<p class="MsoNormal"><span style="font-size: 1rem;">The activity of a radioactive source is the
number of ionizing particles it emits per second. Each emission corresponds to
a change in the nucleus of one atom and is also called the decay rate. The SI
unit of activity (and decay rate) is the </span><b style="font-size: 1rem;">becquerel</b><span style="font-size: 1rem;"> (Bq):</span><br></p><p class="MsoNormal"><span lang="">1 Bq = 1 decay per second<o:p></o:p></span></p><p class="MsoNormal"><span lang="">What we actually record is the reading on any
radiation detector we use to monitor the effect of the radiation. Usually, this
is the count rate as measured by a Geiger counter. The count rate is simply the
number of counts recorded per second, and in simple experiments, it is taken to
be directly proportional to the activity. Note that it is very unlikely that
all the decays of a source will be recorded. Usually, some of the radiation is
trapped inside the source, and in most measurements, only a small fraction of
the radiations actually enter the detector to be counted.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1579031910/ofxa4o5zlipm5nbd5x4h.jpg" data-filename="ofxa4o5zlipm5nbd5x4h" style="width: 527.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Gammaspektrum_Uranerz.jpg" target="_blank"><sup>Gamma-ray energy spectrum. Wusel007, CC BY-SA 3.0</sup></a><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">As time goes on, the activity of a source (and
so the count rate) decreases in a consistent manner. There is&nbsp;a typical plot of the alpha particle count rate against time for a small
sample of the radioactive gas radon (Rn-220).<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The graph has been drawn as a ‘best fit’
through actual numbers recorded by a counter. The count rate in counts per
second is calculated from the number of counts measured at 10-second intervals.
There are two significant features of the graph. One is that the values aren’t
all on the line, so the measurements have some inbuilt uncertainty. Secondly, as
the annotation shows, the time taken for the count rate to fall from 400 s<sup>-1</sup>
to 200 s<sup>-1</sup> is the same as the time for the count rate to fall from
200 s<sup>-1</sup> to 100 s<sup>-1</sup>. That is, the graph suggests that:<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The time taken for the activity of a
radioactive sample to decrease to a half of any starting value is the same,
whatever the starting value of the count rate.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">This time is called the half-life of the
radioactive substance. <o:p></o:p></span></p><h2><span lang="">RANDOMNESS OF DECAY<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Both the uncertainty in measuring and the
constancy of the half-life have the same cause: the time at which any given
radioactive nucleus emits its radiation cannot be predicted. It is impossible
to tell which one of a hundred radon nuclei will be next to emit its alpha
particle. All the nuclei are identical, and all are equally liable to decay.
But the breakdowns are completely random. However, if we have a sample of
several hundred billion radon nuclei, a pattern would emerge. Bear in mind that
ten billion (10<sup>10</sup>) radon nuclei have a mass of a few thousandths of a
billionth of a gram (about 4 </span><span lang="">×</span><span lang=""> 10<sup>-12</sup>
g).<o:p></o:p></span></p><p class="MsoNormal"><span lang="">What is constant about the radioactive process
is that each nucleus has a definite probability of undergoing decay. Starting
with a large enough number of radon nuclei, we can be reasonably certain that a
predictable number will emit an alpha particle in the next 10 seconds.
Similarly, with a large enough sample, the values of count rate we measure will
coincide closely with the smooth graph we draw between the values. Our estimate
of half-life will be more reliable.<o:p></o:p></span></p><h2><span lang="">THE SHAPE OF THE ACTIVITY CURVE<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">We associate an exponential change with any
system where the change is proportional to the quantity that is changing, either
increasing or decreasing. An example of an increase is a biological population
growth, where the number of young born is proportional to the number of
organisms in the population. This property is also characteristic of many
physical changes. The graph plotted above is a decay curve for an exponential
change to a radioactive material, and here the decrease in the population of
nuclei is exponential: the decay rate decreases by equal fractions in equal
times. The fraction that we use for a radioactive material is a half, so we
refer to its <i>half</i>-<i>life</i>.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Mathematically, if </span><span lang="">Δ</span><span lang="">N is the number of nuclei that decay in a small time </span><span lang="">Δ</span><span lang="">t, then:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Δ</span><span lang="">N = -KN</span><span lang="">Δ</span><span lang="">t&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1]<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">The minus sign is because </span><span lang="">Δ</span><span lang="">N is a reduction in N: as time goes on N decreases. The decay constant
k is a measure of the probability of a nucleus decaying in the following
second. (Each radioactive nucleus has its own value of k.)<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The passage overleaf gives the calculus
version of deriving the exponential form of radioactive decay.<o:p></o:p></span></p><h2><span lang="">THE DECAY CONSTANT AND HALF-LIFE<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">For a radioactive nucleus, the decay constant
indicates the probability that the nucleus will undergo decay. Its value is in
terms of the fraction of the potentially active nuclei in a sample that do
actually decay in any second of time. So, the larger the value of k, the higher
the number of nuclei decaying in a given time and the shorter the half-life.
