I need help with this Q! ^.^
What is the wavelength (in units of nm) of a blue light with a frequency of 6.41 x 10^14 Hz?

Question

I need help with this Q! ^.^
What is the wavelength (in units of nm) of a blue light with a frequency of 6.41 x 10^14 Hz?

anonymous · Answer

@ganeshie8 :D

ganeshie8 · Answer

blue light is also light

at what speed does the light travel ?

anonymous · Answer

Oh so it doesn't matter what color light it is? They all have the same speed?

ganeshie8 · Answer

Yes, all electromagnetic radiation travels at the same speed. 

Visible light is just a small part in the huge electromagnetic spectrum

ganeshie8 · Answer

However they will have different wavelengths and frequencies

ganeshie8 · Answer

so do you remember the speed of light ?

anonymous · Answer

Ahhh I see... so I have to use the formula 
$$\lambda =\frac{ v }{ f }$$

ganeshie8 · Answer

Yes, I am just trying to make you derive that formula.
It follows trivially from the formula `distance = speed * time`

anonymous · Answer

Oh it does? :O

ganeshie8 · Answer

$\lambda$ = wave length = `distance` of one cycle

 $v$ = `speed`
 
$T$ = `time` taken to pass one cycle

ganeshie8 · Answer

distance  = speed * time

$\lambda = v * T$

ganeshie8 · Answer

recall the definition of frequency :  number of cycles in one second
therefore $T = \dfrac{1}{f}$

anonymous · Answer

Oh then my formula was wrong... because i divided them

anonymous · Answer

oh actually i take that back XD haha

anonymous · Answer

that makes sense!

ganeshie8 · Answer

your formula is correct too :)
you're using ferquency, i have used timeperiod

anonymous · Answer

Aha! Right! lol :D

ganeshie8 · Answer

btw, normally we use $c$ for the speed of light, not $v$

anonymous · Answer

so I use c= 3*10^8 ?

ganeshie8 · Answer

Yes

ganeshie8 · Answer

$$\lambda =\frac{ c }{ f } = \dfrac{3*10^8}{6.41*10^{14}} =?$$

anonymous · Answer

hmmm... it would be 3/6.41 * 10^-6 ?

anonymous · Answer

Is that exponent correct?

ganeshie8 · Answer

feed it to wolfram

anonymous · Answer

Awesomeness! Thanks so much!!

ganeshie8 · Answer

anonymous · Answer

A little math question!

ganeshie8 · Answer

do you know how to convert to nanometers ?

anonymous · Answer

I know it has something to with 10^-9

ganeshie8 · Answer

Yes, $1nm=10^{-9}m$

so we get : 
$4.68 * 10^{-7}m = 468*10^{-9}m = 468 nm$

anonymous · Answer

how did you get 10^-7 again?

ganeshie8 · Answer

wolfram gave me that

anonymous · Answer

Ohhh i just got confused for a moment! Right right!! XD sorry haha

ganeshie8 · Answer

np, thats just math haha!
it seems our calculation is right, wavelength of blue light is indeed around 468nm : 

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