CHEMISTRY 1000

Nuclear Chemistry

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Radioactivity and Radiation

Nuclear reactions result in changing the nuclei of atoms. These reactions are accompanied by emission of ionizing radiation (which has enough energy to excite electrons out of molecules, ‘ionizing’ them). There are three main types of ionizing radiation:

alpha rays (): helium nuclei (2 protons + 2 neutrons) beta rays (): electrons gamma rays (): high energy photons (higher energy than

x-rays) which have no mass and no charge

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Radioactivity and Radiation

• -particles can be stopped by paper.• -particles require at least a cm of lead (Pb).• -particles require at least 10 cm of lead (Pb).• Neutrinos: zero charged particles even smaller

than electrons.

Energy: > >

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Measuring Radiation

rad = radiation absorbed doserem = radiation equivatlent for manQ = RBE (relative biological effectiveness)Sv = Gy x Q

rad = radiation absorbed doserem = radiation equivatlent for manQ = RBE (relative biological effectiveness)Sv = Gy x Q

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Effects of Radiation Exposure (long term)

Natural and Artificial Sources of Radiation.

Effects of Radiation (Short Term)

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Example: Calculate the radiation dosage (in Sieverts) for a person weighing 68 kg that is exposed to 3.5×108 particles of alpha radiation. Assume that 89% of the radiation is absorbed and each alpha particle has an energy of 6.2×10-13 J, and that the RBE or Q of alpha particles is 15.

Example: Calculate the radiation dosage (in Sieverts) for a person weighing 68 kg that is exposed to 3.5×108 particles of alpha radiation. Assume that 89% of the radiation is absorbed and each alpha particle has an energy of 6.2×10-13 J, and that the RBE or Q of alpha particles is 15.

Calculating Radiation Dosage

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• Safe dose for single exposure is much higher than safe dose for long term exposure

• Annual exposure to background radiation in Canada depends on location but typically about 3 mSv (=3000 µSv = 300 mrem)

• Legal limits to radiation exposure at work (50 mSv/year, 100 mSv over five year)

• Legal doses: LD50 for a single exposure 4 Sv

LD50 for ongoing exposure is …

Short Term Exposure vs Long Term Exposure

http://www.hc-sc.gc.ca/hl-vs/iyh-vsv/environ/expos-eng.php8

Nuclear Medicine: Imaging

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C12

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mass number (A)

atomic number (Z)C

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mass number (A)

atomic number (Z)

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Balancing Nuclear Reactions

In any nuclear reaction, two things are conserved: The sum of the mass numbers of the products is equal to

the sum of the mass numbers of the reactants. The sum of the atomic numbers of the products is equal to

the sum of the atomic numbers of the reactants.

The “atomic number” for an electron () is considered to be -1.

The exact masses of products and reactants are not the same. The small mass difference between mass of products and reactants results in release of energy (E = mc2) and the law of conservation of energy still holds. (The law of conservation of mass is a special case of the law of conservation of energy.)

C12

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mass number (A)

atomic number (Z)C

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mass number (A)

atomic number (Z)

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Balancing Nuclear Reactions

At21885 e0

-1+

Tl20681

42+

U23692 Ba141

56 n10+ 3+

U23592 Th231

90 +

Balance the following nuclear reactions.

Be74 e0

-1+

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Classes of Nuclear Reactions

There are seven classes of nuclear reactions: Alpha emission

Beta emission

Positron emission

Electron capture

Fusion

Fission

Bombardment (to make transuranium elements)

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Classes of Nuclear Reactions

reactants products* ΔZ spontaneous?

alpha emission 1 nucleus 1 nucleus + 1 alpha particle -2 yes

beta emission 1 nucleus 1 nucleus + 1 electron +1 yes

positron emission 1 nucleus 1 nucleus + 1 positron** -1 yes

electron capture

1 nucleus + 1 electron 1 nucleus -1 yes

fission 1 nucleus 2 nuclei + neutron(s) varies no

fusion 2 light nuclei 1 nucleus + neutron(s) varies sometimes

bombardment 2 heavy nuclei 1 nucleus + neutron(s) varies no

* Most nuclear reactions also emit electromagnetic radiation. Emitting an or particle leaves the nucleus in an excited state so it emits a photon as it returns to the nuclear ground state. The energy of the photon is specific to the nuclear reaction.** As antimatter, positrons are not directly observable. A positron is annihilated as soon as it collides with an electron, releasing radiation (a high energy photon).

