Bohr model - Atoms Video Lecture - Class 12 | Best Video for Class 12

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so now that we have studied the line
spectrum hydrogen atom we are good to go
with the Bohr model of hydrogen atom
which is extremely important this model
of hydrogen atom which was given by Bohr
was able to overcome all the limitations
which were there in them rather forsworn
the as I mentioned earlier the main
limitation goes up
I talked that Dragonforce wanted could
not explain them atomic spectra and Bose
model could successfully do that so let
us look at the postulates of the Bohr's
model of hydrogen which was proposed in
1913
so the first postulate was the electron
in the hydrogen atom can move around the
nucleus in a circular path of fixed
radius and energy so Rutherford spoke
only about the radius it only spoke
about the orbit radius but now we're
told that it moves with in a circular
path of fixed radius as well as fixed
energy so these parts are called orbits
or stationary States are allowed energy
states that is where quantization came
into picture because both told that it
is not that electrons can move in just a
circular path there are certain allowed
energy levels or there are certain
allowed orbits on which the electrons
can be born so these orbits are relieved
concentrically around the nucleus like
the next postulates he told that the
energy of an electron in the orbit does
not change with time ok so as long as
the electron is moving in one orbit it
will not change with time but when the
electron moves from a lower stationary
state to a higher stationary state when
required amount of energy is absorbed by
the electron or energy is emitted when
the electron moves from higher in
to lower energy state so that is what we
were studying so far right that gives
rise to the spectra it is suppose these
are the energy levels and is equal to
one two three four now if an electron
jumps from a lower energy state to a
higher energy state that means it will
absorb some energy now if an electron
jumps from a higher energy state to
lower energy state that means it will
emit some energy like but as long as an
electron is there on a particular energy
state there will be no change in energy
of the electron with time so now and
whatever the change of the energy which
is involved due to the change of its
level that is given by this that easy
quite to our n divided by n1 square
minus 1 by n2 square right that is the
red goose formula the frequency of
regulation absorbed or emitted when
transition occurs between two stationary
states that differ in energy by Delta e
is given by nu is equal to beta T by H
that means let us suppose this is one
energy this is one energy level which
has energy e2 this is another energy
level which as energy e1 now if an
electron jumps from this energy level
equal to e1 what is the change of energy
in Boyde Delta e which is equal to e2
minus e1 so what would be the frequency
of radiation which is emitted so this
Delta e will be equal to H continue that
H nu denotes the energy of the photon
which is anything right so therefore the
frequency of the radiation which is
emitted new will be given by Delta e by
H so this would be the frequency of the
radiation which is absorbed or emitted
when an electron moves between two
stationary states the angular momentum
of an electron in a given stationary
state can be expressed as in this
equation that means let us suppose the
electron is in one state it is not
changing its state so the angular moment
of the energy of the electron will
remain constant okay what will be the
angular momentum the
the momentum of the electron which is
given by mass and velocity into the
radius of the orbit now in this case we
are representing the energy level as
straight lines because actually this is
how the orbit looks like right so what
would be the angular momentum of the
electron which is revolving in this way
it would be mass into velocity velocity
into the radius of the circular path
that is the radius of the orbit so this
angular momentum is integral multiple of
H by 2 pi so this was another question
of good now you might be wondering that
from where he discovered this now poor
keep all these postulates depending on
based on his observations and his
experimental calculations but later it
was found that this expression which was
given by Bohr was found to be true even
by the quantum mechanical model it was
found it was proved by the quantum
mechanical model as well so these are
the important postulates which
constitutes the Bohr's model of hydrogen
atom so let us quickly review what are
what modest Bohr model of hydrogen atom
tells it tells that electron moves in
circular orbits but these orbits are
arranged concentrically and the
electrons moving on a particular orbit
will have a fixed energy and a fixed
radius so that change in energy will
take place only when electron jumps from
a higher energy level to a lower energy
level or vice-versa the frequency of
ready whenever electron jumps from lower
energy level to higher energy level it
absorbs energy when you jumps from
higher energy level to lower energy
level it emits energy so the radiation
which is emitted is explique when C is
given by delta T by H the angular
momentum of an electron as long as it is
in a particular state is always an
integral multiple of the constant H 5 to
5 right so these postulates constitutes
the Bohr model of hydrogen atom now let
us discuss the postulates in detail now
let us talk about bone radius
was Bohr's model toward that when an
electron is in a particular orbit I will
have a fixed radius and a fixed energy
so let us try to find out or let us try
to evaluate an expression for the Bohr
radius now according to Bose postulate
what if we saw we saw that the angular
momentum is equal to integral multiples
of n H by 2 pi right now let us suppose
that the radius of the orbit is denoted
by R and the velocity of electron in
this orbit is denoted by V and let us
also say that the values of n this 1 2 3
these are the allowed orbits of
electrons now these allowed orbits of
electrons at moon as are often denoted
by the principal quantum number here we
will not discuss about quantum numbers
in detail but you will study about the
different quantum numbers I guess you
would have studied it in your chemistry
lessons and you would have heard about
principal quantum number magnetic
quantum number spin quantum number and
all those stuff so principal quantum
number is the one which tells which are
the allowed energy levels of the
electron length as I mentioned both all
that energy is quantized electron just
cannot move on a new circular path there
are certain specific circular orbits
which are allowed for the electron
so this principal quantum number that is
this value of n basically denotes which
are the allowed orbits for the electron
ok fine so now from this expression we
can write that V is equal to n H divided
by 2 pi M R let me mark this expression
as 1 now from our concept on electron
orbits we spoke about electron on
website when we were discussing about
the other force model we spoke about
electron orbits and
all of the orbit radius we found out an
expression for all bit radius right so
that expression was R is equal to say is
where divided by 4 pie epsilon-not MV
square so from this we can say these
where is equal to st. T Square divided
by 4 PI epsilon naught M I now right now
we are talking about hydrogen atom
because borse concept was all about
hydrogen atom both focused only on
hydrogen atom right so for hydrogen said
is equal to 1 so this expression can be
written as V is equal to e divided by
root over 4 PI epsilon naught R M so let
me mark this expression as 2 so now if
you compare this equation at this
equation you see that the left-hand side
are the same both of them denote the
velocity of the electron in a particular
orbit so therefore detect equates the
right-hand side so therefore from
equation 1 and equation 2 we can say n H
divided by 2 pi M I is equal to e
divided by root over 4 PI epsilon naught
R M so from this we can say n square H
square divided by PI square M square R
square is equal to e square divided by
PI epsilon naught R M so this M R PI
will get cancelled so this Square will
get cancelled so from this we get R is
equal to n square h square website and 1
divided by n square by M or we can
rearrange it further as n squared H
square epsilon naught divided by PI M
each way so this expression for the
radius of the orbit for the day orbital
radius of electron in hydrogen atom is
known as Bohr radius because we get a
different expression put considering
hydrogen atom as well as considering the
quantization of our little angular
momentum because here we have considered
the fact that the angular momentum of
the electron is integral multiple of H
biting back which is a bold postulate
and at is wise this radius is known as
the Bohr radius now for innermost orbit
for the innermost orbit the value of n
is equal to 1 because n is that n is
equal to 1 is the lowest possible value
of n so this is the lowest possible
energy lowest possible allowed energy
level right so for n is equal to 1 R is
equal to H square epsilon naught divided
by PI M useful right now let us look at
the energy of electron in hydrogen atom
now again from the concept of electron
orbits which we'll discuss to Julie the
rather holds model we found out an
expression for total energy right so
what was that total energy that was
equal to minus ze square divided by 8 pi
epsilon naught R right now in force in
high degrees of hydrogen atom we have to
apply most Theory right so when we are
talking about hydrogen atom we have to
make use of both rails so in this case
