# Speed of fastest electron w\ workfunction & photon energy

1. Aug 24, 2008

### fredwacko40

Hi please help me I have a test tomorrow worth 30% and I cant even work out the most basic of questions because my book assumes prior physics and knowing constants etc which I dont know!

The work function of tungsten is 4.50 eV. Calculate the speed of the fastest electrons ejected from a tungsten surface when light whose photon energy is 5.80 eV shines on the surface.

Ok so I've read all the theory and I havent found anything under the photoelectric section converting KE to speed, I asked my friend and he said KE = (1/2)m*v^2 which didnt work. So far I have

hf = Kmax + (I) where (I) is that funny I in a O symbol
5.8 = Kmax + 4.5
Kmax = 1.3

Im assuming thats correct but please correct me if Im wrong, so I now have the max Kinetic energy but no way to convert it to speed. The back of the book says the mass of an electron is 9.109*10^-31 kg

I've also tried an equation I found on the internet:

V^2/C^2 = (2*Kmax)/mc^2 and after a little searching I found c to be the speed of light, but that returned a value of V = 68.81 which although a nice number wasnt right, 676 km/s is meant to be the answer, perhaps I just have to convert it? I think its in m/s atm though so that would make it 0.06881 km/s? That would be way off.... please help me! I need to pass this test!

2. Aug 24, 2008

### Staff: Mentor

Convert the energy units from eV to Joules (the usual SI units). Then you can calculate the speed using the definition of KE.

3. Aug 24, 2008

### fredwacko40

Ok so the conversion from
eV to joules is 16.02*10^-19
which gives me 2.0826*10^-19

So I plug in the numbers

((KE)/(0.5*m))^(0.5) = V
and that gives me a REALLY tiny number
which is correct but its too small!

6.76*10^-26

Is it because Im putting the mass in as Kg? Thats the first thing Im jumping to because although thats the way the book has the weight of an electron it strikes me as a silly unit for an electron!

Edit: What would be a better unit?

4. Aug 24, 2008

### Staff: Mentor

OK.
Do this calculation over. Carefully. (Kg is the proper unit for mass; note that the mass of the electron is tiny.)

5. Aug 24, 2008

### fredwacko40

Thankyou so much! I dont know what I put in wrong the first time but I now have the correct answer :) I probably would have spent another hour on that not even realising Id already had it right but put in the wrong numbers!