Does Electron Speed Impact Work and Position Uncertainty?

[Stevo11]

Heisenbergs..HELP PLEASE

Homework Statement

Does it take more work to increase an electron’s
speed from 0.5c to 0.9c, or from 0.9c to 0.95c?

i don't know where to start...


If an electron is traveling at 1 km/s, how
uncertain is its position?

I did the Px X=h/2pi and solved for X.. I got (1.2x10^-7) but the book gets 7.24x10^-7 I don't know what's with this


I'm extremely frustrated and pretty sick of this, my teachers quite useless as well... I'll just be honest, I'm going to Vet school but need physics to get into the program, so I just need to pass this course by the skin of my butt, so can someone please just give me the quick and dirty with how to do this because I'm really quite fed up with it ****bangs head off desk****

 

[Zacku]

Hi,

Homework Statement

Does it take more work to increase an electron’s
speed from 0.5c to 0.9c, or from 0.9c to 0.95c?

i don't know where to start...

I assume that you have to use special relativity to solve this problem.
The amount of work to change the velocity of a particle is by definition the change in energy of the particle when it velocity changes from a velocity $$v_1$$ to a velocity $$v_2$$
I suggest you start with the formula for the energy which is
$$E=\sqrt{m^2c^4 + p^2c^2}$$
where $$p=\frac{m v}{\sqrt{1-v^2/c^2}}$$

If an electron is traveling at 1 km/s, how
uncertain is its position?

I did the Px X=h/2pi and solved for X.. I got (1.2x10^-7) but the book gets 7.24x10^-7 I don't know what's with this

It seems that they used h in the Heisenberg relation rather than h/2pi doesn't it?

 

[Stevo11]

They did use Heisenberg relation^ I asked my prof, and somehow my book has errors, but its all good now, thanks for the help :)