## Chapter 1, #27

Genisis Cabral
Posts: 20
Joined: Fri Sep 29, 2017 7:07 am

### Chapter 1, #27

"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 started off the problem by finding the total energy output and I did that by multiplying the 32 W by the 2.0 s and got 64 J as the total energy output. But I'm having a bit of confusion on what formula I would use next to continue the problem. I was thinking of using E=h(c/v) and inputting the values so I was hoping on getting some clarification on whether that would be the correct formula to use in this case. Thank you!

Joyce Lee 1C
Posts: 52
Joined: Fri Sep 29, 2017 7:03 am
Been upvoted: 1 time

### Re: Chapter 1, #27

I also started by finding the total energy; however, I used the formula E=hc/lambda.
The given wavelength is in nm so convert to m.
E = [(6.626 x 10^-34 Js)(3.0 x 10^8 m/s)]/(420 x 10^-9 m) = 4.7 x 10^-19 J
Doing this gives us how much energy in Joules each photon has.
Then, the question tells us that 32 W or 32 J/s is emitted and asks for the number of photons generated in 2.0 s.
Start off by multiplying 32 W by 2, so 64 J are generated in 2.0 seconds. Use the answer we found above to get the number of photons generated.
# photons = 64 J x (1 photon/4.7 x 10^-9 J) = 1.4 x 10^20 photons
As you can see, the joules cancel out, and you're left with photons.
To find the moles of photons, use 6.022 x 10^23 photons/ mol as a conversion factor.

I hope that this helped a bit!~