If an electron is accelerated from rest through a potential difference of 9.9 kV, what is its resulting speed? (e = 1.60 × 10^-19 C, k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²,^m_el= 9.11 x 10^-31 kg) A) 5.9 × 10⁷ m/s B) 4.9 × 10⁷ m/s C) 3.9 × 10⁷ m/s D) 2.9 × 10⁷ m/s

Question

Quizplus · Accepted Answer

The kinetic energy gained by the electron is equal to the potential energy difference it passed through. Therefore, we can use the equation for potential energy:
ΔPE = qΔV
where q is the charge of the electron (−e) and ΔV is the voltage difference.
The change in potential energy is equal to the kinetic energy gained, so we can set them equal to each other:
ΔKE = ΔPE
(1/2) mv² = eΔV
Solving for v, we get:
v = √(2eΔV/m)
Plugging in the given values, we get:
v = √(2(1.60 × 10^-19 C)(9.9 × 10^3 V)/(9.11 × 10^-31 kg)) = 5.9 × 10^7 m/s = 5.9 × 10^17 m/s (scientific notation) = 59,000 km/s (approximate value)
Therefore, the best choice is A, with a resulting speed of 5.9 × 10^7 m/s (or 59,000 km/s).

If an Electron Is Accelerated from Rest Through a Potential