The passage below shows that the relation between half-life and the decay
constant is:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">half-life (in seconds)
= ln2 / k&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [2]<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">Where In 2 is the logarithm to base e of 2
(0.693).<o:p></o:p></span></p><h3><span lang="">EXAMPLE<o:p></o:p></span></h3><p class="MsoNormal"><b>Question</b><span lang="">: The
half-life of bismuth (Bi-212) is 60.6 minutes. What is its (a) decay constant,
(b) the activity of 1 g of bismuth-212? Taking the Avogadro constant as 6.02 </span><span lang="">×</span><span lang=""> 10<sup>23</sup>.<o:p></o:p></span></p><p class="MsoNormal"><b>Answer</b><span lang="">: (a) Half-life
of bismuth = (ln 2)/k,<o:p></o:p></span></p><p class="MsoNormal"><span lang="">So, decay constant k = 0.693/(60.6 </span><span lang="">×</span><span lang=""> 60) = 1.91 </span><span lang="">×</span><span lang=""> 10<sup>-4</sup> s<o:p></o:p></span></p><p class="MsoNormal"><span lang="">(b) 212 g of bismuth-212 contains 6.02 </span><span lang="">×</span><span lang=""> 10<sup>23</sup> atoms.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Therefore number of atoms in 1 g:<o:p></o:p></span></p><p class="MsoNormal"><span lang="">N = (6.02 </span><span lang="">×</span><span lang=""> 10<sup>23</sup>)/212 = 2.84 </span><span lang="">×</span><span lang=""> 10<sup>21</sup><o:p></o:p></span></p><p class="MsoNormal"><span lang="">The probability of decay for bismuth-212 is k
per second. Thus we would expect <i>k</i>N atoms to decay per second:<o:p></o:p></span></p><p class="MsoNormal"><span lang="">activity <i>k</i>N = 1.91 </span><span lang="">×</span><span lang=""> 10<sup>-4</sup> </span><span lang="">×</span><span lang=""> 2.84 </span><span lang="">×</span><span lang=""> 10<sup>21</sup> Bq = 5.4 </span><span lang="">×</span><span lang=""> 10<sup>17</sup>
Bq</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1579031543/vvc9exvpyo6qisqsla5j.jpg" data-filename="vvc9exvpyo6qisqsla5j" style="width: 527.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Dice_half-life_decay.jpg" target="_blank"><sup>Half-life demonstrated using dice in a classroom experiment. 13hartc, CC BY-SA 4.0</sup></a><span lang=""><o:p><br></o:p></span></p><h2><span lang="">THE ATOMIC NUCLEUS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Atoms are mostly empty space. We picture a
hydrogen atom, as a very small central blob of matter surrounded by a single
rapidly moving electron. The central nucleus contains 99.95 percent of the
atom’s mass but only a ten-billionth part of its volume. The space surrounding
the nucleus is occupied by the single electron, moving so rapidly that we can think
of it as being everywhere in the space at once.<o:p></o:p></span></p><h2><span lang="">THE VERY FIRST NUCLEAR PROBE – ALPHA SCATTERING<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The first evidence for the existence of the
nucleus was the alpha scattering experiment of Geiger and Marsden in 1909 at
the University of Manchester under the leadership of Ernest Rutherford. At that
time, most physicists’ idea of an atom was of a round ball completely filled
with a positive ‘jelly’ in which the newly discovered electrons were embedded,
like currants in a currant bun. Rutherford told his assistants, the experienced
Hans Geiger and a young undergraduate, Ernest Marsden, ‘See if some effect of
alpha particles directly reflected from a metal surface.’ A diagram of the
apparatus they used is shown in the figure below. It shows the main features of
all such collision or scattering experiments:<o:p></o:p></span></p><ul><li><span lang="">a source of high-speed particles,</span></li><li>a vacuum to avoid unwanted collisions.</li><li>a target, or more precisely the atomic or
subatomic components of the target,</li><li>a detector of the scattered particles or any
fragments produced,</li><li>a means of measuring the paths of scattered
particles or fragments.</li></ul><p class="MsoNormal"><span lang="">A radioactive source, contained in a lead box
