In Bohr model of hydrogen atom, the force on the electron depends on the principal quantum number as

  • A

    $F \propto 1/{n^3}$

  • B

    $F \propto 1/{n^4}$

  • C

    $F \propto 1/{n^5}$

  • D

    Does not depend on $n$

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Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

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

  • [IIT 1981]

Explain Rutherford's argument for scattered $\alpha $ -particles. 

The number of completely filled shells for the element ${ }_{16} S ^{32}$ is

  • [KVPY 2017]

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?