$A$ proton is fired from very far away towards a nucleus with charge $Q=120 \ e$,where $e$ is the electronic charge. It makes a closest approach of $10 \ fm$ to the nucleus. The de Broglie wavelength (in units of $fm$) of the proton at its start is: (take the proton mass,$m_0 = (5/3) \times 10^{-27} \ kg$,$h/e = 4.2 \times 10^{-15} \ J \cdot s/C$,$\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$,$1 \ fm = 10^{-15} \ m$)

In Rutherford's experiment,the number of particles scattered at a $90^{\circ}$ angle is $x$ per second. The number of particles scattered per second at an angle of $60^{\circ}$ is:

Why are atoms electrically neutral?

$\alpha$-particles of energy $400 \, KeV$ are bombarded on a nucleus of $_{82}Pb$. In the scattering of $\alpha$-particles, what will be the minimum distance of approach from the nucleus?

In the Rutherford's nuclear model of the atom,the nucleus (radius about $10^{-15} \; m$) is analogous to the sun about which the electron moves in an orbit (radius $\approx 10^{-10} \; m$) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom,would the earth be closer to or farther away from the sun than it actually is? The radius of the earth's orbit is about $1.5 \times 10^{11} \; m$. The radius of the sun is taken as $7 \times 10^{8} \; m$.

State the atomic hypothesis regarding the structure of matter.