we will put R is equal to the expression
for Bohr radius and what is go radius it
is n square h square epsilon naught
divided by PI F e squared so if we put
this value we get total energy is equal
to M e to the power 4 divided by 8 n
square epsilon 1 square H 0 so this
becomes the total energy of electron in
Adam now in this case if you see M is
the mass of electron is the charge on
electron epsilon not is again a constant
H is again a constant so if we put the
values of each of these constants which
is somewhat like this M is equal to 9
point 1 into 10 to the power minus 11
kgs
P that is charge on an electron is equal
to 1 point 6 into 10 to the power minus
16 coulombs epsilon not that is
permittivity which is 8 point 8 5 into
10 to the power minus 12 again age that
is Planck's constant which is 6 point 6
7 into 10 to the power minus 34 now if
we put these values here and then
calculate we see that the total energy
comes out to you by the 13 point 6 by n
square electron volt so if this comes
out to be the value of the total energy
so here also we see that total energy is
negative which shows that the electron
is mounted to the nucleus not in at the
ground state that is for n is equal to
Mun the energy of electron in the
hydrogen atom is 13 point 6 electron
volts right so this was the Bohr's model
of hydrogen atom which was able to
overcome some of the limitations of
Rutherford's model however Bohr's model
of a camp also had limitation the first
limitation being it is mainly for
hydrogen this became a very major
limitation right because both gave this
entire Theory only for one atom that is
only for hydrogen atom and there are so
many elements so if something is true
only for one element then I mean it
make much sense it could not explain the
spectra of multi-electron atoms it both
theory was successfully able to explain
how the atomic spectra is formed in the
case of hydrogen but as as other atoms
came into picture they had more number
of electrons because hydrogen had only
one electron right but when we consider
other atoms they have many electrons now
it could not explain how the formation
of spectrum takes place in
multi-electron atoms in Bohr model and
electron is unsealed is regarded as a
charged particle moving in a
well-defined circular orbit about the
nucleus the wave character of the
electron is ignored in more skill
doesn't follow we broke this concept of
a particle duality of maggots
however Bohr's model was able to
overcome the limitation of the atomic
spectra but it still would not talk
about the dual nature of radiation and
method so it could it always considered
the electron as a particle it never
spoke about the vemma character of the
electron it could not explain the
ability of atoms to form molecules by
chemical bonds it did not speak anything
about I mean both main focus since
Rutherford's model failed that one of
the important reason was that it could
not explain that Raman spectra and
atomic spectra was a very important
concept so boastful concentration goes
only on the account of spectra part so
he was able to explain the atomic
spectra successfully that 24 hydrogen
atom but since once explained it for
hydrogen atom it gives an idea to others
that how this atomic spectra could have
been formed it contradicts Heisenberg's
uncertainty principle as I mentioned
before also that de Broglie Heisenberg
Schrodinger they are all quantum
mechanics people so they all talk about
duality but Bohr's model occur at
did not talk about us so it contradicts
Heisenberg's uncertainty principle
z-man effect could not be explained what
is he man effect when atomic spectra is
subjected to an external magnetic field
there are changes in the spectral lines
stark effect the similar thing in
presence of external electric field so
z-man effects that affect could not be
explained so we are not going to study
about Zeeman effect and staff effect
here you will study it in your higher
classes right so here I have listed down
several limitations which the horse
model of acting-wise who have but the
borscht model was a success over another
force model because it was able to
overcome one of the most important
limitation of Rutherford's model and
that was the atomic spectra so therefore
since this model was also not able to
explain things completely
therefore what was the another model
which came up that was nothing but a
quantum mechanical model of a so here we
will not discuss the quantum mechanical
model of a cube in detail but I just
tell you what gave rise to the quantum
mechanical facts Schrodinger equation
describe the electron distributions and
space and allowed energy levels and
atoms in a better way that also I
mentioned right dee broglee heisenberg
Schrodinger they are all on the same
lines so Bohr obviously contradicts
everything
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