The Bohr orbit radius for the hydrogen atom $(n = 1)$ is approximately $0.530 \ \mathring{A}$. The radius for the first excited state $(n = 2)$ orbit is ........... $\mathring{A}$

What is the energy of an electron in the stationary state corresponding to $n=2$?

If each hydrogen atom is excited by giving $8.4 \ eV$ of energy,then the number of spectral lines emitted is equal to :

Positronium consists of an electron and a positron (a particle which has the same mass as an electron,but opposite charge) orbiting round their common centre of mass. Calculate the value of the Rydberg constant for this system.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$:
Assertion $A$: In the photoelectric effect,the electrons are ejected from the metal surface as soon as the beam of light of frequency greater than threshold frequency strikes the surface.
Reason $R$: When the photon of any energy strikes an electron in the atom,transfer of energy from the photon to the electron takes place.
In the light of the above statements,choose the most appropriate answer from the options given below:

The frequency of a certain line of the Lyman series of the atomic spectrum of the $H$ atom satisfies the following conditions:
$(i)$ It is the sum of the frequency of another Lyman line and a Balmer line.
$(ii)$ It is the sum of the frequency of a certain line,a Lyman line,and a Paschen line.
$(iii)$ It is the sum of the frequency of a Lyman and a Paschen line but no Brackett line.
To what transition does this frequency correspond?