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)

In the Rutherford's nuclear model of the atom, the nucleus (radius about $10^{-15} \;m$ ) is analogous to the sun about which the electron move in orbit (radius $\approx 10^{-10} \;m$ ) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than actually it is? The radius of earth's orbit is about $1.5 \times 10^{11} \;m.$ The radius of sun is taken as $7 \times 10^{8}\;m$

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

Ionization potential of hydrogen atom is $13.6 V$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 eV.$ The spectral lines emitted by hydrogen atoms according to Bohr's theory will be

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