Homework 1B.9

[April Meza 3K]

A lamp rated at 32 W (1 W 5 1 J*s) 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?

Can some explain how I would approach this question? Thanks!

[Katie Kyan 2K]

Knowing that 32 W = 32 J/sec, this means that 64 J will be emitted in 2 seconds. Therefore, you can find the Energy per photo for violet light of wavelength 420 nm using the equation E=hc/wavelength. Then, divide 64 by the energy per photon to get the number of photons emitted in that time interval of 2 seconds. From there, divide by Avogadro's number to get the moles of photons.

[Ada Chung 1C]

Here's a step by step walk through of the problem I hope it helps.
1. Find total energy which is 32Wx2=64J
2. You are given wavelength is 420 nm so convert this to SI units m
3. Now using the formula E=hc/lambda plug in our wavelength and constants E=((6.626x10^-26)(3.0x10^8))/(4.2x10^-7m)= 4.7x10^-19 Joules
4. Remember that E=hc gives you the amount of energy one single photon so:
(1 photon/4.7x10^-19J) x 65J= 1.4x10^20 photons
5. 1.4x10^20 photons x 1 mol/6.022x10^23 photons= 2.3x10^-4 moles

[April Meza 3K]

Thank you!