Protons are released from rest in a Van de Graaff accelerator. They start from a region where the potential is 7.15 MV then travel through a vacuum region to a region where the potential is zero. Find the speed of the protons when they reach the zero potential region. (proton mass - 1.66 x 1027 kg) A) 1.40 x 10 m/s B) 9.68 x 1014m/s C) 3.70x 10' m/s D) 2.62 x 10 m/s

3.7 x 10⁷ m/s

Explanation:

ΔV = Potential difference through which the proton moves = 7.15 MV = 7.15 x 10⁶ Volts

q = magnitude of charge on the proton = 1.6 x 10⁻¹⁹ C

v = speed of the proton as it reach zero potential region

m = mass of the proton = 1.66 x 10⁻²⁷ kg

Using conservation of energy

Kinetic energy gained by proton = Electric potential energy lost

(0.5) m v² = q ΔV

(0.5) (1.66 x 10⁻²⁷) v² = (1.6 x 10⁻¹⁹) (7.15 x 10⁶)

v = 3.7 x 10⁷ m/s