Which of the following statements are true regarding Bohr's model of hydrogen atom

$(I)$ Orbiting speed of electron decreases as it shifts to discrete orbits away from the nucleus

$(II)$ Radii of allowed orbits of electron are proportional to the principal quantum number

$(III)$ Frequency with which electrons orbits around the nucleus in discrete orbits is inversely proportional to the principal quantum number

$(IV)$ Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbitsSelect correct answer using the codes given belowCodes :

The ratio of ionization energy of Bohr's hydrogen atom and Bohr's hydrogen like lithium atom is

Given below are two statements :

$Statement$ $I$ : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.

$Statement$ $II$ : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

In the light of the above statements, choose the most appropriate from the options given below.

According to the classical electromagnetic theory, calculate the initial frequency of the light emitted by the electron revolving around a proton in hydrogen atom.

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)

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