Textbook Problem 1B.9

[Daria Obukhova 2B]

Hi, could anyone please help with textbook problem 1b.9

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?

So when it's asking for amount of photons, would that just be frequency? Because I tried to do 32 J⋅s−1 x 2s = 64 J. So now I plugged into E=hv, and got v= 9.66x10^-34 1/s. The answer is 1.4 3 1020 photons.

[Stuti Pradhan 2J]

The step you did was correct. However, that gives you the total energy of the lamp, so to find the number of photons, you first need to find the energy per photon. To do this, simply convert the given wavelength into meters and then use the equation
to find the energy per photon. Then, divide the total energy of the lamp by the energy per photon to find the number of photons the lamp can generate in 2.0 s.

Hope this helps!

[StephanieIb]

After finding the total energy, I recommend following the equation hc/wavelength. Then to find the number of photons, divide the energy of the lamp (64J) by the energy of the photon you just calculated (4.704143 X 10^-19J). You should get 1.4 x 10^20 particles. Lastly, to get the number of particles, divide the number of photons (1.4 x 10^20) by Avogardos (6.022x10^23 particles/mol). Your final answer should be 2.3x10^-4 mol.