If an electron is accelerated from rest through a potential

If an electron is accelerated from rest through a potential difference of 6 kV, what is its resulting speed? (e = 1.60 × 10-19 C, k = 1/40 = 8.99 × 109 N m2/C2, mel = 9.11 x 10-31 kg). (Give your answer to the nearest km/s).

Solution

Apply conservation of energy to find the speed:

U_i + K_i + W_nc = U_f + K_f

There are no non-conservative forces acting, the initial kinetic energy is zero.

This gives K_f = 1/2 mv² = q V so:

v = [ 2qV /m ]^1/2 =45940 km/s