An $\alpha$- particle of $5\ MeV$ energy strikes with a nucleus of uranium at stationary at an scattering angle of $180^o$. The nearest distance upto which $\alpha$- particle reaches the nucleus will be of the order of

The wavelengths of ${K_\alpha }$ $X-$ rays of two metals $'A'$ and $'B'$ $\frac{4}{{1875R}}$ and $\frac{1}{{675R}}$ respectively, where $'R'$ is Rydberg's constant. The number of elements lying between $'A'$ and $'B'$ according to their atomic numbers is

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?

The ratio of the speed of the electrons in the ground state of hydrogen to the speed of  light in vacuum is

In Rutherford scattering experiment, what will be the correct angle for $\alpha $ scattering for an impact parameter $b = 0$…..$^o$