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Classes of Nuclear Reactions

An unstable nuclide undergoes spontaneous nuclear reaction to form a more stable nuclide. If this product is also unstable, it undergoes another nuclear reaction (and another and another, etc. until a stable nuclide is reached). Such a series of alpha- and beta-emissions is called a radioactive decay series:

“nuclide” = a specific type of nucleus (i.e. containing a specific #protons and #neutrons)

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Classes of Nuclear Reactions

Some classes of nuclear reaction, on the other hand, will never occur spontaneously. Instead, they must be induced (often by hitting the nucleus with a neutron to generate a highly unstable nucleus which will then undergo the desired nuclear reaction). This is true of fission and bombardment:

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Why Do Nuclear Reactions Occur?

What factors affect stability of a particular nuclide? A nucleus consists of protons and neutrons held together

by nuclear binding energy. At the same time, there is electrostatic repulsion between

the positively-charged protons. If this repulsion is too great, the nucleus will be unstable.

Neutrons lessen this repulsion by increasing the distance between protons; however, neutrons are inherently less stable than protons. Excess neutrons will decompose into proton/electron pairs.

It is therefore possible to make a few generalizations: Nuclides containing more protons need more neutrons

(to keep the protons apart). Nuclides containing fewer protons need fewer neutrons

(to maximize stability). There is a maximum number of protons beyond which

the nuclear binding energy cannot hold the nuclide together stably (because the electrostatic repulsion is too great).

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Why Do Nuclear Reactions Occur?

The number of stable nuclides is relatively small. Plotting #protons (Z) vs. #neutrons (N) for all nuclides that have been made/found gives a narrow band of stable nuclides (black dots) surrounded by a wider band of unstable nuclides (red dots). The stable nuclides form the band of stability.

Nuclides farthest from the band of stability are least stable, decaying fastest.

Heavy nuclides decay faster than light ones.

N-to-Z ratio in stable nuclides is predictable:

If Z = 1-20 (H to Ca), N Z is ideal If Z = 20-83 (Sc to Bi), N > Z up to N 1.5

Z If Z 84 (Po and larger), no stable nuclides

exist Even values for Z & N are conducive to

stability. Almost 60% of stable nuclides have both even. Less than 2% of stable nuclides have both odd!

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Why Do Nuclear Reactions Occur?

The type of nuclear reaction which a nuclide is most likely to undergo can be predicted from its N-to-Z ratio.

A nucleus which has “too many neutrons” (i.e. N/Z is too high) will tend to undergo beta emission. How does this improve N/Z?

A small nucleus which has “too many protons” (i.e. N/Z is too low) will tend to undergo either positron emission or electron capture. How does this improve N/Z?

A large nucleus which has “too many protons” (i.e. N/Z is too low) will tend to undergo alpha emission. How does this improve N/Z?

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Nuclear Binding Energy

When nucleons (protons and neutrons) come together to make a nucleus, energy is released. This energy is referred to as nuclear binding energy (E) and a nuclide’s nuclear binding energy can be calculated using Einstein’s famous equation:

The nuclear binding energy for any nuclide can thus be calculated by comparing its mass to the total mass of the protons and neutrons it contains. You may have already noticed that atomic masses are not exactly equal to the sum of the masses of the protons, neutrons and electrons in the atom!

In order for a nuclide to be stable, its nuclear binding energy must be greater than the electrostatic repulsion between its protons.

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Nuclear Binding Energy

Since they release more energy upon formation, nuclides with greater nuclear binding energies would at first seem to be more stable; however, we must also factor in the number of nucleons brought together. Otherwise, larger nuclides appear to be excessively stable are simply because they contain more nucleons.

