Understanding Electric Potential and Kinetic Energy in Particle Movement

[physicsuser]

I am reading a book about general physics kinematics, optics, waves, etc.
It focuses more on history than on explaining equations or sample problems.

One of the sample problems in Electric Fields section asks to find energy and speed when a positron moves from one plate that has electric potential of 1e6 V to another that has zero electric potential.

As far as the energy is concerned it is the potential which equals
U=1e6 x 1.6e-19 = 1.6e-13 which is what the answer is at the back of the book states.

But for the speed I get a different answer.
I assume that potential is turned into kinetic as positron reached the other plate so:
Ek=0.5mvv

then v=sqr(2Ek/m)

m=9.1e-31 Kg
Ek=1.6e-13

so from above v=5.9e8

but in the book the answer is 1.4e7m/s


What am I missing or not understanding?

 

[pervect]

But for the speed I get a different answer.
I assume that potential is turned into kinetic as positron reached the other plate so:
Ek=0.5mvv

then v=sqr(2Ek/m)

m=9.1e-31 Kg
Ek=1.6e-13

so from above v=5.9e8

but in the book the answer is 1.4e7m/s


What am I missing or not understanding?

This one had me scratching my head for a bit, until I noticed that 5.9e8 m/s is about twice the speed of light.

So what you need to do is to use the realtivistic formula for energy, not the Newtonian one.

The relativistic formula will be

m_ec^2 / sqrt(1-(v/c)^2) = U + m_ec^2

It's simpler if you remember (or look up) the fact that m_ec^2 is .51 Mev (million electron volts)

But I still don't get the answer the book quoted, so maybe something else is wrong here.

 

[physicsuser]

Ok sorry I found what is wrong... the problem started by saying that the positron is moving but ended up asking the speed and energy of a proton ...

the author must be laughing at how stupid some people are...

Sorry about this.