Homework question 1.27

[Aneri Chouhan]

A lamp rated at 32 W(1W=1 Js^-1) emits violet light of wavelength 420nm. How many photons of light are emitted in 2 seconds. How many moles of photons are emitted in this time interval?

[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 wavelength 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 :)

[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 wavelength 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 :)