Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be 6.7 X 10 -27 Kg.

 v₂ /v₁ = 2.3 10⁺²

Explanation:

The energy is conserved so the total potential energy must be transformed into kinetic energy

          K = U

          ½ m v² = q ΔV

          v =

a) Let's find the speed of the electron

           m = 9.1 10⁻³¹ kg

as they do not indicate the value of the power difference, we will assume that ΔV = 1 V is worth one

           v =

           v =

           v1 = 0.593 10⁶ m / s

b) the velocity of a hydrogen ion

            M = M_H + m

            M = 1.673 10⁻²⁷ + 9.1 10⁻³¹

            M = 1.67391 10⁻²⁷ kg

            M = 1.67 10⁻²⁷ kg

            v =

             v =

             v₂ = 1.38 10⁴ m / s

the relationship between these speeds is

           v₂ / v₁ = 1.38 10⁴ / 0.593 10⁶

           v₂ /v₁ = 2.3 10⁺²

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