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

Electrons with de-Broglie wavelength $\lambda $ fall on the target an $X-$ ray tube. The cut off wavelength of emitted $X-$ ray is

In the spectrum of hydrogen atom, the ratio of the longest wavelength in Lyman series to the longest wavelength in the Balmer series is

In the following diagram, which particle has highest $e/m$ value?

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?

Rutherford’s $\alpha$-particle experiment showed that the atoms have