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Atomic
Structure and the Pascal Triangle
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Atoms are made of 3 types of particles :
electrons, protons and neutrons.The atom of hydrogen has one
proton and one electron. The proton and electron stay together
because the opposite electrical charges attract each other.
The electron is constantly spinning around the center of the
atom ( called the nucleus ). |
The familiar model of an atom is that of a small nucleus composed of protons and
neutrons surrounded by rapidly moving electrons. Typically, the atomic diameter is on
the order of l0-10 m while that of the nucleus is on the order of 10-15 m. Protons and
neutrons have about the same mass (1.00728 and 1.00867 amu respectively) and each
is about 1800 times as heavy as an electron. A neutron is electrically neutral, but a
proton has a positive charge (+1.6 x 10-19 coulomb*) which is exactly the opposite of
the negative charge of an electron. In a neutral atom, the number of electrons around
the nucleus equals the number of protons in the nucleus.
The number of protons in the nucleus (the "atomic number", Z) characterizes a
chemical element. Atoms of a given element all have the same number of protons, yet
may have different masses. The atomic mass number of an atom, A, is given by
A = Z + N, where N is the number of neutrons in the nucleus. Since an element is
characterized solely by Z, it follows that atoms of a given chemical element may have a
varying number of neutrons. Subspecies of chemical elements with the same Z but
differing N and A are called isotopes. The atomic weight of an element is the weighted
average of the atomic masses of the various naturally occurring isotopes of the
element, and the atomic weight scale is based on a value of exactly 12, after the carbon
isotope that has an atomic mass number of 12.
The nucleus of an atom weighs less than the sum of the weights of its isolated
component particles. The difference between the actual mass and that of the
components is called the mass defect. The nuclear
forces which bind protons and neutrons together are strong, and the binding energy per
nuclear particle (nucleon) amounts to about 1.4 x 10-12 Joules. The greatest nuclear
binding energy is found in nuclei of medium atomic number (such as Fe) where N is
approximately equal to Z. For nuclei of larger atomic number, such as uranium, N is
about equal to 1.5 Z, and the binding energy per nucleon is less. As a consequence of
this decreased nuclear stability, some isotopes (of uranium, for example) are unstable.
That is, if the uranium isotope,92U235 (Z = 92, A = 235), is bombarded with neutrons,
the following reaction can take place:
92U235 + n = 39Y94 + 53I140 + 2n
Here the reaction products are smaller nuclei of increased stability. (In the above
convention, subscripts indicate the atomic number and the superscripts the mass
number.) Notice that one incident neutron generates fission products including two
neutrons - the basis for chain reactions in nuclear reactors and nuclear explosions.
Heavy nuclei (even light nuclei) which have an unfavorable ratio in the number of
protons and neutrons can spontaneously decay by the emission of particles (helium
ions) or particles (electrons). These nuclei are referred to as radioactive.
Numbers, known as figurate
or polygonal numbers, appeared in 15th-century arithmetic books and
were probably known to the ancient Chinese; but they were of
especial interest to the ancient Greek mathematicians. To the
Pythagoreans (c. 500 BC), numbers were of paramount significance;
everything could be explained by numbers, and numbers were invested
with specific characteristics and personalities. Pascal`s Triangle
is an arrangement of numbers such that each number is the sum of two
numbers immediately above it in the previous row.Pascal simply
discovered one of nature`s structural formulas.
The Electronic
Configuration Pattern can be found in Pascal`s Triangle of the Second Kind (squar numbers).
The elements of Group 18, the noble gases, are:
| |
symbol |
electron configuration |
| helium(#2) |
He |
1s2 |
| neon(#10) |
Ne |
[He]2s22p6 |
| argon(#18) |
Ar |
[Ne]3s23p6 |
| krypton(#36) |
Kr |
[Ar]3d104s24p6
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| xenon(#54) |
Xe |
[Kr]4d105s25p6
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| radon(#86) |
Rn |
[Xe]4f145d106s26p6
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The connection between
magic numbers of noble gases on one side and squar numbers, on the other,
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1 |
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= |
1 |
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2 |
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4 |
1 |
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= |
5 |
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10 |
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4 |
4 |
1 |
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= |
9 |
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18 |
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9 |
4 |
4 |
1 |
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= |
18 |
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36 |
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9 |
9 |
4 |
4 |
1 |
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= |
27 |
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54 |
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16 |
9 |
9 |
4 |
4 |
1 |
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= |
43 |
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86 |
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16 |
16 |
9 |
9 |
4 |
4 |
1 |
= |
59 |
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118 |
is highly amusing.
Natural materials are made of natural existing elements or nuclides. Some of these elements have more than one stable isotope, and some may have long-live isotopes. Stable nuclides are the stable isotopes of all elements.
Elements with Z = 2, 8, 20, 28, 50, and 82 have many isotopes. Thus, these numbers are called magic numbers. For example, the stable isotopes of calcium (Z = 20) have mass numbers 40, 42, 43, 44, 46, and 48, a total of six.
Double-magic-number nuclides :Nuclides 4He2, 16O8, 40Ca20,
48Ca20, and 208Pb82 have magic numbers of protons and magic number of neutrons.Nuclei with magic numbers of protons or neutrons exhibit certain properties,
which are analogous to closed shell properties in atoms, including anomalously low masses,
high natural abundances and high energy first excited states.
Even Z elements are more abundant than odd Z ones of comparable mass.
Also, there
is a remarkable connection between magic numbers of nucleons on one side and
tetrahedral numbers and triangular numbers, on
the other.
This discovery will lead to a better understanding of the
periodic atoms and even quantum physic.
Belorussian translation
German translation
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