Textbook Problem 1B.9

[Mia Glinn 1I]

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 2.0 s? How many moles of photons are emitted in that time interval?

I’m confused as to where to start on this problem… any help is appreciated!

[Emily Engelkemier 1E]

For part a, you can find the total energy generated in 2.0 seconds using 32 J/s * 2.0 s = 64 J = Etotal
The energy per photon = hc/lambda
Then, find the number of photons using Etotal/E per photon=number of photons. Then you can convert to moles.
Hope this helps!

[Jericho Ansay 1C]

To find the number of photons of light that the lamp can generate in 2.0 s, you would first find the energy per photon, using the equation E = hc/lambda. Plugging in 6.626 x 10^-34 for planck's constant (h) and 3.00 x 10^8 for the speed of light (c), and 4.20 x 10^-7 for lambda (converted to meters), you get E = 4.733 x 10^-19 J. In order to find the number of photons, you would then determine that 64 J would have been used in 2 seconds, to which you would divide 64 J by 4.733 x 10^-19 J/photon to get a total of 1.4 x 10^20 photons. Then, to determine moles of photons, you would simply divide by Avagadro's number of 6.022 x 10^23 to get 2.25 x 10^-4 mols.

[Mia Glinn 1I]

For part a, you can find the total energy generated in 2.0 seconds using 32 J/s * 2.0 s = 64 J = Etotal
The energy per photon = hc/lambda
Then, find the number of photons using Etotal/E per photon=number of photons. Then you can convert to moles.
Hope this helps!

Thank you Emily, that's very helpful I didn't even think of doing that first step of converting our given information into total energy. That set the whole problem up nicely thank you!