# Work on an electron

1. Dec 12, 2007

### AnnieD

1. The problem statement, all variables and given/known data

How much work is required to accelerate an electron from rest to 1.6 x 10 ^8m/s. (m= 9.1 x 10 ^ -31kg)?

The answer should be: 2.7 x 10 ^ -18

2. Relevant equations
a = Fnet/m
W = F x d
W = E

3. The attempt at a solution
I can't see a way to figure this problem out. It seems I need the distance, but I can't figure it out because I don't have a time to use to figure that out, or the acceleration rate. I tried rearranging a = Fnet/m .. but was again then stuck with the distance/time problem. Am I missing something?

2. Dec 12, 2007

### hotcommodity

The total work done on an object is defined as the objects change in kinetic energy:

$$W_{TOT} = \Delta K$$

where $$\Delta K = 0.5mv^2_f - 0.5mv^2_0$$

All you have to figure out now is the electrons inital and final kinetic energies. Does that help?

3. Dec 12, 2007

### fantispug

You don't know the acceleration (for you are not given how long it takes to accelerate the electron to this speed - if it takes 1 second a=1.6 x 10^8 m/s^2 or if it takes 2 seconds a=0.8*10^8 m/s^2), and you don't know the distance so
W=F d and F = m a are not going to be too helpful.
Look more closely at your 3rd equation - what energy did the electron initially have? What energy does it have finally?
(Warning: This method should work but I got a different result to the one stated - though I am assuming it is in SI units)

4. Dec 12, 2007

### AnnieD

Yes, forgot to mention that I also tried the W = delta E equation.
So E = Ek2 - Ek1
but the answer I ended up getting wasn't the right one.
I ended up with a final answer of 1.1648 x 10 ^ - 14

5. Dec 12, 2007

### kudoushinichi88

You may have copied the question wrongly... or the answer is wrong. I calculated and got $$1.16 \times 10^{-14} J$$ as well.

Last edited: Dec 12, 2007
6. Dec 12, 2007

### hotcommodity

I believe that should be $$10^{-14}$$ and in units of Joules.

It would be a good idea to double check your values, as kudoushinichi suggested. Text book authors have been know to make errors.

7. Dec 12, 2007

### kudoushinichi88

Oops... typed without thinking much... Sorry...

8. Dec 13, 2007

### rl.bhat

When the electron is moving with the velocity = 1.6*10^8 m/s we have to consider the relativistic mass and energy.

9. Dec 13, 2007

### kudoushinichi88

Oh I totally forgot about relativity... since I haven't really studied that in a formal class...

So we use the equation

$$E_k = (\gamma - 1)mc^2$$

right?

But then I plugged in the values and yielded $$1.49 \times 10^{-14} J$$ instead....

Last edited: Dec 13, 2007
10. Dec 13, 2007

### AnnieD

Thanks everyone for your help! We've come to the conclusion (my physics teacher) that the book is wrong. The correct answer is the one others as well as myself mentioned earlier as the value. I don't know anything about relativity- it's only a gr.12 class, but thank you for trying nonetheless! Much appreciated. :)