Question

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.

Answer 1

Answer:

 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 = $\sqrt{\frac{2q \Delta V}{m} }$

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 = $\sqrt{ \frac{2 \ 1.6 \ 10^{-19} \ 1}{9.1 \ 10^{-31}} }$

           v = $\sqrt {0.3516 \ 10^{12}}$

           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 = $\sqrt{ \frac { 2 \ 1.6 \ 10^{-19} \ 1}{1.67 \ 10^{-27}} }$

             v = $\sqrt{ 1.916167 \ 10^8 }$

             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