Question

What is the rest energy of an electron, given its mass is (9.11 × 10⁻³¹ ) kg? Give your answer in joules and MeV.

( E = mc² )
(a) (8.19 × 10⁻¹⁴) J, 0.51 MeV
(b) (9.11 × 10⁻³¹) J, 0.11 MeV
(c) (1.62 × 10⁻¹³) J, 1.02 MeV
(d) (5.67 × 10⁻¹⁴) J, 0.35 MeV

Answer 1

The rest energy of an electron with a mass of 9.11 × 10⁻³¹ kg can be calculated using E = mc² and is found to be (8.19 × 10⁻¹⁴) J or 0.51 MeV.

Step-by-step explanation:

To find the rest energy of an electron, we use the equation E = mc², where E is the rest energy, m is the mass of the electron, and c is the speed of light. The mass of the electron is given as 9.11 × 10⁻³¹ kg. The speed of light, c, is a constant with the value of 3 × 10⁸ m/s. Plugging these values into the equation, we get:

E = (9.11 × 10⁻³¹ kg) × (3 × 10⁸ m/s)²

Calculating this we obtain:

E = 9.11 × 10⁻³¹ kg × 9 × 10¹⁶ (m²/s²)

E = 8.19 × 10⁻¹⁴ J

Using the conversion factor of 1 eV = 1.602 × 10⁻¹⁹ J, the rest energy in electron volts (eV) is:

E = (8.19 × 10⁻¹⁴ J) / (1.602 × 10⁻¹⁹ J/eV)

E ≈ 0.51 MeV

Therefore, the rest energy of an electron in joules and MeV is (a) (8.19 × 10⁻¹⁴) J, 0.51 MeV.