Photo-electric Effect

Homework Statement

http://www.astro.uvic.ca/~jwillis/teaching/phys215/phys215_assign_2.pdf

It's question 2.

Work = U/t
E = hf
f = c/lambda
I=Q/t

The Attempt at a Solution

f = c/lambda = (3.00x10^8 m/s)/(530x10^-9 m) = 5.66x10^14 Hz

E = hf = (6.626x10^-34 Js)(5.66x10^14Hz) = 3.75x10^-19 J/photon

Work = 2.00x10^-3 J/s ----> in one second U = 2.00x10^-3 J

#photons = U / E = 5.33 x 10^15 photons

#photo-electrons produced = (5.33 x 10^15)/(10^5) = 5.33x10^10 photo-electrons

Q = (5.33x10^10)(1.60x10^-19 C) = 8.54x10^-9 C

I = 8.54x10^-9 C/s

The thing is I did not use the work function of cesium to solve this. Hence I am unsure if this is right... Any help would be appreciated.

THANKS!

work function only comes in when you want to know the energy of the photo-electron..but you are only concerned with the amount of them (ie. current) the most you could do is to check that the incoming photon energy can indeed overcome the work function: $$E_\text{photon} > \phi$$. I don't think there is any problem with that