Problem 4: An electron moves with a speed of v = 0.85 c. Find its total energy and K.E in electron volts.

Solution

Explanation: When the electron moves with the given relativistic speed, it possesses energy, E = mc2. However, from relativistic point of view (as Einstein opined) this energy has two parts; one the mass of electron (energy and mass inter-convertible!) and the other K.E of the particle. So, to calculate the total mass we apply the above equation and to calculate the K.E we subtract the rest mass energy of electron from it.

Given
Speed of electron, v = 0.85c
rest mass of electron, m0 = 9.11 × 10-31 kg

Find: Total energy and K.E of the electron

Formula: E =mc2

Now to find the relativistic mass of the electron, apply formula

Put this value in the formula to find the total energy of the electron.

The energy is required in eV. The conversion is

1.6 × 10-19 J = 1 eV ⇒ 1 J = (1/1.6×10-19)J. Therefore,

Now to find rest mass energy of the electron, E = m0c2, we have,

Convert to electron-volts,

Therefore, the K.E of the electron will be the difference of the relativistic energy and rest mass energy.