Rutherford model: Electron orbitals & limitation - Atoms Video Lecture - Class 12

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file so now let us talk about the
electron orbits so the two important
things which rather for told us was one
was nucleus he told us about nucleus and
the second was the electron orbits so we
have already discussed about the nucleus
back so now it is time to discuss that
electron orbits so what did I make what
did he tell about the electron
coordinates so according to leather
foots model nucleus was at the centre
and the electrons were there working
around it so there was a force between
the electron and the nucleus as I
mentioned in the previous slide that
that why are the electrons held in those
orbits it is because of an electrostatic
force of attraction between the nucleus
and the electron so what does this
electrostatic force of attraction it is
denoted as f e now since this is my
nucleus and this is my electron which is
revolving somewhat like this so there is
one electrostatic force of attraction
but at the same time since it is moving
in a circular orbit there is a
centripetal force
so this electrostatic force of
attraction gets balanced by them
centripetal force right now what is the
electrostatic force of attraction it is
nothing but given by Coulomb's law 1 by
4 PI epsilon naught into charge on an
electron that is key into charge on the
nucleus so let us denote the charge on
the nucleus as Z e divided by R square
so this is equal to the centripetal
force which is nothing but
MV square by r so this R and this R will
get cancelled so from this we can say
that I is equal to Z T square divided by
4 PI epsilon naught into 1 by MV square
so from this we can say R is equal to Z
e square divided by
whole pie epsilon-not everybody's wet so
what is this this ad is the radius of
the orbit in which the electron is
moving so often this R is known as orbit
radius and what is this V this V is that
electron velocity that is the velocity
with which the electron is moving around
the nucleus right so this and how
Rutherford defined the orbit of an
electron that he told that electrons
will move in orbits so what would be the
radius of that orbit and with what
velocity the electron would be moving
would be given by this expression so now
from this expression he also evaluated
the kinetic energy associated with a
moving electron so the kinetic energy
denoted by K is nothing but half MV
square right so this will be half M into
V square so V V what we can write V as
so from the previous expression of orbit
radius we can write velocity in terms of
radius R so this will be Z T Square
divided by 4 PI epsilon naught M and so
this M and this M will get cancelled so
we get set G square divided by 8 pi
epsilon naught R so this would be the
kinetic energy associated with the
moving electron now let us talk about
the potential energy potential energy
denoted by U is given by 1 by 4 PI
epsilon naught into q1 q1 is the charge
of the electron into q2 that is the
charge on the nucleus so this charge is
positive and discharges negative right
so this divided by I that is is the
distance between the electron and the
nucleus so this comes out to be minus Z
is where divided by 4 pi
not add so this is the potential energy
associated with them system
so now that we have calculated kinetic
energy as well as potential energy we
can very well calculate the total energy
so what would be the total energy in
word that is kinetic energy plus
potential energy it comes out to be Z
key square divided by H by epsilon R
plus minus Z in square divided by 4 PI
epsilon naught I so this comes out to
remind us that in square divided by 8 5
epsilon not R so this is the total
energy associated with them electrons
now what do we observe from this we see
that the total energy is as a negative
sign with it what is it show this shows
that the electrons are bound to the
nucleus at the total energy being
positive in that case if we have meant
that the electrons are not bound to move
in the orbits they can play a key and
they can move anywhere right so this
total energy pack calculated by brother
fool also supported his observation and
conclusion because he we had told that
electrons moving orbits so this
calculation of total energy also
supported this statement that since the
total energy is negative that means that
electrons are bound to the nucleus and
they are bound in this electron orbits
right so now from this what we observe
if you look at these three expressions
of kinetic energy potential energy and
total energy you can see that kinetic
energy is nothing but negative of total
energy I mean magnitude of the kinetic
energy and total energy is the same so
you can say the connecticut
is negative of total energy similarly if
you compare the potential energy with
the total energy you can see that
potential energy is twice of the total
energy so you can say that potential
energy is equal to twice of the total
energy right so this was all that was
told by Brotherhood regarding the
electron orbits so this was Rutherford's
model of atom now this other force model
was able to explain many things
