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Solve the following.
A charged particle of energy, E = 1/2mv² bombards a heavy target of charge Ze, then shows with the…
A charged particle of energy, $E = \frac{1}{2}mv^2$ bombards a heavy target of charge Ze, then shows with the help of a graph how the distance of the closest approach varies with the mass of the particle.
Answer
Answer
At the closest approach the whole kinetic energy has become electrostatic potential energy:
$E = \frac{1}{4\pi\varepsilon_0}\frac{Zeq}{r_0} \Rightarrow r_0 = \frac{Zeq}{4\pi\varepsilon_0 E}$
The energy $E = \frac{1}{2}mv^2$ is fixed, so $r_0$ does not depend on the mass of the particle. The graph of $r_0$ against $m$ is a straight line parallel to the mass axis.