A student wants to make a very small particle accelerator using a 9 V battery. What speed will a proton have after being accelerated from rest through the 9 V potential difference? What speed will an electron have after being accelerated from rest through the 9 V potential difference?

v = 4.15 10⁴ m / s

Explanation:

Suppose that all the energy in the battery is converted into kinetic energy of the proton

U = K

q V = ½ m v²

v = √ 2q V/m

v = √ (2 1.6 10⁻¹⁹ / 1.67 10⁻²⁷ 9)

v = √ (17.2455 10⁸)

v = 4.15 10⁴ m / s

Relativistic corrections are not needed as this speed is much less than the speed of light