The rest energy of an electron is 0.511 MeV. The electron is accelerated from rest to a velocity 0.5 c. The change in its energy will be

Question

The rest energy of an electron is 0.511 MeV. The electron is accelerated from rest to a velocity 0.5 c. The change in its energy will be (A) 0.026 MeV (B) 0.051 MeV (C) 0.079 MeV (D) 0.105 MeV

Tardigrade Admin · Accepted Answer

According to Einstein's equation relation between rest energy and moving energy is

E = E_{0} (1 - \frac{v ^{2}}{c ^{2}})^{- 1/2}

Given,

v = 0.5 c

∴ E = E_{0} (1 - \frac{( 0.5 c ) ^{2}}{c ^{2}})^{- 1/2}

E = E_{0} (1 - 0.25)^{- 1/2}

= \frac{E _{0}}{0.75}

Change in energy

Δ E = E - E_{0}

= \frac{E _{0}}{0.75} - E_{0}

= E_{0} (\frac{1}{0.75} - 1)

= 0.511 (\frac{1}{0.75} - 1)

= 0.079 M e V

Q. The rest energy of an electron is 0.511MeV. The electron is accelerated from rest to a velocity 0.5c. The change in its energy will be

0.026 MeV

0.051 MeV

0.079 MeV

0.105 MeV

Q. The rest energy of an electron is $0.511 M e V$ . The electron is accelerated from rest to a velocity $0.5 c$ . The change in its energy will be