In an atom, two electrons move around the nucleus in circular orbits of radii $R$ and $4R.$ The ratio of the time taken by them to complete one revolution is : (neglect electric interaction)

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

What is the atomic number of gold ? 

In a Rutherford scattering experiment when a projectile of charge $z_1$ and mass $M_1$ approaches a target nucleus of charge $z_2$ and mass $M_2$, the distance of closest approach is $r_0$ The energy of the projectile is 

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4$. Then the number of spectral lines in the emission spectra will be

The energy of hydrogen atom in $n^{th}$ orbit is $E_n$, then the energy in $n^{th}$ orbit of singly ionised helium atom will be