Question 1.27 (Sixth Edition)

[Steve Magana 2I]

Question: 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 was wondering if someone can help me see what I've been doing wrong because I keep getting a different answer for this question. Thank you!

[aisteles1G]

since 32 watts = 32 J/s and its for 2 seconds you do 32*2 to get 64 J/s for that time. From the given wavelength you use c=Freq*Wavelength and get V(frequency) = 7.14*10^14 Hz and using delta E you get the energy per photon to be (delta)E= 4.73*10^-19. now you divide the total E (64J) by your energy per photon to get how many photons it generated, which is 1.35*10^20 photons. Then to get the number of moles divide by Avagadro's Number and it should be around 2.24*10^-4 moles. Hope this helps!

[Atul Saha 3D]

Hey Steve,

First calculate the energy from the lamp, which is Wattage (32 J/s) * time (2s) = 64 J. You can next calculate the energy corresponding to the given wavelength 420 nm (utilize the formula E=hc/wavelength), which provides the energy per ONE photon. From here, use dimensional analysis total energy released (64 J) ÷ (energy per photon) to find the answer.

Much Joy,
Atul

[Asia Yamada 2B]

First, you find the total energy by multiplying 2.0 s by the conversion factor 32 W (32 J/s). The seconds will cancel and you will get 64 J as the total energy. Then you have to find the energy per photon. You have to convert given wavelength into meters which is 4.2 x 10^-7 m. Plug this into the equation c=v•wavelength and solve for frequency (v). You will get 7.14 x 10^14 Hz. Plug this frequency into the equation, E=hv. The energy per photon is 4.74 x 10^-19 J. Then, to find the number of photons, you divide 64J by (4.74 x 10^-19)J to get 1.4 x 10^20 photons. Then, divide this by Avogadro’s number to get the moles of photons emitted which is 2.3 x 10^-4 moles of photons.