Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be triple its rest energy? (m_e = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,and q_e = 1.6 × 10−¹⁹ C) A) 5.1 × 10⁵ V B) 1.6 × 10^-19 V C) 1.0 × 10⁶ V D) 2.6 × 10⁵ V

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Quizplus · Accepted Answer

The total energy of an electron can be given by E = mc², where m is its mass and c is the speed of light. Initially, the electron is at rest, so its total energy is simply its rest energy: E₀ = (9.11 × 10⁻³¹ kg)(3.00 × 10⁸ m/s)² = 8.19 × 10⁻¹⁴ J.
To triple its total energy, we need to add 2E₀ more energy to the electron. The potential energy gained by a charge q moving through a potential difference ΔV is given by ΔPE = qΔV. Thus, we need to find the potential difference ΔV that gives the electron 2E₀ more energy:
2E₀ = qΔV
ΔV = 2E₀/q = 2(8.19 × 10⁻¹⁴ J)/(1.6 × 10⁻¹⁹ C) = 1.02 × 10¹⁶ V ≈ 1.0 × 10¹⁶ V
Therefore, the best choice is C, 1.0 × 10¹⁶ V.

Through What Potential Difference Would an Electron Initially at Rest