Answer:
[tex]v=\sqrt{\frac{ev}{m} }[/tex]
Explanation:
The helium ion has:
a potential difference in vacuum = V,
Charge = 2e
and mass = 4m,
speed = v,
mass = 4m
From electrostatics, the work done is the product of charge and its potential difference.
Therefore, Work done = charge × potential difference = 2e × V = 2eV
This work done is in form of kinetic energy, therefore:
Kinetic energy = 1/2 × mass × speed²
⇒ Work done = Kinetic energy
[tex]2eV=\frac{1}{2} *4m*v^2=2m*v^2\\v^2=\frac{2eV}{2m}\\ v^2=\frac{eV}{m}\\ v=\sqrt{\frac{ev}{m} }[/tex]
