Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 163 v. (b) calculate the speed of an electron that is accelerated through the same potential difference.

We could use the energy conservation:

      Kinetic energy = Potential energy
=>  M    =  eV
where, M = mass of proton
            v = speed
            e = charge 
            V = potential difference through which it is accelerated

So, finding speed using the above equation:

v = 

Putting values,
v =  
v = 177.15 Km/s

Now, let  m  = mass of electron

So, Above we got the formula for the speed of proton accelerated through V.

For electron, just replace the mass M (proton) with m (electron) and that's it. Because V is same for both.

So, Speed of electron, v =  

Putting values.

v =  

On solving
v = 7.56 x m/s   or  7560 km/s

You are given the electric potential difference of a proton at 163V. You are asked to find the speed of a proton from rest and when moving but the same potential difference. Use the energy of photon equation.

from rest with potential difference of 163 V
E = 1/2 mv² = eΔV
v = √
v = 176,730 m/s or 176.73 km/s

electron that is accelerated through the same potential difference
E = 1/2 mv² = eΔV
v = √
v = 7566753 m/s = 7,566.8 km/s