Homework Problem 1B.9

[Talia Dini - 3I]

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

I'm not completely sure how to do this problem. I'd greatly appreciate it if someone could please help me with it!!

[Isaac Wen]

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

I'm not completely sure how to do this problem. I'd greatly appreciate it if someone could please help me with it!!

Hi Talia!

So the equations you need for the problem are E=hv and c=λv. You want to combine the two by rewriting the second one as v=c/λ and plugging that into the first to get E=hc/λ.

Part A:
1. First thing you want to do for part a is find the energy per photon. Just solve for E with the equation we just derived. E=hc/(420 * 10^-9)= 4.7 * 10^-19
2. 1 Watt is 1 J/s, meaning W=E/t. (just look at the SI units!) Solve for E. E=Wt=32W * 2s = 64 J. This is the total energy.
3. To find the number of photons, divide the total energy by energy per photon. 64/(4.7 * 10^-19).

Part B:
1. All you have to do is take your answer from part a and convert photons into moles by dividing it by avogadro's number.

Hope this helps!