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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