successfully it could explain the
existence of nucleus the arrangement of
electrons the electron orbits so it
could explain a plenty of things however
this model also has certain limitations
let us look at the limitations of the
rather force model the first limitation
was it could not explain the stability
of an atom why it could not explain
stability because rather for told that
electrons are moving around the nucleus
and it is moving in orbits because it is
balanced by the electrostatic force of
attraction now electrons should be
attracted by the positively charged
nucleus every now and then right so now
according to the electromagnetic clearly
of Maxwell if you remember your lesson
on electromagnetic waves you'd remember
that Maxwell and given is clearly
stating that charged particles when
accelerated they emit electromagnetic
radiation so this was a theory which was
very well true and given by matchstick
we don't that whenever there is a
charged particle which is accelerated it
will emit electromagnetic radiation so
now if you look at these electrons what
are these electrons they are charged
particles negatively charged particles
they are also getting since they are
getting attracted by the nucleus so they
are also getting accelerated as they are
moving on their circular orbits
therefore these accelerated negatively
charged electrons should also end
magnetic radiation now if they had a
meeting electromagnetic regulation then
what's happening that is the orbit of
the Elektra warming electron with keep
on becoming smaller and smaller
following a spiral path and ultimately
the electron will fall in even in case
this is what it should happen let us
suppose if this is my nucleus I think
this is my electron now rather for
thought that electron moves in this
orbit right now if this electron is but
he did not consider the emission of
electromagnetic radiation but according
to Maxwell's theory this electron being
a charged particle it is getting
accelerated as it moves in this path so
it should emit some electromagnetic
radiation that means some part of its
energy is lost in emitting this
radiation so as a result this electrons
radius will keep decreasing and
gradually the electron will fall into
the nucleus so that means the atom will
not be stable but that is what which
doesn't happen actually right I mean in
reality or in nature you see everything
which is around yourself is made up of a
common things are stable right so that
means there is something which defines
the stability of akkem which rather
force mod it could not so this became a
very big limitation of Rutherford's
model also it seems nothing about the
electronic structure of atoms that is
about the distribution and relative
energies of electrons around the nucleus
rather therefore just told about the
path followed by the electrons he did
not talk about like how many I mean
every atom when we talk of an atom it
does not consist of one electron right
there are plenty of electrons so rather
for neighbors forth about the
distribution of those n number of
electrons he just told that every
electron will move in a in an orbit but
when there are 100 electrons how will
these those hundred electrons move in
different orbits whether they will move
in
different orbits or they will move in
one more bid or how will they be
distributed so he did not talk anything
about that so distribution and relative
energies of electrons was not at all
explained are discussed by Dragan dual
nature of electromagnetic regulation
could not be explained as will you saw
in our previous lessons that there are
several experiments which prove that
dual nature of variation is true that
means every particle can behave as a
particle as well as wave
similarly every wave and behave as a
particle as well as we but rather force
model could not explain this dual nature
experimental results regarding atomic
spectral emission lines could not be
explained now what are these atomic
spectral emission lines we will talk
about them in detail in the next few
slides so these spectral lines are a
very important concept in science I mean
they are extremely useful in different
research work and all
so this another for model of atom could
not explain anything about this in
spectral lines they could not explain
why this spectral lines occurred right
so these are some of the limitations of
Rutherford's model because of which it
was not a full move or it was not
completely accepted however he told many
things which were correct I mean it was
the first model to at least give an idea
of the correct picture of atom right but
there were so many these advantages as
well so in order to overcome these
disadvantages came up the next model
that was the Bohr's model of atom now
before we get into Bohr's model of atom
let us understand what is atomic spectra
because here I mentioned you that it
could not explain the atomic spectral
emission line side so before you
before I introduce the warden to you it
is good good if you understand what is a
table expect line that is you will be
able to understand the horse model in a
better way so what is atomic spectra
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