Calculate the energy in joule corresponding to light of wavelength $45 \ nm$. (Planck's constant,$h = 6.63 \times 10^{-34} \ J \ s$,speed of light,$c = 3 \times 10^8 \ m \ s^{-1}$)

Find the wavelength of the third line in the Brackett series of the hydrogen spectrum.

Find the wavelength in the Lyman series for $n_2 = 3$ and $n_1 = 1$.

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:

Which of the following is the radius of the first orbit of $He^{+}$ (in $pm$)?

If the energy of a photon is $14 \, eV$ and it interacts with a hydrogen atom,which of the following is correct?