Alpha Particle Scattering — Prelims Questions

In Rutherford's alpha particle scattering experiment, what percentage of alpha particles passed through the gold foil undeflected?

An alpha particle with kinetic energy $K$ is directed towards a nucleus of atomic number $Z$. The distance of closest approach is $r_0$. If the kinetic energy of the alpha particle is doubled, what will be the new distance of closest approach?

Which of the following statements is NOT a limitation of Rutherford's atomic model?

An alpha particle with kinetic energy $K$ has an impact parameter $b$ and is scattered through an angle $heta$. If the impact parameter is halved ($b/2$), what can be said about the new scattering angle $heta'$ (assuming $K$ and $Z$ remain constant)?

An alpha particle of mass $m$ and charge $2e$ approaches a gold nucleus ($Z=79$) with initial velocity $v$. If the distance of closest approach is $r_0$, what is the kinetic energy of the alpha particle in terms of $r_0$ and other constants?

According to Rutherford's model, what is the ratio of the volume of the nucleus to the volume of the atom?