An electron has a speed of 0.643c.Through what potential difference would the electron need to be accelerated (starting from rest)in order to reach this speed? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19 C,m_el = 9.11 × 10^-31 kg) A)160 kV B)130 kV C)180 kV D)200 kV

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The correct answer is A.The kinetic energy of the electron is:$$K = \frac{1}{2}mv^2 = \frac{1}{2}(9.11 	imes 10^{-31} 	ext{ kg})(0.643 	imes 3.00 	imes 10^8 	ext{ m/s})^2 = 1.60 	imes 10^{-14} 	ext{ J}$$The potential difference through which the electron must be accelerated is:$$V = \frac{K}{e} = \frac{1.60 	imes 10^{-14} 	ext{ J}}{1.60 	imes 10^{-19} 	ext{ C}} = 160 	ext{ kV}$$

An Electron Has a Speed of 0