Fun Video: Nuclear Forces and Binding Energy, Mass Energy Equivalence & others Video Lecture | Physics for JEE Main & Advanced

E=mc^2
You hear it all the time.
But what does it mean?
During his study of special relativity, Albert
Einstein found that mass and energy are equivalent,
and that they can be converted back and forth
between one another.
He described that relationship mathematically,
saying that the energy of a particle is equal
to its mass, times the speed of light squared.
This mass-energy equivalence is critical to
the study of nuclear physics – the study
of the atomic nucleus.
This is a branch of physics that introduces
you to two of the four fundamental forces.
One in which an element can turn into an entirely
different element, in just an instant.
And one that has allowed us to unleash the
incredible energy that’s contained inside
every atom.
[Theme Music]
Before we can dive into the wonders of nuclear
physics, we need to recall a little bit about
the thing that makes it all tick: the nucleus!
The nucleus of any atom consists of protons
and neutrons.
The proton is positively charged, while the
neutron is electrically neutral, and both
particles have nearly the same mass.
With the exception of hydrogen, which only
has a single proton in its nucleus, every
element has both protons and neutrons.
Because of this, we’ll often refer the two
particles collectively as nucleons.
We can describe how many protons and neutrons
are in an atom’s nucleus using its atomic
and mass numbers.
An atomic number is how many protons are in
a nucleus, which also determines what element
the atom consists of.
The mass number, meanwhile, is how many protons
and neutrons combined make up a nucleus.
So if there are 6 protons and 6 neutrons in
a nucleus, then its atomic number would be
6, making it a carbon nucleus, and the mass
number would be 6+6, or 12!
And if there were 6 protons and 8 neutrons,
then it would still be a carbon nucleus, but
with a mass number of 14.
Let’s put these carbon nuclei in nuclear
notation to better show the differences between them.
First, we start with the chemical symbol for
the nucleus, which is determined by its atomic number.
Then on the bottom left of the chemical symbol,
we write the atomic number, which will be
the same for both Carbon nuclei, 6.
Finally, we write the mass number on the top
left, to signify how many protons and neutrons
there are in the nucleus.
So for our carbon atom with six neutrons,
we’d take the Carbon chemical symbol, a
capital C, and write the atomic number, 6,
in the bottom left and the mass number, 12,
in the top left.
For the atom with two extra neutrons, the
upper left mass number becomes 14.
Any two nuclei that have the same atomic number
but different mass numbers are known as isotopes,
with most elements having one isotope that
is more common than the others.
For instance, 99% of the carbon on Earth is
Carbon-12, carbon with a mass number of 12.
Only a tiny fraction of all carbon on earth
is Carbon-14, since carbon is most stable
when the number of protons equals the number
of neutrons.
It’s important to know the masses of different
nuclei, since nuclear interactions are all
about mass-energy conversion.
To quantify the mass of a nucleus, we use
the unified atomic mass unit, written just
as a small u, with a single neutral carbon-12
atom equaling exactly twelve unified atomic mass units.
This means that one unified atomic mass unit
is equal to 1.6605 times 10^-27 kilograms.
Okay, now that we have a notation for describing
elements and their isotopes, we can talk about
the energy associated with a nucleus and its
bonds.
The first thing you should know is that the
total mass of a stable nucleus is always less
than the total mass of the individual protons
and neutrons put together.
For instance, the mass of a neutral helium
atom is 4.002603 unified atomic mass units.
But two neutrons and two protons – the component
parts of a helium atom – taken together
have a mass of 4.032980 unified atomic mass
units.
That means that the nucleus of a helium atom
has 0.030377 unified atomic mass units less
mass than its component parts.
How can that be?
Well, that difference in mass is equal to
an amount of energy, specifically the total
binding energy of the nucleus.
That binding energy is how much energy you
would have to add to the helium atom in order
to break it apart its nucleus.
The amount of energy required to break up
a nucleus into its component particles gets
larger as the atomic number increases, with
iron having one of the highest binding energies
per nucleon.
But while the total binding energy still increases
for nuclei larger than iron, the binding energy
per nucleon, in fact, decreases.
This means that very large nuclei are not
held together as strongly as small nuclei.
And since binding energy accounts for the
missing mass, you can calculate it using – you
guessed it! – e equals m c squared.
Now, you might be wondering how a nucleus
is held together in the first place.
You’ve got neutral neutrons that have no
problem getting close to one another, but
what about all the positive protons? Shouldn’t
the repulsive electric force keep them apart?
Well, one of the four fundamental forces of
physics is the strong nuclear force, an attractive
force that acts between protons and neutrons
in a nucleus.
This strong force is substantial enough to
overcome the repulsive force between protons,
but it only acts over very small distances,
while the electric force acts over longer distances.
