Question

Through what potential difference does an electron have to be accelerated, starting from rest, to achieve a speed of 0.970 c ?

The correct answer for this was 1.6 x 10^6 V.

What is the kinetic energy of the electron at this speed? Express your answer in joules. (J)

What is the kinetic energy of the electron at this speed? Express your answer in electron volts. (eV)

I am struggling with the other two questions probably because of the units. I am really not sure what I am doing wrong.

Answer 1

Part A:

Potential difference = 1.6*10^6 V

Part B.

Kinetic energy of electron is given by:

KE = Total energy - rest energy

rest energy = m*c^2

m = mass of electron = 9.1*10^-31 kg

c = speed of light = 3*10^8 m/sec

Total energy = *m*c^2 = m*c^2/sqrt (1 - (v/c)^2)

= 1/sqrt (1 - (v/c)^2)

v/c = 0.970

So,

kinetic energy = m*c^2*(1/sqrt (1 - (v/c)^2) - 1)

kinetic energy = 9.1*10^-31*(3*10^8)^2*(1/sqrt (1 - 0.970^2) - 1)

kinetic energy = 2.55*10^-13 J

Part C.

1 eV = 1.6*10^-19 J

So,

KE = 2.55*10^-13/(1.6*10^-19) = 1.59*10^6 eV

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