Question

Suppose that an electron is traveling at 0.7 c. What is the Rest Energy of the electron? Use 9.11 x 10^-31 kg for the mass of the electron, use c = 2.9979 x 10⁸ m/s, calculate the Rest Energy in units of Joules, convert the units to eV, and then convert the units to MeV. Give your answer in MeV.

What is the mass of the electron in units of MeV/c²?

Use your answer for the mass of the electron in units of MeV/c² to determine the Relativistic Total Energy of the electron? Give your answer in MeV.

Use your answer for the mass of the electron in units of MeV/c² to determine the Relativistic Kinetic Energy of the electron? Give your answer in MeV.

Suppose that an electron is accelerated to a Relativistic Total Energy that is 2.3 times larger than its Rest Energy. What is the speed of the electron? Give your answer in terms of “c” and keep 3 significant figures

Answer 1

Rest energy is given as

E = mc²

E = 9.11 x 10^-31 kg * (0.7*2.9979 x 10⁸ )²

E = 4.01188e-14 J

In eV

250401.865 eV

In MeV

0.250401865 MeV

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Mass of electron is 0.511 MeV/c² ( Is the question asking for standard mass ? please make this clear)

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Relativistic total energy

E = $\gamma$mc²

where $\gamma$ = 1 / sqrt (1 - v² / c²)

$\gamma$ = 1.4

so,
E = 0.7155 MeV

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Relativistic kinetic energy

E = ($\gamma$ - 1)mc²

E = (1.4 - 1) * 0.511 MeV/c²

E = 0.2044 MeV