Since the strong force only works across such
tiny distances, larger atoms with high atomic
numbers actually require additional neutrons
to overcome the electromagnetic force and
maintain stability within the nuclei.
Those extra neutrons are necessary for atoms
with atomic numbers higher than thirty or
so, as you can see in this chart relating
the number of neutrons to the number of protons
in a stable atom.
And when a nucleus is UNstable, it can break
down into a more stable state.
This decay of unstable nuclei, accompanied
by emission of energetic particles, is known
as radioactivity.
Natural radioactivity was first discovered
by Henri Becquerel, who observed how a chunk
of mineral that contained uranium affected
a photographic plate that was covered up by paper.
Even though the paper was blocking out visible
light, the radiation from the uranium penetrated
the paper and left its mark on the plate.
Later scientists studied such decays and categorized
the emitted rays or particles into three different
groups, based on their penetrating power.
First, there’s alpha decay, which is released
when an unstable nucleus loses two protons
and two neutrons, becoming a different element
in the process.
In alpha decay, there’s a parent nucleus
– which is the original, unstable nucleus
– and it decays into a daughter nucleus
and an alpha particle, which is actually just
the nucleus of a Helium atom.
This decay occurs because the parent nucleus
is too large, and the strong force is no longer
sufficient to hold all the nucleons together.
For example, if the parent nucleus is radium,
it would decay into radon and emit a single
alpha particle.
The process of the nucleus changing from one
element to another is known as transmutation.
Note that the atomic number of radon is just
two units less than that of radium, and the
mass number is four less than radium’s.
In alpha decays, the sum of the atomic and
mass numbers are always equal on either side
of the equation.
But even though those numbers of nucleons
add up, remember: Mass and energy are equivalent.
So the products of this reaction always have
less total mass – as measured in unified
atomic mass units – than the parent nucleus
has.
The rest of mass turned into kinetic energy,
and the kinetic energy released in nuclear
reactions is what’s used to generate nuclear
power!
But alpha particles have the least penetrating
power of the three groups – they’re barely
able to pass through a piece of paper.
The second type of decay that can occur is
beta decay, when an unstable nucleus emits
a beta particle, which is just an electron.
You’ll see that whenever an electron is
produced, so is a neutrino.
A neutrino is a particle with a very small
mass that is electrically neutral.
Its existence is inferred from the conservation
of energy.
For example, when a nucleus at rest decays
into two fragments, it should give each fragment
the same amount of momentum.
If the nucleus decayed into the daughter nucleus
and an electron, the electron would always
have the same momentum, and the same energy.
But electrons from beta decay have been found
to have energies that vary greatly.
This suggests that a third particle must be
carrying away the rest of energy.
And experiments have confirmed that these
tiny, neutral neutrinos are responsible for
that missing energy.
Now, a unique part of beta decay is that no
nucleons are emitted during the decay process.
Instead, one of the neutrons changes into
a proton.
And to compensate for the change in charge,
the neutron emits an electron.
And although these electrons come from nuclear
decay, they’re the same kind of electrons
that orbit a standard nucleus.
Once the neutron changes into a proton, the
nucleus changes from one element to another,
again an instance of transmutation.
And beta decay is caused by the fourth fundamental
force, the weak force.
While the strong force acts on nucleons, the
weak force alters quarks, the fundamental
particles that make up both protons and neutrons.
By converting quarks of one type into another,
the weak force causes the neutron to turn
into a proton.
As for their penetrating power, beta particles
are typically stopped by a few millimeters
of aluminum.
The third kind of decay is gamma decay, which
is what results when a nucleus emits high-powered
photons, in what are known as gamma rays.
This kind of decay usually occurs when a nucleus
is in an excited state, which can happen because
the nucleus is decaying from a larger form,
or because it collided with a high-energy
particle, among other reasons.
But the point is, when a nucleus is excited,
it wants to transition to a lower-energy state,
which it can do by releasing a photon.
Unlike alpha and beta decay, no transmutation
occurs in gamma decay.
Instead, the excited nucleus just decays into
a ground state nucleus and a gamma ray.
Gamma rays have the highest penetrating power,
requiring large amount of concrete or lead
to stop their propagation.
And there’s so much more we could talk about
if we had the time! Half-lives, radiocarbon
dating, the basics of nuclear power, just
to name a few.
But, e=mc squared – now at least you know
what it means, and how such tiny objects as
atoms can release such enormous power.
That’s worth 10 minutes of your time, right?
Today we learned the very basics of nuclear
physics, including atomic number, mass number,
and how to use them in nuclear notation.
We also discussing binding energy and mass-energy
equivalence, as well as the strong and weak
nuclear forces.
Finally, we discussed the three major types
of radioactive decay: alpha, beta, and gamma.
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