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 × 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

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Quizplus · Accepted Answer

The kinetic energy gained by the electron is equal to the electrical energy given by the potential difference, which can be calculated using the formula $KE = eV$, where $e = 1.60 \times 10^{-19} C$ is the charge of an electron and $V = 9.9 \times 10^3 V$ is the potential difference. The kinetic energy is also given by $KE = \frac{1}{2}mv^2$, where $m = 9.11 \times 10^{-31} kg$ is the mass of the electron. Equating the two expressions for kinetic energy and solving for $v$ gives the speed of the electron.

If an Electron Is Accelerated from Rest Through a Potential