A proton is fired from very far away towards a nucleus with charge $Q=120 \ e$, where $e$ is the electronic charge. It makes a closest approach of $10 \ fm$ to the nucleus. The de Brogle wavelength (in units of $fm$ ) of the proton at its start is :

(take the proton mass, $m _0=(5 / 3) \times 10^{-27} kg , h / e =4.2 \times 10^{-15} J / s / C ; \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 m / F ; 1 fm =10^{-15} m$ ) 

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number $Z$ of hydrogen like ion is

In Rutherford's experiment, number of particles scattered at $90^{\circ}$ angle are $x$ per second. Number particles scattered per second at angle $60^{\circ}$ is

What radioactive source did the Geiger and Marsden use in the scattering experiment?

In the spectrum of hydrogen atom, the ratio of the longest wavelength in Lyman series to thelongest wavelength in the Balmer series is