Textbook Problem 1B.9

[Adam_Ventura_1H]

So I am not sure how to go about this problem. I do not know what to do with the W. I think I need to use the E=hc/lambda but i am sure really. Hopefully someone can help me out. Thanks
Question: 1B.9 A lamp rated at 32 W (1W=1J⋅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?

[America Alvarado]

Yea, you're right. You use E=hc/lambda. Then you multiply 32W times 2 because it's asking in 2 seconds. Then you divide 64W by what you got from E=hc/lambda and that is how many photons are generated. For the second part, you use Avogadro's constant to find the moles. Hope this helped!

[Austin Aldujaili 2D]

Remember if you ever get stuck on problems that ask for an answer in specific units to go through it step by step through dimensional analysis. There you can see how the J will cancel out and leave you with photons/sec and you can convert photons to moles using Avagrado's number.

[Brendan Duong 1I]

For part A,
you first translate 420nm into m; then you translate that wavelength into Energy per photon by using the equations c=wavelength/freq and E=hv. Then you divide 32J by the energy you found to get photons produced in one second. This is because 32W is equal to one Joule per second. Then you multiply the number of photons by 2 since you are asked how many are made in 2 seconds
For B,
you just multiply what you got in A by avogadros number to translate atoms into moles

[anikamenon2H]

This problem is daunting at first but the key is to examine the units that are given and go from there. In this case, the problem tells you that a watt is equivalent to 1 J/s. Therefore you know you need to find something with units in joules, aka energy. So like you said, you would use E = hc / lambda in order to calculate the energy. Now this calculated energy is the energy per photon or J/photon. The wattage given (which would be 64 since 32 W over 2 seconds) is the total energy given off. So you would divide the total energy by the energy per photon in order to find the number of photons. Once you find the number of photons, you divide by Avogadro’s number to find the Joules/moles.

Hope this helps!

[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.