Download Introduction to Radioactivity and Radioactive decay

GROUP 4
Firdiana Sanjaya (4201414050)
Ana Alina (4201414095)
The Nucleus

The nucleus of an atom is comprised of protons and neutrons; it is therefore
positively charged. The number of protons within the nucleus of a given
atom is equal to the atomic number of the corresponding element, which
can be found on the periodic table. For example, the atomic number of
helium is two. Therefore, the number of protons is also two. The number of
neutrons within the nucleus of a given atom can be found by subtracting
the atomic number from the atomic mass
The mass number is the sum of protons and neutrons.
Atomic Mass Number = Number of Protons + Number of Neutrons
To find the number of neutrons, subtract the atomic number, the
number of protons, from the mass number.
Notation of a specific element follows this format:
where E is a specific element, A is mass number, Z is the atomic
number, and C is the charge. For helium, the notation is as follows:
Helium has 2 protons, 2 neutrons and a charge of zero.

How big is a nucleus? We know that atoms are a few
angstroms, but most of the atom is empty space. The
nucleus is much smaller than the atom, and is typically a
few femtometers. The nucleus can be thought of as a bunch
of balls (the protons and neutrons) packed into a sphere,
with the radius of the sphere being approximately:
Problem
Complete the chart below
Answer
The strong nuclear force
What holds the nucleus together? The nucleus is tiny, so
the protons are all very close together. The gravitational
force attracting them to each other is much smaller than
the electric force repelling them, so there must be another
force keeping them together. This other force is known as
the strong nuclear force; it works only at small distances.
The strong nuclear force is a very strong attractive force
for protons and neutrons separated by a few femtometers,
but is basically negligible for larger distances.

The tug-of-war between the attractive force of the strong
nuclear force and the repulsive electrostatic force between
protons has interesting implications for the stability of a
nucleus. Atoms with very low atomic numbers have about
the same number of neutrons and protons; as Z gets larger,
however, stable nuclei will have more neutrons than
protons. Eventually, a point is reached beyond which there
are no stable nuclei: the bismuth nucleus with 83 protons
and 126 neutrons is the largest stable nucleus. Nuclei with
more than 83 protons are all unstable, and will eventually
break up into smaller pieces; this is known as radioactivity.
Nuclear binding energy and the
mass defect
A neutron has a slightly larger mass than the proton. These
are often given in terms of an atomic mass unit, where one
atomic mass unit (u) is defined as 1/12th the mass of a
carbon-12 atom.
The mass of the nucleus is a little less than the mass of the individual
neutrons and protons. This missing mass is known as the mass defect, and is
essentially the equivalent mass of the binding energy.
Einstein's famous equation relates energy and mass:
In any nucleus there is some binding energy, the energy you would need to
put in to split the nucleus into individual protons and neutrons. To find the
binding energy, then, all you need to do is to add up the mass of the
individual protons and neutrons and subtract the mass of the nucleus:
The binding energy is then:
Radioactive decay
Radioactive decay, also known as nuclear decay or radioactivity,
is the process by which a nucleus of an unstable atom loses energy
by emitting ionizing radiation
During radioactive decay, principles of conservation apply. Some of
these we've looked at already, but the last is a new one:
 conservation of energy
 conservation of momentum (linear and angular)
 conservation of charge
 conservation of nucleon number
Alpha decay
 In alpha decay, the nucleus emits an alpha particle; an alpha
particle is essentially a helium nucleus, so it's a group of two
protons and two neutrons. A helium nucleus is very stable.
 An example of an alpha decay involves uranium-238:
The process of transforming one element to another is known
as transmutation.
 Alpha particles do not travel far in air before being absorbed;
this makes them very safe for use in smoke detectors, a
common household item.

Beta decay
 A beta particle is often an electron, but can also be a
positron, a positively-charged particle that is the antimatter equivalent of the electron. If an electron is
involved, the number of neutrons in the nucleus decreases
by one and the number of protons increases by one. An
example of such a process is:


In terms of safety, beta particles are much more
penetrating than alpha particles, but much less than
gamma particles.
Gamma decay
 The third class of radioactive decay is gamma decay, in
which the nucleus changes from a higher-level energy state to
a lower level. Similar to the energy levels for electrons in the
atom, the nucleus has energy levels. The concepts of shells,
and more stable nuclei having filled shells, apply to the
nucleus as well.
 When an electron changes levels, the energy involved is
usually a few eV, so a visible or ultraviolet photon is emitted.
In the nucleus, energy differences between levels are much
larger, typically a few hundred keV, so the photon emitted is
a gamma ray.
 Gamma rays are very penetrating; they can be most
efficiently absorbed by a relatively thick layer of high-density
material such as lead.
Radioactivity
Making a precise prediction of when an individual nucleus will
decay is not possible; however, radioactive decay is governed by
statistics, so it is very easy to predict the decay pattern of a large
number of radioactive nuclei. The rate at which nuclei decay is
proportional to N, the number of nuclei there are:
 is known as the decay constant.
Whenever the rate at which something occurs is proportional to the
number of objects, the number of objects will follow an exponential
decay. In other words, the equation telling you how many objects
there are at a particular time looks like this:

Where No is the original number of particles.

The decay constant is closely related to the half-life,
which is the time it takes for half of the material to
decay. Using the radioactive decay equation, it's easy
to show that the half-life and the decay constant are
related by:
Radioactive dating

Radioactivity is often used in determining how old
something is; this is known as radioactive dating. When
carbon-14 is used, as is often the case, the process is called
radiocarbon dating, but radioactive dating can involve other
radioactive nuclei. The trick is to use an appropriate halflife; for best results, the half-life should be on the order of,
or somewhat smaller than, the age of the object.
Example