Chapter 1 Question 27

[Keshav Bhatnagar 1H]

Hi, I'm not sure how to do this problem and the solutions manual doesn't really help. Here is the problem:

A lamp rated at 32 W (1 W  1 Js1) 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?

[katherinemurk 2B]

First convert 420 nm to m. Then solve for the energy per photon by using the equation E=hc/(wavelength). Once you have that answer, you can divide the total energy which is 64J (1 W= 1 J.s, so 32 x 2=64 J) and divide that by the energy per photon. This will get you the amount in photons. To solve for moles of photons you basically just take the number of photons and divide by Avogadro's number. Sorry if this was confusing but I hope it helps.

[305144105]

1. Find the total energy that is emitted in the 2s time interval.
32W * 1Js^-1/W * 2s = 64J

2. Calculate the energy that is emitted per photon using the formula E = hc/λ. (Remember to convert 420nm to m.)
E = hc/λ = (6.626*10^-34) * (3*10^8) / (420*10-9) = 4.73*10-19 J / photon

3. Calculate how many photons, each emitting 4.73*10-19 J of energy, is needed to achieve the total energy of 64J.
64 / 4.73*10-19 = 1.35*10^20 photons

4. Convert the number of photons to moles.
1.35*10^20 * 1mol / 6.022*10^23 = 2.3*10^-4 mol of photons