Give the relationship between impact parameter and scattering angle.

If the number of alpha particles scattered at an angle of $90^\circ$ is $56$,how many particles will be scattered at an angle of $60^\circ$?

We consider the Thomson model of the hydrogen atom in which the proton charge is distributed uniformly over a spherical volume of radius $R = 0.25 \,\mathring A$. Applying the Bohr quantization condition in this model,the ground state energy (in $eV$) of the electron will be close to:

An $\alpha$-particle of $5 \; MeV$ energy strikes a stationary uranium nucleus at a scattering angle of $180^o$. The distance of closest approach of the $\alpha$-particle to the nucleus will be of the order of:

State and explain Dalton's atomic theory.

Answer the following questions,which help you understand the difference between Thomson's model and Rutherford's model better.
$(a)$ Is the average angle of deflection of $\alpha$-particles by a thin gold foil predicted by Thomson's model much less,about the same,or much greater than that predicted by Rutherford's model?
$(b)$ Is the probability of backward scattering (i.e.,scattering of $\alpha$-particles at angles greater than $90^{\circ}$) predicted by Thomson's model much less,about the same,or much greater than that predicted by Rutherford's model?
$(c)$ Keeping other factors fixed,it is found experimentally that for small thickness $t$,the number of $\alpha$-particles scattered at moderate angles is proportional to $t$. What clue does this linear dependence on $t$ provide?
$(d)$ In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of $\alpha$-particles by a thin foil?