1Chemistry 2C Lecture 24: May 26 th, 2010 1)Belts of Stability 2)Magic Numbers 3)Einstein and his...

1Chemistry 2C Lecture 24: May 26th, 2010

1) Belts of Stability2) Magic Numbers

3) Einstein and his Equation4) Artificial Radioactivity

5) Nuclear kinetics6) Binding Energies

7) Fusion and Fission

Lecture 24: Nuclear


What kind of particle is emitted in this radioactive decay?

Question

Yes: The mass number is unchanged and the nuclear number is increased by one. A neutron has decomposed to a proton and an electron, thus emitting

an electron from the nucleus.

231 23190 91 ?Th Pa

Option 3: Perhaps the nucleus has emitted a beta particle?

Option 1: Perhaps the nucleus has emitted an alpha particle?No: The mass number hasn’t changed, which should by four if an alpha

particle is emitted!

Option 2: Perhaps the nucleus has emitted a gamma particle?

Yes/No?: The emission of a gamma particle (by itself) doesn’t change both the nuclear number and the mass number. This doesn’t fly with the info

above!


RadioactivityThe amount of radioactive contamination

released by human activity is rather small, in global terms, but the radiation

background is also rather low. Some sources claim that the Earth's background

radiation level has tripled since the beginning of the twentieth century. In fact, the total amount of radioactivity

released by man is inconsequential to the large quantities of radioactivity in the

natural environment

Fiestaware was a very popular brand of ceramic tableware. Before the early 1940's the orange color of it was made with uranium in the glaze

(uranium was used to get the color, not just accidentally)


The belt of Stability

Answer: Many factors contribute to this question, but we can make some

observations. Some patterns exist!

Question: Why do nuclei decay. Why are they unstable?

It turns out that certain numbers of protons or of neutrons are specially

stable in nuclides. Protons and neutrons are treated separately. The sum is not

the important number. Even numbers are more stable than odd numbers. When

those two rules don't predict, then nearness to the belt of stability predicts.


As Z increases, the number of neutrons has to go up faster

than Z goes up because the

“nuclear glue” that makes the nucleus stable is provided by the neutrons. Remember the

positively charged protons are

electrically repelled from each other! Above Z=83, all

elements are radioactive!

Most Z>83 nuclides decay via emission

Positron (+) emission or electron capture

preferred here!

emission preferred here!

The Belt of Stability


# of Protons

Magic Numbers

# of Neutrons

Upshot: Nature prefers even number of protons or neutrons

# of stable nuclides

odd odd 4

even odd 55

odd even 50

even even 163

examples

21 H

63 Li

136 C

4722Ti

2311 Na

2713 Al

126 C

168 O

Magic numbers

# of protons: 2, 8, 20, 28, 50, 82, 114# of neutrons: 2, 8, 20, 28, 50, 82, 126,

184

These numbers correspond to the filling of nuclear shells in a similar way that filled electron orbitals are stable (e.g. noble gases)


Radioactive Anomalies

All elements above 83 are radioactive, but below that

only technetium (Z=43) and promethium (Z=61) have no

stable isotopes).

Note: Both have odd number of protons!

Tc isotopes:

Half-life: 2.6x 106 y



9743Tc9843Tc9943Tc

Pm isotopes:

Half-life: 17.7 y

Half-life: 5.5 y

Half-life: 2.62 y

14561 Pm

14761 Pm

14661 Pm


Einstein’s Famous FormulaThe theoretical physics equation E = mc2 states a relationship between energy (E), in whatever

form, and mass (m). In this formula, c², the square of the speed of light in vacuum, is the conversion factor required to formally convert from units of mass to units of energy, i.e. the

energy per unit mass.

In chemical reaction, mass changes aren’t noticeable.

In nuclear reaction, mass changes are noticeable and large energies are involved.

Example:238 234 492 90 2U Th He

238.0003 u

233.9942 u

4.0015 u

237.9957 u

For nuclides (ignoring electrons)


Einstein’s Famous Formula

Example: 238 234 492 90 2U Th He

238.0003 u

233.9942 u

4.0015 u

237.9957 u

For nuclides (ignoring electrons)

m = 0.0046 u / nucleus

m = 0.0046 g / mol

E=mc2

=(0.0046 g / mol) ( 2.9979 x108 m/s)2

=4.13 x 1011 J/mol

That is a lot of energy!!!!


Artificial Radioactivity Not all nuclear reactions are spontaneous. These reactions occur when

stable isotopes are bombarded with particles such as neutrons. This method of inducing a nuclear reaction to proceed is termed artificial

radioactivity. This meant new nuclear reactions, which wouldn't have been viewed spontaneously, could now be observed. Since about 1940, a set of

new elements with atomic numbers over 92 (the atomic number of the heaviest naturally occurring element, Uranium) have been artificially

made. They are called the transuranium elements.

The first artificial radionuclide that was discovered was by Irene Jolet-Curie and Frederic Joliot.

27 4 30 113 2 15 0Al He P n

30 30 015 14 1P Si neutron


Artificial Radioactivity

Example 26-2

Write a nuclear equation for the production of 124I by bombardment of 121Sb with particles

121 4 12451 2 53 ?Sb He I

Whilst the nuclear number is balanced in the equation, the mass number is not! If a neutron were also ejected after the absorption of an -particle,

then both will be balanced.

