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The Atomic Nucleus
The electrolysis experiments carried out by Michael Faraday demonstrated that there is an exact
relationship between the masses of metals deposited at the cathode in an electrolysis experiment
and the current flowing through the electrolysis cell. These experiments suggested that the
carrier of electrical charge has a discrete value associated with that negative charge.
Others who contributed to understanding the nature of negative charge:
J. J. Thomson (1897) used “cathode rays” to determine the charge/mass ratio of the
electron
R. A. Millikan (1906), in his “oil drop” experiment, measured the charge independently
At the beginning of the 20th century, it was recognized that matter is electrically neutral, and
therefore, the amount of negative charge must be balanced by the amount of positive charge in
an atom. The “Plum Pudding” model of the atom suggested that both kinds of charge were
essentially uniformly mixed throughout the entire volume of an atom.
Ernest Rutherford, at the Cavendish Laboratory in England, carried out a very important
experiment in 1910 designed to probe the nature of positive charge in atoms. He did not expect
the experiment to produce an important result, so he assigned one of his “average” students to
the problem. The experiments used a collimated source of alpha particles (doubly-charged
helium nuclei) impinging on a very thin gold foil. The first sketch shows how the experiment
was done. The expectation was that because
positive charge was uniformly distributed in atoms,
the alpha particle would pass through without
significant deflection. Trajectories A and B showed
the expected behavior.
The real surprise came from trajectories like “C”, in
which a strong backward deflection was observed.
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It was possible to analyze the data to determine the actual “size” of the center of positive charge
in the nucleus.
Although the dimensions of an atom were known (from density measurements on AgCl, for
example), for example to be on the order of 10-10 m (1 Angstrom), the Rutherford experiments
sowed that the positive charge in an atom is localized in a volume of characteristic length scale
of 10-15 m. This length scale is one femtometer or one Fermi
Why nuclear chemistry in this course?
There are three important reasons why a study of the atomic nucleus is appropriate for a
freshman chemistry course based on “Energy and the Environment”:
•
The idea that the positive charge in an atom is localized in the nucleus was
revolutionary
•
The measurement of mass, just as was the case for Dalton, Avogadro, and
Cannizarro, provided further confirmation of an atomic theory of matter
•
Einstein’s famous realization that mass and energy are interconvertible led to the
prediction that huge amounts of energy are stored in nuclei. This idea forms the basis
for fission and fusion as energy sources
Einstein and E = mc2
Einstein, using concepts from his theory of relativity, speculated that energy and mass could be
interconverted. The disappearance of mass ∆m was accompanied by the creation of an
equivalent amount of energy ∆E/c2.
Suppose 1 amu of matter is converted into energy:
1 amu = 1.67 × 10-27 kg → 1.67 × 10-27 kg × (3 × 108 m sec-1)2 × (1 eV/ (1.6 × 10-19 J)) × 10-6
MeV eV-1
= 931 MeV.
Thus, 1 amu is equivalent to 931 MeV.
Precision mass spectrometry for determining the masses of individual nuclei provided the first
confirmation of this idea. Cockroft and Walton (1932) took a beam of protons accelerated to
high energy by a particle accelerator based on the ideas of Ernest O. Lawrence, and bombarded
lithium nuclei:
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1
1
H +
7
3
Li →
4
2
He + 42 He
This was the first time the atom was “split”. A national holiday was declared in Ireland when
this occurred.
Here’s what is important, however: From the masses of the reactants and products, it is possible
to calculate the energy liberated in the splitting process:
Masses:
7
Li = 7.016005
He = 4.0026033
1
H = 1.00782505
4
∆m = 2(4.0026033) - 7.016005 - 1.00782505 = -0.019118 amu.
This corresponds to -0.019118 amu × 931 MeV/amu = –178 MeV.
Cockcroft and Walton measured the kinetic energies of the alpha particle produced by splitting
the Lithium nucleus, and found that each particle had 89 MeV of kinetic energy. This was in
perfect accord with E = mc2, and provided the first experimental validation of this idea.
Is E = mc2 important in chemistry?
In nuclear processes that give off energy (they are exothermic), the reaction products are lighter
than the reactants. This fact is also true in chemical reactions. For the combustion of CH4, for
example,
CH4 + 2O2 → CO2 + 2H2O the energy liberated is 900 kJ/mol.
This is about 9 eV = 9 × 10-6 MeV.
This corresponds to 9 × 10-6 MeV/931 MeV/amu ≈ 10-10 amu or 10-10 grams per mole of CH4
combusted. At present, this is about a factor of 10 smaller than the limits on mass spectrometry,
but we do expect that within several years, it should be possible to estimate enthalpy changes for
chemical reactions by weighing reactants and products.
Nuclear binding energies:
Precise mass determinations give us the best data to predict energy output in nuclear reactions.
Let’s take a couple of examples: the deuteron, 21 H , has a mass of 2.0141022 amu. Just like for
molecules, we can calculate binding energies:
2
H → 1H + 1n
1
H = 1.00782505;
1
n = 1.00866544 amu
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∆H = 1.00782505 + 1.00866544 - 2.0141022 amu × 931 MeV/amu = 2.2 MeV
This number represents the binding energy of the proton to the neutron in the deuterium nucleus.
The binding energy per nucleon can be calculated from a knowledge f the mass of the nuclide in
question:
Consider 168 O : mass = 15.99482 amu. The sums of the masses of the constituent nucleons is
16.13193 amu.
→ 8 protons + 8 neutrons: ∆E = 931 MeV × (16.1393 – 15.99482) = 127.6 MeV. This is
the binding energy per 16 nucleons. The binding energy per nucleon is 7.97 MeV. By
calculating this quantity for each nucleus, a plot like that shown below result. This plot is the
von Weiszäcker plot.
16
8O
The plot shows that the most stable nucleus is the iron-56 nucleus, and that light nuclei tend to
form thermodynamically more stable nuclei by processes of fusion. Heavier nuclei tend to form
more stable nuclei by fission.
At the time von Weiszäcker showed this relationship, the possibility that low energy neutrons
could cause the uranium-235 nucleus to undergo fission was not known. It was primarily the
work of Hahn, Strassmann, and Meitner in Berlin that demonstrated that nuclear fission could
occur readily. It was Einstein who recognized the strategic importance of energy produced in
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this way. He and Leo Szilard wrote President Roosevelt to encourage him to pursue
development of a fission weapon before the Germans made progress in this area.
Energy from Nuclear Reactions
For any nuclear process, it is possible to estimate the energy output from the relationship
Nuclear scientists like to use the symbol Q to stand for energy output in a reaction:
Q = (mass of products – mass of reactants) × 931 MeV/amu
Fusion:
and
2
1H
+ 21 H → 23 He + 01 n
Q = (3.0162930 + 1.00866490 – 2.0141079 – 2.0141079)(931) = -3.27 MeV
2
1H
+ 21 H →
3
1
H +
1
1
H
Q = -4.03 MeV
This is the “D-D” reaction.
2
1H
+ 31 H → 42 He + 01 n
Q = -17.6 MeV
This is the “D-T” reaction, the one used by LLE at he University of Rochester.
Fission:
235
92 U
+ 01 n →
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38 Sr
+
143
54 Xe
+3 01 n
Q ≈ -200 MeV
Note that it is only U-235 that is fissionable with low energy neutrons. The natural
abundance of this isotope is only 0.7%, so enrichment is necessary. Not also in this reaction,
three neutrons are produced for each neutron going in, so a self-sustained chain reaction can
occur. Note also that the identity of the fission products is not unique. The nuclides shown
represent only one of many possibilities.