The wavelength of ${K_\alpha }$ line for an element of atomic number $29$ is $\lambda $ . Then the wavelength of ${K_\alpha }$ line for an element of atomic no $15$ is (Take mosley‘s constant $b = 1$ for both elements)

If the potential difference applied across $X-$ ray tube is $V$ volts, then approximately minimum wavelength of the emitted $X-$ rays 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?

In an atom for the electron to revolve around the nucleus, the necessary centripetal force is obtained from the following force exerted by the nucleus on the electron

What is plum pudding model of the atom ? 

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