= N(0) is the initial

quantity, i.e. the quantity at time t = 0.


Half-­‐life:Cme required for the decaying quanCty to fall to one half of its iniCal


This Cme is called the half-­‐life, and oYen denoted by the symbol t 1 / 2


The half-­‐life can be wriZen in terms of the decay constant, or the mean lifeCme,


Example: 14 C…..0.693/5730 yrs =1.21 x10 -­‐4 /yr

or λ=ln2/t 1/2

Example: How old is an object whose 14C content is 10% of what it is in living

organisms today?


Fusion Energy (how the sun gets its energy)

In a fusion reaction, two light atomic nuclei fuse together to form

heavier ones, as is shown in the figure. The fusion process releases a

large amount of energy, which is the energy source of the sun and the


Proton + neutron=deuterium

Proton + 2 neutrons=tritium

D+ T= 4 He +n + 17.6 MeV


H+ 3 H= 4 He

Fusion energy

Fusion Inside the Stars

• Fusion in the core of stars is reached when

the density and temperature are high

enough. There are different fusion cycles

that occur in different phases of the life

of a star. These different cycles make the

different elements we know. The first

fusion cycle is the fusion of hydrogen into

Helium. This is the stage that our Sun is in.

The long-term objective of

fusion research is to harness

the nuclear energy provided

by the fusion of light atoms to

help meet mankind´s future

energy needs.

The enormity of the nuclear binding energy can perhaps be better appreciated

by comparing it to the binding energy of an electron in an atom. The comparison

of the alpha particle binding energy with the binding energy of the electron in a

hydrogen atom is shown below. The nuclear binding energies are on the order of

a million times greater than the electron binding energies of atoms.

Nuclear Binding Energy:

Responsible for the creation of all the elements in the universe….ground rules of


Nuclei are made up of neutrons and protons but the mass of the nucleus is

always less than the masses of its constituents.

Nuclear binding energy is calculated by the change in mass or = Δmc 2

For the alpha particle Δm= 0.0304 u which gives a binding energy of 28.3 MeV.

1 u= 1 atomic mass unit


Compare with ionization energy of electrons from the atom

Nuclear binding energy = Δmc 2

For the alpha particle Δm= 0.0304 u which gives a binding energy

of 28.3 MeV.

The binding energies of nucleons are in the range of millions of electron

volts compared to a few eV for atomic electrons.

Atomic Transitions: emit a photon of a few eV

Nuclear Transitions: emit gamma rays with several MeV

galactic abundance distribution

Signatures of Nucleosynthesis


Elemental Abundances

Human Body

Oxygen 65

Carbon 18

Hydrogen 10

Nitrogen 3

Calcium 1.5

Phosphorus 1.2

Potassium 0.2

Sulfur 0.2

Chlorine 0.2

Sodium 0.1

Magnesium 0.05


Iron, Cobalt, Copper, Zinc,Iodine

M. Wiescher

Elements are made in Stars…




How Were the Elements from

Iron to Uranium made ?

How do you decide which nuclei to measure???




Ge, 85-90 As,


Se, 93-95 Br


Cu and 78 Ni first bottle necks in n-capture flow ( 80 Zn later)

(half-lives 79 Cu: 188 ms (Kratz et al, 1991)


Ni : (predicted to be comparable)

Environmental and safety aspects of nuclear energy

Not in My Back Yucca

What are our alternatives for storing

radioactive waste?

Environmental Statement on Nuclear

Energy and Global Warming

June 2005

Too expensive – power plants…

Too dangerous-­‐ terrorist groups

Too polluCng-­‐ radioacCve waste

ENERGY | 9/11/2011 @ 6:29PM |138,781


Is Thorium the Biggest Energy Breakthrough

Since Fire? Possibly.


So what is the big deal about thorium? In 2006, wriCng in the magazine Cosmos,

Tim Dean summarized perhaps the most opCmisCc scenario for what a Thorium-­‐powered

nuclear world would be like:

What if we could build a nuclear reactor that offered no possibility of a meltdown, generated its

power inexpensively, created no weapons-­‐grade by-­‐products, and burnt up exisCng high-­‐level

waste as well as old nuclear weapon stockpiles? And what if the waste produced by such a

reactor was radioacCve for a mere few hundred years rather than tens of thousands? It may

sound too good to be true, but such a reactor is indeed possible, and a number of teams around

the world are now working to make it a reality. What makes this incredible reactor so different

is its fuel source: thorium.

Thorium: Is It the Better Nuclear Fuel?

What is special about thorium?

(1) Weapons-grade fissionable material (uranium 233 ) is harder to retrieve safely

and clandestinely from the thorium reactor than plutonium is from the

uranium breeder reactor.

(2) Thorium produces 10 to 10,000 times less long-lived radioactive waste than

uranium or plutonium reactors.

(3) Thorium comes out of the ground as a 100% pure, usable isotope, which does

not require enrichment, whereas natural uranium contains only 0.7%

fissionable U 235 .

(4) Because thorium does not sustain chain reaction, fission stops by default if

we stop priming it, and a runaway chain reaction accident is improbable.

Lightbridge CorporaCon, a pioneering nuclear-­‐energy start-­‐up company based in McLean,

VA, is developing the Radkowsky Thorium Reactor in collaboraCon with Russian researchers.

In 2009, Areva, the French nuclear engineering conglomerate, recruited Lightbridge for a

project assessing the use of thorium fuel in Areva’s next-­‐generaCon EPR reactor, advanced

class of 1,600+ MW nuclear reactors being built in Olkiluoto, Finland and Flamanville,


Atomic Energy of Canada Limited and a clutch of Chinese ourits began an effort in mid-­‐2009

to use thorium as fuel in nuclear reactors in Qinshan, China.

