HW Question Ch #27 [ENDORSED]

[Yuchien Ma 2L]

A lamp rated at 32 W (1 W = 1 J * s^-1) emits violet light of wavelength 420 nm. How many photons of violet light can the lamp generate in 2.0s? How many moles of photons are emitted in that time interval?

I got the first part, 32 J * s^-1 * 2.0 s = 64 J

But I'm confused about the second part. I am given the wavelength and the energy, how do I convert that to number of photons?
Thanks in advance for your help.

[Manpreet Singh 1N]

To begin the problem we need to find the energy of the light. So we use the E=(hc)/wavelength
so energy= ((6.626x10^-34 Js)(3x10^8m/s))/(420x10^9m)
I changed the units of wavelenth from nm to m, so that is why I multiplied 10^-9 to the given wavelength.
We get the energy to be about 4.7x10^-19J. I like to think of this value of J/photon because that is what the energy corresponds to, but when we do the equation we leave out the per photon and just keep it at J for simplicity.

amount of photons=Etotal/Ephoton

so now to find the amount of photons by dividing the total energy 64J( which we got by multiplying 34 Js-1 by 2 seconds) by the energy per photon (4.7x10^-19).

amount of photons=(64 J)/(4.7x10^-19)=1.4x10^20 photons.

then moles of photon=(1.4x10^20 photon)((1 mole)/(avagadro's number=6.022x10^23 photons)=2.3x10^4 moles of photons.

hopefully that helps :)

[Yuchien Ma 2L]

Thanks for the explanation!
It's so much clearer than the one in the solutions manual :D

[Sylvia_Cai_3D]

I had a similar question, but I am still confused about how it is 6.022X10^23 photons per mole. Is it just a known constant that just like atoms there are a certain number of photons per mole?

[Dan_Jin_1K]

To Sylvia,

One mole is 6.022 x 10^23 of "things". The mole can be 6.022 x 10^23 atoms, which can be said as 1 mol of atoms, or it could be 6.022 x 10^23 donuts, which would be said as 1 mol of donuts.

For this case, 1 mol of photons, just means 6.022 x 10^23 of those "things" (photons), so you'd have 6.022 x 10^23 photons in 1 mol of photons.

[Alex_Wagas_3K]

I had a similar question, but I am still confused about how it is 6.022X10^23 photons per mole. Is it just a known constant that just like atoms there are a certain number of photons per mole?

6.022x10^23 is a constant that can be expressed as per mole of anything. As stated above, it can represent photons per mole or that of a similar nature