What is the percentage of $\alpha -$ particles that have more than $1^o$ scattering in Geiger-Marsden experiment? 

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

The size of an atom is of the order of

The graph which depicts the results of Rutherform gold foil experiment with $\alpha$ -particales is

$\theta:$ Scattering angle

$\mathrm{Y}:$ Number of scattered $\alpha$ -particles detected

(Plots are schematic and not to scale)

  • [JEE MAIN 2020]

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?

In a hydrogen atom, the electron is in $n^{th}$ excited state. It may come down to second excited state by emitting ten different wavelengths. What is the value of $n$ :