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

The relation between the rest energy and moving energy is

E = \frac{E _{0}}{1 - v ^{2} / c ^{2}}

∵ v = 0.5 c

∴ E = \frac{E _{0}}{1 - 0.25}

= \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

The relation between the rest energy and moving energy is E=1−v2/c2​E0​​ ∵v=0.5c ∴E=1−0.25​E0​​ =0.75​E0​​ Change in energy ΔE=E−E0​ =0.75​E0​​−E0​ =E0​(0.75​1​−1) =0.511(0.75​1​−1) =0.079MeV

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