In Rutherford scattering experiment, what will be the correct angle for $\alpha $ scattering for an impact parameter $b = 0$.....$^o$

The following diagram indicates the energy levels of a certain atom when the system moves from $4E$ level to $E$. A photon of wavelength $\lambda _1$ is emitted. The wavelength of photon produced during it's transition from $\frac{7}{3}E$ level to $E$ is $\lambda_2$. The ratio $\frac{{{\lambda _1}}}{{{\lambda _2}}}$ will be

The binding energy of the electron in a hydrogen atom is $13.6\, eV$, the energy required to remove the electron from the first excited state of $Li^{++}$ is ......... $eV$

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.

What is shown by Thomson's experiments of electric discharge through gases ? And explain the plum pudding model.

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