Focus 1B #9

[405513470]

This problem involves J/s, wavelength but also time which I found unusual.
A lamp rated at 32W(1W=!J/s) emits violet light of wavelength 420 nm. How many photons of violet light can the lamp generate in 2 seconds? How many moles of photons are emitted in that time interval?
In a bit confused on where to get started with this problem as it includes a time interval and none of the equations include such thing.

[Henry_2A]

Hi!
The time intervals just tell us the total energy in a time period. Since it's 32 J/S, we know two seconds will yield 64 J.

We can use E = hc/lambda, where E will be J/photon. Divide the total Joules (64) by E to get the number of photons. Convert the # of photons to moles of photons by dividing by Avogrado's #.

I hope this helps

[Genelle Marcelino-Searles 2G]

For this question, you should first use the given wavelength to find the energy of photon with Planck's Equation (E=hv)
This gives you the energy of one photon, and you should divide the 32J/s by this in order to get the amount of photons per second. Then multiply this by 2 for two seconds.
To get the amount of moles just divide this number by Avogadro's constant.

[Alyssa Ly 2G]

Hello!

PART A -- For this problem, you can start by finding the energy generated within 2 seconds. Then, to find how many photons of violet light can be emitted within these 2 seconds, you use the equation E = h(frequency) and c=(wavelength)(frequency).

32 W = 32J/s
(32J/1s)*(2s) = 64J
E = hv & c = (wavelength)(frequency) --> E = (hc)/wavelength
E = [(6.63x10^-34 Js)(3 x 10^8 m s^-1)]/(420 x 10^-19m) = 4.74 x 10^-19 J/photon

(64 J) * (1 photon/4.74 x 10^-19 J) = 1.4 x 10^20 photons

PART B -- To find the moles of photons, you can use Avogadro's number!

(1.4 x 10^20 photons) * (1 mol/6.022 x 10^23 photons) = 2.3 x 10^-4 moles of photons

Hope this helped!! :D