121 4 124 151 2 53 0Sb He I n


Artificial Radioactivity Example 26-2

Write the nuclear equation for the subsequent decay of 124I by positron emission.

124 ? 053 ? 1 X I

Balance the nuclear number and mass number separately!

• Mass number is unaffected by the change of a proton to a neutron and emission of a positron!

• The nuclear number decreases by one after this process

124 124 053 52 1 Te I


Artificial Radioactivity The making of new elements is very important!

1) Make new elements2) Make isotopes for cancer therapy and bone scans, etc.

Here on campus, we have the Crocker Nuclear Law, a medium –sized circular accelerator call a cyclotron. It can produce charged particles

with a lot of kinetic energy which in turn can cause neutrons to be formed. At UC Berkeley, there is the Lawrence Radiation Lab (Lawrence

Berkeley National Lab), where many new elements have been made: Americium (Z=95), Berkelium (Z=97), Californium (Z=98).

To make new elements, nuclei of the lighter elements are used to bombard heavier

ones:249 15 260 198 7 105 0 4 Cf N Db n


Transuranium Metals

Americium is the only synthetic (man-made) element that can be purchased at Walmart. It does

not exist in nature and all of it that exists in the world, and at Walmart, was creating in nuclear

reactors and extracted from spent fuel rods during reprocessing

It's illegal to disassemble a smoke detector and remove the tiny radioactive dot that is contained in every ionization detector.

Berkelium and Californium can be created in nuclear reactors and have few industrial applications. They are extremely radioactive, extremely

toxic, and extremely hard to get.


TimescalesSome of the artificially produced elements have long enough lifetimes to get some measurable amount of product formed, but sometimes only a

few atoms have been detected.

All radioactive nuclei will decay, eventually, but when? For a single nucleus, it’s impossible to predict when, but for a collection of atoms there

is a statistical probability for decay.

This process is a first order process, with the rate of decay is called activity

A=N

Rate of decay: Decay constant # of atoms

Units: Activity of a Radioactive Material: New: The becqueral (1dis/sec)

Old: The Curie (3.7 x 1011 dis/sec)dis=disintegration event


Timescales

This can be integrated directly to give ln N = -t + C, where C is a constant of integration.

Although radioactive decay involves discrete events of nuclear disintegration, the number of events is so large that it can be treated like a continuum and the methods of calculus employed to predict the behavior. The result from the decay probability can be put in the differential form:

Taking the exponent of both sides gives

so the standard form of the decay equation is


Timescaleshe rate of radioactive decay is typically expressed in terms of either the

radioactive half-life, or the radioactive decay constant. They are related as follows:

The half-life and the decay constant give the same information, so either may be used to characterize decay. Another useful concept in radioactive decay is

the average lifetime.

Only because of the underlying 1st order kinetics


Timescales

Half-lived vary immensely among radionuclides

t1/2 = 5730 years146 C

4019 K

21484 Po

12353 I

11149 In

t1/2 = 1.25 x 109 years

t1/2 = 1.64 x 10-4 years

t1/2 = 13.3 hours

t1/2 = 10 hours

Used in carbon dating

Used in thyroid imaging

Used in spinal and cranial fluid imaging

natural

artificial


Unlike Chemical reactions

Unlike chemical reaction, these half-lived are Temperature independent and also do not depend at all on the state of the

mater or type of chemical combination

k=Ae-Ea/RT


Binding Energy

It is found that the nuclei weigh less than the masses of the individual particles in them. This is called the “mass deficit.”

When the nuclear particles (nucleons) come together to form a nuclear, energy is released (this is an exothermic reaction)

The binding energy is the energy needed to break the nucleus into individual protons and neutrons


Binding EnergyThe 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

A lot of energy!

For -particle, the mass deficit is 0.0305uPlugging into E=mc2, gives you an energy of 1.492 x 10-10 J


Binding EnergyNuclear energy can be extracted by generating nuclides with greater binding

energy from those of lesser (thus releasing energy that can be used for constructive uses.

Fe is the most stable nuclide with greatest binding energy

Fusion works on this side of Fe (taking small nuclides to

make bigger ones)

Fission works on this side of Fe

(taking big nuclides to

smaller ones)


Fission and FusionDuring the search for new elements in the 1930’s, it was discovered that bombarding a nucleus with neutrons could cause a nuclear to absorb a

neutron and then split into two large fragments.

This gives overall increase in energy as the sum of the binding energies for Ba and Kr are higher than for U!

235 1 23692 0 92U n U

236 92 141 192 36 56 0 3U Kr Ba n

E=8.2x107 kJ/g of 235U = 3 tons of coal combustion

More neutrons are produced as products faster than being absorbed! This is a chain reaction that exponentially increases the rate =

explosion!!!!


Fission and Fusion

The chain reaction is the basis for both a nuclear bomb and for a nuclear fission reactor. Hopefully, in a reactor, the chain reaction is controlled, and

generated heats which is used to make steam and run a turbine to generate electricity.

1Chemistry 2C Lecture 24: May 26 th, 2010 1)Belts of Stability 2)Magic Numbers 3)Einstein and his...

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