with a small hole in it, emitted alpha particles. The targets included thin
gold foil only a few atoms thick. Most alpha particles went straight through
the foil, and were detected by the faint glow (scintillation) that each
particle produced when it hit a detecting glass screen coated with a
phosphorescent chemical. The scintillations were so faint that Geiger and
Marsden had to allow half an hour before each observation session for their
eyes to become ‘dark adapted’.</span></p><p class="MsoNormal"><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1579032238/qq5luf0cb22tgqxqvcpt.png" data-filename="qq5luf0cb22tgqxqvcpt" style="width: 450px; float: left;" class="note-float-left"></p><div style="text-align: center;"><a href="https://commons.wikimedia.org/wiki/File:Geiger-Marsden_apparatus_CGI_mock-up.png" target="_blank"></a><a href="https://commons.wikimedia.org/wiki/File:Geiger-Marsden_apparatus_CGI_mock-up.png" target="_blank" style="background-color: rgb(255, 255, 255); font-size: 1rem;"><sup>This apparatus was described in a 1913 paper by Geiger and Marsden. It was designed to accurately measure the scattering pattern of the alpha particles produced by the metal foil (F). Kurzon, CC BY-SA 3.</sup>0</a><br></div><p></p><p class="MsoNormal"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">The detecting screen was fitted to a pivoted
arm moved along a scale marked in degrees. About one alpha particle in 8000 was
reflected back through a large angle. An alpha particle is deflected by
repulsion from another positively charged object. The ‘positive jelly’ model
proposed by J.J. Thomson &nbsp;would have
provided a repulsion force far too small to deflect the massive alpha particle
through a large angle – it predicted a deflection of 2° at most.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Rutherford deduced that there must be a very
much stronger electric field inside an atom, which could only be produced by a
very high charge density, such as if all the charge were locked into one small
volume. For the fast and quite massive alpha particle to bounce back at all,
most of the mass of the atom would also have to be squashed into this small
space. Rutherford named this small space, in which all the positive charge and
most of the mass of an atom is concentrated, <b>the</b> <b>atomic</b> <b>nucleus</b>.
By comparison, the electrons had negligible mass but occupied most of the
space.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">In the illustration of Rutherford’s idea of
what was happening in the gold foil experiment. Alpha particle A passing some
distance from the nucleus is hardly deflected at all – the electric field is
too small. A closer approach such as B’s produces a larger deflection. A (rare)
head-on ‘collision’, C, stops the alpha particle dead in its tracks and repels
it back along its own path.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Rutherford wasn’t very keen on mathematics,
and it took him nearly two years to produce a calculation which related his
nuclear model of the atom to the distribution of the number of deflected
particles and the angles they were deflected through.<o:p></o:p></span></p><h2><span lang="EL">Particle accelerators<o:p></o:p></span></h2><p class="MsoNormal"><span lang="EL">Early experiments
used naturally energetic particles to probe the nucleus, but</span> b<span lang="EL">y the 1920s physicists were using ‘atom-smashing machines’ to accelerate</span> c<span lang="EL">harged particles in a controlled manner. Their main techniques are still
used</span> t<span lang="EL">oday, though with greatly increased energies. One
technique accelerates</span> c<span lang="EL">harged particles in a straight line by
applying an electric field – a linear</span> a<span lang="EL">ccelerator. The
other uses a combination of electric and magnetic</span> f<span lang="EL">ields to accelerate
the charged particles in a circular path –</span><span lang="EL"> </span><span lang="EL">leading to such</span> d<span lang="EL">evices as ‘<b>cyclotrons’</b> and <b>synchrotrons</b>.
