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How to pronounce 656 in English?

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I'm sure that most you know the famous
story of Isaac Newton where he took a
narrow beam of light and he put that
narrow beam of light through a prism and
the prism separated the white light and
to all the different colors of the
rainbow and so if you did this
experiment you might see something like
this rectangle up here so all of these
different colors of the rainbow I'm
gonna call this a continuous spectrum
it's continuous because you see all
these colors right next to each other so
they kind of blend together so that's a
continuous spectrum if you did this
similar thing with hydrogen you don't
see a continuous spectrum so if you
passed a current through a tube
containing hydrogen gas the electrons
and the hydrogen atoms are going to
absorb energy and jump up to a higher
energy level when those electrons fall
down to a lower energy level they emit
light and so we talked about this in the
last video this is the concept of
emission if you use something like a
prism or diffraction grating to separate
out the light for hydrogen you don't get
a continuous spectrum you'd see these
four lines of color so since you see
lines we call this a line spectrum so
this is the line spectrum for hydrogen
so you see one red line and it turns out
that that red line has a wavelength that
red light has a wavelength of 656
nanometers you'll also see a blue green
line and so this has a wavelength of 486
nanometers a blue line 434 nanometers in
a violet line at 410 nanometers and so
this emission spectrum is unique to
hydrogen and so this is one way to
identify elements and so this is a
pretty important thing and since line
spectrum are unique this is pretty
important to explain where those
wavelengths come from and we can do that
by using the equation we derived in the
previous video so I call this equation
the Balmer Rydberg equation and you can
see that 1 over lambda lambda is the
wavelength of light that's emitted is
equal to R which is the Redbird constant
times 1 over I squared where I is
talking about
the lower energy level minus one over J
squared where J is referring to the
higher energy level for example let's
say we were considering an excited
electron that's falling from a higher
energy level n is equal to three so let
me write this here so we have an
electron that's falling from n is equal
to three down to a lower energy level
and is equal to two all right so it's
going to emit light when it undergoes
that transition so let's let's look at
the at a visual representation of this
and then let's see if we can calculate
the wavelength of light that's emitted
alright so if an electron is falling
from n is equal to three to n is equal
to two let me go ahead and draw an
electron here so electrons falling from
n is equal to three energy level down to
n is equal to two and the difference in
those two energy levels are the
difference in energy is equal to the
energy of the photon and so that's how
we calculated the Balmer Rydberg
equation in the previous video all right
let's go ahead and calculate the
wavelength of light that's emitted when
the electron falls from the third energy
level to the second so we have 1 over
lambda is equal to the Redbird constant
as we saw in the previous video is one
point zero nine seven times ten to the
seventh the units would be 1 over meter
all right 1 over I squared so I I refers
to the lower energy level right so the
lower energy level is when n is equal to
2 so we plug in 1 over 2 squared and
then from that we're going to subtract 1
over the higher energy level that's n is
equal to 3 right so this would be 1 over
3 squared so 1 over 2 squared minus 1
over 3 squared 1 over 2 squared that's
1/4 so that's point 2 5 minus 1 over 3
squares that's 1 over 9 so 1/4 minus 1/9
gives us point 1 3 8 repeating and if we
multiply that number by the Redbird
constant right that's one point zero
nine seven times 10 to the seventh we
get 1/5
two three six one one so let me go and
write that down so now we have one over
lambda is equal to one five two three
six one one so to solve for lambda all
we need to do is take one over that
number so one over that number gives us
six point five six times ten to the
negative seven and that would now be in
meters so we have lambda is equal to six
point five six times ten to the negative
seven meters so let's convert that into
let's go like this let's go 656 that's
the same thing as 656 times 10 to the
negative ninth meters and so that's 656
nanometers 656 nanometers and that
should sound familiar to you alright so
let's go back up here and see where
we've seen 656 and nanometers before 656
nanometers is the wavelength of this red
line right here so that red line
represents the light that's emitted when
an electron falls from the third energy
level down to the second energy level so
let's go back down to here and let's go
ahead and show that so we can say that a
photon right a photon of red light is
given off as the electron falls from the
third energy level to the second energy
level so that explains the red line in
the line spectrum of hydrogen so how can
we explain these other lines that we see
right so we have these other lines over
here and right we have this blue green
one this blue one and this violent one
so if you do the math you can use the
Balmer Rydberg equation right you can do
this and you can plug in some more
numbers and you can calculate those
values so those are those are electrons
falling from higher energy levels down
to the second energy level so let's uh
let's go ahead and draw them on our
diagram here so let's say an electron
fell from the fourth energy level down
to the second right so that energy
difference if you do the calculation
that turns out to be the blue green line
in your line
spectrum so I'll represent the light
emitted like that and if an electron
fell from the fifth energy level down to
the second energy level that corresponds
to the blue line that you see on the
line spectrum and then finally the
violet line must be the transition from
the sixth energy level down to the
second so let's go ahead and draw that
in so now we have a way of explaining
the this line spectrum of hydrogen that
we that we can observe and since we
calculated this Balmer Rydberg equation
using the Bohr equation using the Bohr
model I should say the Bohr model is
what allowed us to do this so the Bohr
model explains these different energy
levels that we see so when you look at
the line spectrum of hydrogen it's kind
of like you're seeing energy levels at
least that's how I like to think about
it cuz your your it's the only real way
you can see the difference of energy
alright so energy is quantized
we call this the Balmer series so this
is called the Balmer series for a
hydrogen but there are different
transitions that you could do for
example let's think about let's think
about an electron going from the second
energy level to the first alright so
let's get some more room here and if I
drew a line and here again not drawn to
scale think about an electron going from
the second energy level down to the
first so from n is equal to 2 to n is
equal to 1 let's use our equation and
let's calculate that wavelength next so
this would be 1 over lambda is equal to
the Rydberg constant 1.09 7 times 10 to
the 7th that's 1 over meters and then
we're going from the second energy level
to the first so this would be 1 over the
lower energy level squared so n is equal
to 1 squared minus 1 over 2 squared all
right so let's let's get some more room
get out the calculator here so 1 over 1
squared is just 1 minus 1/4
so that's 0.75 and so if we take if we
take 0.75 of the Redbird constant let's
go
do that so one point zero nine seven
times 10 to the seventh is a redbrick
constant if we multiply that by 0.75
all right so 3/4 then we should get that
number there so that's eight two two
seven five zero zero so let's write that
down one over the wavelength is equal to
eight two two seven five zero two so to
solve for that wavelength just take 1
divide it by that number and that gives
you one point two one times 10 to the
negative 7 and that'd be in meters so
the wavelength here is equal to one
point let me see what that was again one
point two one five one point two one
five times ten to the negative seventh
meters and so if you move this over to
right that's 122 nanometers so this is
122 nanometers but this is not a
wavelength that we can see so 122
nanometers right that falls into the UV
region the ultraviolet region region so
we can't see that we can see the ones in
the visible spectrum only and so this
will represent a line in a different
series and you can use the Balmer
Rydberg equation to calculate all the
other possible transitions for hydrogen
and that's beyond the scope of this
video so here I just wanted to show you
that the visit the emission spectrum of
hydrogen can be explained using the
Balmer Rydberg equation which we derived
using the Bohr model of the hydrogen
atom so even though the Bohr model the
hydrogen atom is not is not reality it
does allow us to figure some things out
and to realize that energy is quantized

I'm sure that most you know the famous

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How to pronounce 656 in English?

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