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in this video we're gonna focus on a few
problems that asked to find the
wavelength and the frequency of a photo
so let's start or this one calculate the
wavelength of a photon that has a
frequency of 2.5 times 10 to the 12
Hertz so what equation do we need
perhaps you've seen this one C is equal
to lambda times nu now C has the speed
of light lambda represents the
wavelength in meters and nu is the
frequency in Hertz so the wavelength is
going to be the speed of light divided
by the frequency the speed of light you
need to know it's 3 times 10 to the 8
meters per second the frequency is 2.5
times 10 to the 12 Hertz which is the
same as seconds to the minus 1 or 1 over
a second so basically we just need to
divide these two numbers and so you
should get 1.2 times 10 to the negative
4 meters and so that's all you need to
do in order to get the answer now
sometimes you may need to convert it to
a different unit because this number is
pretty small so let's convert it to
micrometers how can we convert meters to
micrometers what is the value of one
micrometer micro represents 10 to the
minus 6 so 1 micrometer is 10 to the
negative 6 meters you can take this
number and move it to the top by
changing the exponent from negative 6 to
positive 6 so this is equivalent to 1.2
times 10 to the minus 4 multiplied by 10
to the positive 6 and when you multiply
by a common base you need to add the
exponents so negative 4 plus 6
is to so the answer is 1.2 times 10 to
the 2 micrometers now 10 squared is 100
and 100 times 1.2 is 120 so the
wavelength you could say is 120
micrometers so if you have a
multiple-choice test you answer maybe in
meters or it could be in a different
unit micrometers so you might have some
conversions with these problems as well
just be ready for that now let's move on
to number two what is the frequency of a
photon that has a wavelength of one
point five times 10th and negative eight
meters so go ahead and try that problem
so starting with this equation we need
to solve for the frequency so nu is
equal to the speed of light divided by
the wavelength the speed of light is
going to be the same it's three times
ten to the eighth meters per second and
when using this formula the wave love
has to be meters which it's already in
meters so now we just got to divide
these two things so 3 divided by 1.5 is
2 now what's 1038 divided by 10 to the
negative 8 when you divide by a common
base you need to subtract the exponents
so you take the top exponent which is
positive 8 and subtracted by the bottom
one which is negative 8 8 minus negative
8 is the same as a plus 8 so that's 16
so the answer is 2 times 10 to the 16
Hertz so that's the frequency of this
photon and you could type it in to make
sure that we do indeed have the right
answer which it is that answer
now what about number three what is the
frequency of a photon that has a
wavelength of 350 nanometers so let's
use the same formula the frequency is
the speed of light divided by the
wavelength but this time the wavelength
is not in meters it's in nanometers
which means we need to convert it to
meters so how do we go about doing that
it turns out that all you need to do is
replace nanometers with 10 to the minus
9 meters and it's gonna work out if you
want to write it out here's what you can
do start with what you're given and know
that one nanometer is equivalent to 10
to the minus 9 meters so these units
will cancel and all you have is 350
times 10 to the minus 9 so you just got
to replace this with 10 to minus 9
meters and the speed of light is not
going to change in a vacuum it's
constant however when light passes
through a different material let's say
water or through diamond the speed of
light does change it decreases but in
pure empty space in the vacuum it's 3
times 10 to the 8 meters per second
so the frequency is gonna be eight point
five seven times ten to the 14 Hertz or
seconds to the minus one so this is the
answer for this problem
number four determine the wavelength of
a photon that has the frequency of
ninety five megahertz so to calculate
the wavelength we know it's the speed of
light divided by the frequency now let's
convert megahertz into Hertz so what is
the value of Omega a mega hurt is
basically a million Hertz mega
represents 10 to the 6 so what we have
now is 95 times 10 to the 6 Hertz so
that's the frequency so now that we
changed a unit we can plug it in to the
equation
so let's go ahead and divide these two
numbers so you should get three point
one six meters so that's the wavelength
of a photon with that frequency now has
a question for you what happens to the
wavelength of a photon as the frequency
increases so we know that wavelength is
the speed of light divided by the
frequency notice that the frequency is
in the bottom of the equation which
means it's inversely related to the
wavelength so as the frequency increases
the wavelength decreases and vice versa
so as the wavelength increases the
frequency decreases so these two are
always going to be inversely related to
each other and so that's all you need to
know about photons and the relationship
between wavelength and frequency when
one goes up the other goes down now what
if you're given the energy of a photon
how can you calculate the frequency the
equation that relates the energy of a
photon to the frequency is this equation
the energy of the photon is basically
the product of Planck's constant
represented by the symbol H multiplied
by the frequency now the value of
Planck's constant is it's six point six
to six times 10 to the negative 34
joules times seconds so if you wish to
calculate the frequency it's simply the
energy of the photon divided by Planck's
constant so it's going to be three point
five times ten to the minus 18 joules
divided by six point six to six times
ten to the negative 34 joules times
seconds so as you can see the unit
joules will cancel leaving the unit one
over seconds which is equivalent to the
hurt or hurts so let's divide these two
numbers
so the frequency is going to be five
point two eight times ten to the 15
Hertz and so that's how you can
calculate the frequency of a photon and
given it to energy now this is gonna be
the last problem determine the
wavelength of a photon with an energy of
four point three times ten to the
negative 19 joules so what we're gonna
do in this problem it's just like before
we're gonna calculate the frequency
first and once we have the frequency
then we're gonna calculate the
wavelength so the frequency is going to
be the energy divided by Planck's
constant so it's four point three times
10 to the negative 19 joules divided by
six point six two six times 10 4 minus
34 so for the frequency you should get
six point four nine times ten to the 14
Hertz so now that we have the frequency
let's go ahead and calculate the
wavelength now we know that the
wavelength is going to be the speed of
light divided by the frequency so that's
3 times 10 to the 8 meters per second
divided by six point four nine times 10
to the 14 Hertz
so you should get four point six two
times ten to the negative seven meters
now let's go ahead and convert this to
nanometers so keep in mind one nanometer
is equivalent to 10 to the minus 9
meters so I'm going to take this and
move it to the top so then it becomes
four point six two times ten to the
minus seven times ten to the positive
nine a negative seven plus nine is 2 so
it's four point six two times 10 to the
2 nanometers that we know 10 squared is
a hundred so 100 times the four point
six two it's 462 nanometers so that's
the wavelength in nanometers this is the
answer