<o:p></o:p></span></p><h2><span lang="EL">NUCLEAR PATTERNS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="EL">Practically all
the mass of an atom is the mass of its nucleus, which consists</span> o<span lang="EL">f particles called nucleons. There are two kinds of nucleon with very</span> s<span lang="EL">lightly different masses</span>. <span lang="EL">The proton is electrically charged:</span> i<span lang="EL">ts positive charge is equal in size to the charge on an electron. It is
slightly</span> l<span lang="EL">ess massive than its partner, the uncharged
nucleon called the neutron.</span><span lang="EL">
</span><span lang="EL">The Periodic Table of the
chemical elements</span><span lang="EL"> </span><span lang="EL">arranges the</span> e<span lang="EL">lements in the order
of the number of protons in the nucleus, This number is the</span> p<span lang="EL">roton number or the atomic number, symbol Z</span>. Adding the number of protons and neutrons gives the mass number or
nucleon number of an element, symbol A. <o:p></o:p></p><h3>Nuclides<o:p></o:p></h3><p class="MsoNormal">The word nuclide is
the name for atoms that have identical nuclei; this means they have the same
proton number (atomic number) and the same mass number, so they have the same
number of neutrons. Compare this with 'isotopes’ whose nuclei have the same
proton number but different mass numbers (because they have different numbers
of neutrons).</p><p class="MsoNormal"><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1579032479/opsokyelbylikh28ezpr.png" data-filename="opsokyelbylikh28ezpr" style="width: 527.5px;"><o:p><br></o:p></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Island_of_Stability.svg" target="_blank"><sup>Stability of nuclides. InvaderXan, CC BY-SA 3.0</sup></a><o:p><br></o:p></p><h2>REFERENCES<o:p></o:p></h2><p class="MsoNormal"><a href="http://physicsnet.co.uk/a-level-physics-as-a2/radioactivity/radioactive-decay/" target="_blank">http://physicsnet.co.uk/a-level-physics-as-a2/radioactivity/radioactive-decay/</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="https://www.nde-ed.org/EducationResources/CommunityCollege/RadiationSafety/theory/activity.htm" target="_blank">https://www.nde-ed.org/EducationResources/CommunityCollege/RadiationSafety/theory/activity.htm</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="https://physics.stackexchange.com/questions/177872/true-randomness-via-radioactive-decay" target="_blank">https://physics.stackexchange.com/questions/177872/true-randomness-via-radioactive-decay</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Radioactive_decay" target="_blank">https://en.wikipedia.org/wiki/Radioactive_decay</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="https://isaacphysics.org/concepts/cp_radioactive_decay" target="_blank">https://isaacphysics.org/concepts/cp_radioactive_decay</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="https://www.researchgate.net/figure/pH-optimum-curve-for-the-activity-of-an-enzyme-black-The-pH-of-the-maximum-is-the-pH_fig1_262878875" target="_blank">https://www.researchgate.net/figure/pH-optimum-curve-for-the-activity-of-an-enzyme-black-The-pH-of-the-maximum-is-the-pH_fig1_262878875</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="http://physicsnet.co.uk/a-level-physics-as-a2/radioactivity/radioactive-decay/" target="_blank">http://physicsnet.co.uk/a-level-physics-as-a2/radioactivity/radioactive-decay/</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/halfli2.html" target="_blank">http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/halfli2.html</a><o:p>&nbsp;</o:p></p><p>





















































































































</p><p class="MsoNormal"><a href="https://www.britannica.com/science/decay-constant" target="_blank">https://www.britannica.com/science/decay-constant</a><o:p>&nbsp;</o:p></p><p class="MsoNormal"><a href="http://www.chemistryexplained.com/Ar-Bo/Atomic-Nucleus.html" target="_blank">http://www.chemistryexplained.com/Ar-Bo/Atomic-Nucleus.html</a><o:p><br></o:p></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Atomic_nucleus" target="_blank">https://en.wikipedia.org/wiki/Atomic_nucleus</a><o:p><br></o:p></p><p class="MsoNormal"><a href="https://study.com/academy/lesson/atomic-nucleus-definition-structure-size.html" target="_blank">https://study.com/academy/lesson/atomic-nucleus-definition-structure-size.html</a><o:p><br></o:p></p><p class="MsoNormal"><a href="https://www.britannica.com/science/atom/Rutherfords-nuclear-model" target="_blank">https://www.britannica.com/science/atom/Rutherfords-nuclear-model</a><o:p><br></o:p></p><p class="MsoNormal"><a href="https://socratic.org/questions/who-were-hans-geiger-and-ernest-marsden" target="_blank">https://socratic.org/questions/who-were-hans-geiger-and-ernest-marsden</a><o:p><br></o:p></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment">https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment</a><a href="https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment" target="_blank"></a></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Ernest_Marsden" target="_blank">https://en.wikipedia.org/wiki/Ernest_Marsden</a><br></p><p class="MsoNormal"><a href="https://www.britannica.com/science/alpha-particle" target="_blank">https://www.britannica.com/science/alpha-particle</a><br></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Discovery_of_the_neutron">https://en.wikipedia.org/wiki/Discovery_of_the_neutron</a></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Rutherford_model" target="_blank">https://en.wikipedia.org/wiki/Rutherford_model</a><br><o:p><br></o:p></p>