An electron and a proton have their masses in the ratio 1:1840. What will be the ratio of their kinetic energy if they have equal momentum?

1840:1

Explanation:

If m is the mass of the electron, and 1840m is the mass of the proton, then:

p₁ = p₂

m₁v₁ = m₂v₂

m v₁ = 1840m v₂

v₁ = 1840 v₂

The kinetic energy of the electron is:

KE₁ = ½ m₁ v₁²

KE₁ = ½ m (1840 v)²

KE₁ = 1692800 mv²

The kinetic energy of the proton is:

KE₂ = ½ m₂ v₂²

KE₂ = ½ (1840m) v₂²

KE₂ = 920 mv²

The ratio of the kinetic energies is:

KE₁ / KE₂

(1692800 mv²) / (920 mv²)

1840:1