An electron is to be accelerated from a velocity of 5.00*106 m/s to a velocity of 9.90*106 m/s. through what potential difference must the electron pass to accomplish this

Potential difference needed = 207.9 V

Explanation=

using work energy principle

Work done on the electron = change in kinetic energy

W = 1/2m Vf² - 1/2 mVi²

m = mass of electron=9.11 x 10⁻³¹ Kg

Vf = final velocity = 9.9 x 10⁶ m/s

Vi = initial velocity = 5 x 10⁶ m/s

so W = 1/2 (9.11 x 10⁻³¹) (9.9 x 10⁶) ² - 1/2 (9.11 x 10⁻³¹) (5 x 10⁶) ²

W=3.33 x 10⁻¹⁷ J

Now work done = q V

q = charge of electron = 1.6 x 10⁻¹⁹J

V = potential difference

3.33 x 10⁻¹⁷ = (1.6 x 10⁻¹⁹) V

v = 207.9 V