Thorium is more abundant than

uranium in the Earth’s crust. The world

has an esCmated 4.4 million tons of

total known and esCmated Thorium

resources, according to the

InternaConal Atomic Energy

AssociaCon’s 2007 Red Book.

The most common source of thorium is

the rare earth phosphate mineral,

monazite. World monazite resources are

esCmated to be about 12 million tons,

two-­‐thirds of which are in India. Idaho

also boasts a large vein deposit of

thorium and rare earth metals.

Here is the thorium sequence in the Rubbia reactor: A neutron is captured by

90 Th232 , which makes it 90 Th 233 .

90 Th232 + 0 n1 -> 90 Th233 [1]

Thorium-233 spontaneously emits a beta particle (an electron from the nucleus),

leaving behind one additional proton, and one fewer neutron.

90 Th233 -> 91 Pa233 + ß [2]

The element with 91 protons is Protactinium (Pa). The isotope 91 PA 233 also

undergoes beta decay,

91 Pa233 -> 92 U233 + ß [3]

The U 233 isotope that is produced in step [3] is fissionable, but has fewer neutrons

than its heavier cousin, Uranium-235, and its fission releases only 2 neutrons, not 3.

92 U233 + 0 n1 -> fission fragments + 2 0 n 1 [4]




Nuclear Energy 2

Preventing the Next Fukushima…..

Science Vol. 333 September 16, 2011 arCcle…

How do we get energy from fossil fuels?

Nuclear fuels?

One example….


A water turbine is a

rotary engine that

takes energy from

moving water.

Boiling Water Reactor

In the boiling water reactor the same water loop serves as moderator, coolant for the core,

and steam source for the turbine.

Boiling Water Reactor

In the boiling water reactor (BWR), the water which passes over the reactor core to act as moderator and

coolant is also the steam source for the turbine. The disadvantage of this is that any fuel leak might make the

water radioacCve and that radioacCvity would reach the turbine and the rest of the loop.

A typical operaCng pressure for such reactors is about 70 atm at which pressure the water boils at about 285

C. This operaCng temperature gives a Carnot efficiency of only 42% with a pracCcal operaCng efficiency of

around 32%, somewhat less than the pressure water reactor.

Pressurized Water Reactor

In the pressurized water reactor, the water which flows through the

reactor core is isolated from the turbine.

In the pressurized water reactor (PWR), the water which passes over the reactor core

to act as moderator and coolant does not flow to the turbine, but is contained in a

pressurized primary loop. The primary loop water produces steam in the secondary loop

which drives the turbine. The obvious advantage to this is that a fuel leak in the core

would not pass any radioactive contaminants to the turbine and condenser.

Another advantage is that the PWR can operate at higher pressure and temperature,

about 160 atm and about 315 C. This provides a higher Carnot efficiency than the

BWR, but the reactor is more complicated and more costly to construct. Most of the

U.S. reactors are pressurized water reactors.

Liquid-Metal Fast-Breeder Reactor

In the LMFBR, the fission reaction produces heat to run the turbine while at the same time

breeding plutonium fuel for the reactor.

The most common breeding reaction is that of plutonium-239 from non-fissionable uranium-238. The

term "fast breeder" refers to the types of configurations which can actually produce more fissionable

fuel than they use, such as the LMFBR. This scenario is possible because the non-fissionable

uranium-238 is 140 times more abundant than the fissionable U-235 and can be efficiently converted

into Pu-239 by the neutrons from a fission chain reaction.

France has made the largest implementation of breeder reactors with its large Super-Phenix

reactor and an intermediate scale reactor (BN-600) on the Caspian Sea for electric power and


Breeding Plutonium-239

Fissionable plutonium-239 can be produced from non-fissionable uranium-238

The plutonium-239 breeder reactor is commonly called a fast breeder reactor, and the cooling

and heat transfer is done by a liquid metal. The metals which can accomplish this are sodium

and lithium, with sodium being the most abundant and most commonly used. The construction

of the fast breeder requires a higher enrichment of U-235 than a light-water reactor,

typically 15 to 30%. The reactor fuel is surrounded by a "blanket" of non-fissionable U-238.

No moderator is used in the breeder reactor since fast neutrons are more efficient in

transmuting U-238 to Pu-239. At this concentration of U-235, the cross-section for fission

with fast neutrons is sufficient to sustain the chain-reaction. Using water as coolant would

slow down the neutrons, but the use of liquid sodium avoids that moderation and provides a

very efficient heat transfer medium.

The Super-Phenix

The Super-Phenix was the first large-scale breeder reactor. It was put into service

in France in 1984.

The reactor core consists of thousands of stainless steel tubes containing a mixture

of uranium and plutonium oxides, about 15-20% fissionable plutonium-239.

Surrounding the core is a region called the breeder blanket consisting of tubes

filled only with uranium oxide. The entire assembly is about 3x5 meters and is

supported in a reactor vessel in molten sodium. The energy from the nuclear fission

heats the sodium to about 500°C and it transfers that energy to a second sodium

loop which in turn heats water to produce steam for electricity production.

Such a reactor can produce about 20% more fuel than it consumes by the breeding

reaction . Enough excess fuel is produced over about 20 years to fuel another such

reactor. Optimum breeding allows about 75% of the energy of the natural uranium

to be used compared to 1% in the standard light water reactors.

Example: Spontaneous Fission of 238 U results in 140 55 Cs +92 37Rb + how

many neutrons?

Example: What about 239 Pu?

It is not naturally occurring…..has to be made in a reactor…..

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