The transition from the state $n = 4$ to $n = 3$ in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition
$2 \to 1$
$3 \to 2$
$4 \to 2$
$5 \to 4$
In an atom, two electrons move around the nucleus in circular orbits of radii $R$ and $4R.$ The ratio of the time taken by them to complete one revolution is : (neglect electric interaction)
The Rutherford $\alpha$-particle experiment shows that most of the $\alpha$-particles pass through almost unscattered while some are scattered through large angles. What information does it give about the structure of the atom
In 1911 , the physicist Ernest Rutherford discovered that atoms have a tiny, dense nucleus by shooting positively charged particles at a very thin gold foil. A key physical property which led Rutherford to use gold was that it was
$\sqrt{d_{1}}$ and $\sqrt{d_{2}}$ are the impact parameters corresponding to scattering angles $60^{\circ}$ and $90^{\circ}$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For $d_{1}=x d_{2}$, the value of $x$ will be ________
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?