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Natural Radioactivity
Natural Radioactivity was discovered at the end of the 19th centaury.
Protons and neutrons we consider today as occupants of a nucleus. The
electron flays out from a nuclei as a  particle, is not occupant of nuclei.
Simply is to show it use of the Heisenberg uncertainty principle: The
electron cannot be in nuclei. Energy of the electron should be about 200
MeV, but such  particles we do not observe in nature. One previous
apparatus to investigate radioactivity can be seen in Fig 1. A magnetic field
is perpendicular to the surface of the figure.
Fig.1
A reader of this book should get explanations. One of the important
physical laws is the Heisenberg uncertainty principle. This principle refers
us we can’t localise particle because its momentum is equal to infinite.
Instead, energy very often we take momentum of a particle. The
momentum, which is multiplication of its mass and velocity, is a vector and
we can give this quantity direction. After Heisenberg, we say:
x
Or for energy and time:
p ≤ h/2,
E
If:
≤ h/2
x - uncertainty of location (dimension of a nuclei ~10-17 m),
p - uncertainty of a momentum and
h - Universal Plank’s constant (6.63 x 10-34 J s)
At 1918, the Plank got the Nobel Price. In the second equation: E
and are uncertainties of energy and time, respectively. Proton we
marked as 1p1 and neutron as 1n0, (sometime we write down markers on
one side of letters). The 1p1 (we called) proton has a charge one (q = +1
(1.6 x 10-19 Coulomb), and a mass equal to one. A proton has mass equal
to 1.007825AM (average atomic mass) exactly. A neutron has no charge.
Its big magnetic momentum indicates a neutron has internal charges. A 1p1
particle is one of nuclear particles. A  particle is a polarised electron. A
polarised electron means the electron, which has angular momentum and
velocity correlated. Angular momentum is often called spin.  particles
move very fast, often with speed closely to the speed of light (3 x 10 8 m/s).
The Einstein relativistic laws should apply to any calculation. Einstein was
the Nobel price winner from 1931. Nobody understood his General
Relativistic Theory and he got the Nobel Price for external photo-effect.
Energy of disintegration we can calculate from a range in metals, for
instance in Al (Aluminium). Sometimes, we write down the number and
symbol of an atom. For example, 1H or 3H means 1Hydrogen and
3Hydrogens (Tritium), respectively. An Isotope we call a nucleus that has
different numbers of neutrons. Mathematical shorthanded are often in use. I
will say nothing about Auger’s electrons (read Oze) and internal conversion
of .
I will apply all shorts to secundus as example.
We call ;
Ts
equal
to
1012s
called
terra-seconds
G
=|=
109s
=|=
giga-seconds
Ms
=|=
106s
=|=
mega-seconds
ks
=|=
103s
=|=
kilo-seconds
s
=|=
second
=|=
second
ms
=|=
10-3s
=|=
mili-seconds
μs
=|=
10-6s
=|=
micro-seconds
ns
=|=
10-9s
=|=
nano-seconds
ps
=|=
10-12s= | =
pico-seconds
For example, for another unity, we will call Volt and write down: nV, GV V
or pV and so on.
What is the primary and what is the secondary particle, we can
discuss. Protons and neutrons have in Quarks, but these “particles” not
exists alone. Quarks have charges but fractional of the primary charge,
only. Feynman used to say, “As far as we know.”
N = A – Z are number of neutrons in nucleus;
A – Atomic Mass
Z – Atomic Numbers
All above are taking from the table of elements.
Instead of Joule (J) as unity of energy in nuclear physic, we frequently use
electronvolt (eV). One unit 1 eV is there if charge of one electron is moving
across Potential Difference of one Volta.
1 eV = q x 1V = 1.6 x 10-19J
Hydrogen has two “brothers.” The first “brother” called Deuterium and
the second one called Tritium.
The following figure shows two “brothers” of the Hydrogen. We call
these isotopes.
Fig.2
Tritium is radioactive and has virtually long Half Life Time; you can obtain it
only in Nuclear Reaction. Half Life Time (T½) we called such period, after
which half mass of radioactive material (radioactive isotope), left only. Life
Time ( of radioactive material (isotope) is longer than T½.
 = T½ /
Radioactive disintegrations have general formula. You can calculate many
things from this.
I = I0e-
If:
- disintegration constant (decay constant)
I – radiation intensities after time ()
I0 –beginning intensity
 and  are tree natural disintegrations of radioactivity. The last one
is always a companion to  or  radiations. We know only one example so
called “clean”  decay.  disintegration is nuclei of Helium, which consists
of two protons and two neutrons. “Why Helium” we can ask? I will not
explain a theory even many books have been written in this subject.
Radioactive element, which produce  particle, coming back in table of
element two unities and its atomic mass diminished four units. Figure 3
shows creation of the  particle.
Fig.3
A recoil nucleus (A-4YZ-2) is usually at excited state, after emission of
particle. A recoil nucleus when becoming normal, produce  particle.
Normal  obtain from natural radioactivity not coming through piece of
paper.  particle strong ionised environment. Ionising means produce many
ions (atoms with orbital electrons added o subtracted from atoms). Recoil
nucleus often is radioactive it self. Next generations of  and 
offcourse can be produces.
