Question

A singly ionized 'He' ion and 'H' ion are accelerated from rest through a potential difference 'V' to velocities 'U(He)' and 'U(H)' respectively. What is the ratio of 'U(He)/U(H)'?

Answer 1

• `u_(He)/u_(H) = 1/2`

Explanation:

Use conservation of energy.

`Delta T + Delta U = 0`

For each ion that means:

`1/2 m u^2 = qV, qquad "with charge, "q = +1 e`

`:. qquad u = sqrt((2qV)/m)`

As `q" and " V` are the same:

• `u_(He)/u_(H) = sqrt( m_H/m_(He) ) = sqrt((1" u")/(4 " u")) = 1/2`

[Approx mass figures used, and assumed non-relativistic]