So, a more useful quantity to calculate is the nuclear binding energy per nucleon (Eb):

where A = mass number = #nucleons = Z + N

Nuclides with larger Eb values are more stable.

AE

Eb

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Nuclear Binding Energy

Calculate Eb for the helium isotopes: 3He (3.016029310 g/mol) and 4He (4.002603250 g/mol). Which isotope is more stable?

Mproton = 1.0072765 g/mol Mneutron = 1.0086649 g/molMelectron = 0.0005486 g/mol

For this type of calculation, ALWAYS use the mass of the specific isotope or nuclide.NEVER use the average atomic mass listed on the periodic table

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Nuclear Binding Energy

4He is one of the most stable nuclide. When Eb is plotted as a function of A, the most stable nuclide is found to be 56Fe:

This plot also shows which nuclides can undergo fusion (increasing Eb by increasing A) and which nuclides can undergo fission (increasing Eb by decreasing A).

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Nuclear Binding Energy

Since a nuclear reaction involves conversion of one (or more) nucleus to another, it can be modeled as destruction of the original nucleus followed by creation of a new nucleus:

So, we can calculate the energy released by any nuclear reaction as long as we know the masses of the nuclides involved.e.g. A neutron (1n, 1.0087 g/mol) strikes 235U (235.0439 g/mol) to give 138Xe (137.908 g/mol), 95Sr (94.913 g/mol) and 3 1n.

Activity (A) = Disintegrations/time = (k)(N)

where N is the number of radioactive atoms

k is decay constant (in s-1) and is characteristic of a particular decay.

Activity can be measured using a Geiger counter or scintillation counter

Rates of Radioactive Decay

If there are N1 atoms before decay and N2 atoms after decay, then the number of disintegrations ΔN = N2-N1 during a time change of Δt = t2 - t1

So A = -ΔN/Δt = (k)(N) 24

Can We Find the Decay Constant by Graphing?

From A = -ΔN/Δt = kN, if we can measure A and N in the lab, we can graph A vs. N to find k, as A = kN is a linear equation like y = ax. The slope of the line A vs. N would give k.What does this graph look like?

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However, even if we can measure Δt and N in the lab, a graph of N vs. Δt would not be linear and therefore not useful in finding k, as N = (-ΔN/k)Δt is not a linear equation like y = ax, but a non-linear equation like y = a/x. What does this graph look like?

Can We Find the Decay Constant by Graphing?

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Fortunately, Radioactive Decay is a first-order reaction

 

The rate of the reaction only depends on the “reactant” concentration.

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What Is the Half-Life of a Radioactive Decay?

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After each successive half-life, one half of the original amount remains.

Finding Half-Life from a Graph

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Willard Libby (1908-1980)Libby received the 1960 Nobel Prize in chemistry for developing carbon-14 dating techniques. He is shown here with the apparatus he used. Carbon-14 dating is widely used in fields such as anthropology and archeology.

Radiocarbon Dating

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Radioactive 14C is formed in the upper atmosphere by nuclear reactions initiated by neutrons in cosmic radiation:14N + 1

0n 14C + 1H

The 14C is oxidized to CO2, which circulates through the biosphere.When a plant dies, the 14C is not replenished.But the 14C continues to decay with t1/2 = 5730 years.Activity of a sample can be used to date the sample.

Radiocarbon Dating

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Is There a Limit for Carbon-14 Dating?

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106Sg

Transuranium Elements & Glenn Seaborg

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Nuclear Fission

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Fission chain reaction has three general steps:

Initiation: Reaction of a single atom starts the chain (e.g., 235U + neutron)

Propagation:236U fission releases neutrons that initiate other fissions

Termination:Consumption of the fissionable material is completed

Nuclear Fission

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109Mt

Nuclear Fission & Lise Meitner

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Currently about 103 nuclear power plants in the U.S. and about 435 worldwide.

17% of the world’s energy comes from nuclear reactions.

Nuclear Fission & Power

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