When an $\alpha$-particle of mass $m$ moving with velocity $v$ bombards a heavy nucleus of charge $Ze$,its distance of closest approach from the nucleus depends on $m$ as

$A$ neutron collides head-on with a stationary hydrogen atom in its ground state. Which of the following statements are correct? (Assume that the hydrogen atom and neutron have the same mass):

In the gold foil experiment,the number of deflected $\alpha$-particles at an angle of $90^o$ is $63$. What is the number of $\alpha$-particles deflected at $120^o$?

In the Rutherford experiment,$\alpha$-particles are scattered as shown in the figure. Which of the four paths is not possible?

If an alpha particle with energy $7.7 \text{ MeV}$ is bombarded on a thin gold foil, the closest distance from the nucleus it can reach is . . . . . . $\text{m}$. (Atomic number of gold $= 79$ and $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9$ in $SI$ units)

In a Rutherford scattering experiment,when a projectile of charge $Z_1$ and mass $M_1$ approaches a target nucleus of charge $Z_2$ and mass $M_2$,the distance of closest approach is $r_0$. The energy of the projectile is: