If an electron is accelerated from rest through a potential difference of 1 200 V,find its approximate velocity at the end of this process.(e = 1.6 × 10−¹⁹ C;m_e = 9.1 × 10−³¹ kg) A)2.5E+7 m/s B)2.1E+8 m/s C)2.1E+7 m/s D)4.2E+7 m/s E)1.8E+8 m/s

Question

Quizplus · Accepted Answer

The kinetic energy gained by the electron is equal to the potential energy it lost, which is given by qΔV, where q is the charge of the electron and ΔV is the potential difference. Therefore, the kinetic energy gained by the electron is (1.6 × 10^-19 C) x (1200 V) = 1.92 × 10^-16 J. Using the formula for kinetic energy (K = 1/2 mv^2), we can solve for the velocity v:

1/2 mv^2 = 1.92 × 10^-16 J

v^2 = (2 x 1.92 × 10^-16 J) / m

v = sqrt[(2 x 1.92 × 10^-16 J) / m] = 2.08 x 10^7 m/s

Rounding to two significant figures gives a final answer of 2.1 x 10^7 m/s, which is choice C.

If an Electron Is Accelerated from Rest Through a Potential