Radioactive element, which produce  particle going forward one
place in a table of elements and its atomic mass, remains the same. The
figure 4 shows creation of  particle.
Fig. 4
Both of radioactive decays and 
 particle. This
is shown in Figure 5
Fig. 5.
K capture and positronium emissions belong to artificial radioactivity.
K capture is taking off an electron from orbita of k (the first one) and
capture it into a nucleus. Only a neutrino flays from a nucleus. At emission
of the positronium, we observe positive electron (antiparticle to an
electron). An element created going back one place at table of element and
this atomic mass does not changed. This is shown in Figure 6.
Fig. 6.
An element produces positronium going back one place at table of element
and this atomic mass does not changed. During production of positronium,
neutrino is created. Positronium creation shows next figure.
Fig.7.
An element can stand on the top with radioactive “family” if it has very long
live time. These are related to both decays  and . All created elements
(isotopes) are radioactive and all are finish with isotope of Lead, which are
not radioactive. An isotope of a Lead means Lead with different atomic
masses (different numbers of neutrons inside). We have tree radioactive
series (family) of elements on the earth.
In the first family or series on the top of its family is an isotope of a
238
U92 (238 Uranium), decayed to an isotope of
234
Th90 (234 Thorium) with a
very long lifetime and equal to approximately 4.51 x 109 years. A mass of
those “sisters” and “brothers” maybe calculated from the equation of 4n + 2,
where n is equals to positive integers (1, 2, 3… and so on).
In the second family on the top, is an isotope of
decays to  particle and
231
235
U92 (235 Uranium),
Th90 (231Thorium) with a lifetime equal to 7.53 x
109 years. All members of this family have Atomic Mass calculated as 4n +
3.
Next and last family is family of isotope of
isotope of
228
232
Th90 (232Thorium), decays to
Ra88 (228Radon) and  particle with a lifetime of 1.39 x 1010
years. All members of this family have Atomic Mass calculated as 4n.
We had another “family” in pas, but all members of this family decays
and they should have Atomic mass equal to 4n+1. The longest lifetime from
this family had isotope of Neptune and on the bottom of this family should
bee isotope of
205
Tl81 (209Talium). Members of this family may be created
in Nuclear Reactions.
We have radioactive elements do not belong to families such as of
40K, 50V, 196Hg, 204Pb and all Transuranic (bigger than Uranium).
Atomic Numbers (Z) we don’t write down very often. Instead of writing
down the full name of an elements such as
205
Tl81 or different, we simple
write down 205Tl. Thallium have 124 neutrons (205 - 81 = 124).
 and  radiations are always companions to  particle, as I have
mentioned. If a nucleus that been created is in exciting state, this event
produces  particle, which is similar to light. This Phenomenon is similar to
a light creation but with bigger energy (hν), where h – Plank constant and 
- frequency. Figure 8 shows this phenomenon, where * - recoil nucleus in
exciting state and  - normal state.
Fig.8
Energy is equal distributed between  particle and a coil nucleus. Is
not equally distributed in a decay of  particle, where the spectrum of
energy is different. We say this energy spectrum is continuous (see chapter
about neutrinos).
Different counter can applied to radioactive particles. Standard
counter is a G-M counter. We have also other counters like scintillating
counter and semi-conductor counter, respectively. G-M counters profits
ionisation by ionising particles entering volume of ionising chamber.
Separate problems are quenching of avalanche of ions in the G-M counter,
so counter can recorded next ionising particle. Very small scintillation time,
can record tiny scintillations and record these by special electronic device
called a multiplier. Each sort of radiation has different a scintillator. Semi
conductor counters works tis way that ionised p-n junction in counters by
entering of ionized radiation. I do not describe counters.
Intensity of radiations we can measure using Becquerel (Bq) or kiore
(Ci).
1 Bq = 1 disintegration/secund
1 Ci = 3.7 x 1010 disintegration/secund is equal to Radon, which is in
balance with 1 g of Radium.
1 Ci = 3.7 x 1010 Bq.
Ci is not a standard unit, but is widely recognised in the world. By applying
an external magnetic or electric field, we can also observe momentum of a
particle. Momentum of a particle giving as more information than energy of
a particle, because also is giving its direction. We do it in a Wilson
Chamber or in a Glaser bubble chamber. Wilson Chamber applied to
superheated steam and bubble chamber applied to supercooled liquid
(liquid hydrogen). Any ionising particles we can trace in both chambers.
Superheated steam is over heated steam and supercooled liquid is over
cooled liquid. The Glaser bubble chamber applied to high-energy particles
because bigger density than the Wilson Chamber.
Becquerel and couple of Curie were Nobel Price winners at the 1903.
Maria Skłodowska (original name) did a PhD thesis and married P. Curie,
taking his name. Her husband, Pierre, had horse carriage accident and
died soon after. Marie Curie was the Nobel Price winner again, 1911, in
Chemistry for discovery Polonium. She was one of the first causality of
radiation. C.T.R. Wilson, F. Heisenberg and D. Glaser got a Nobel Prices in
1927, 1932 and 1957, respectively. R. P. Feynman got the Nobel Price at
1967.