The frequency of radiation emitted when the electron falls from $n = 4$ to $n = 1$ in a hydrogen atom will be (Given ionization energy of $H = 2.18 \times 10^{-18} \ J \ atom^{-1}$ and $h = 6.625 \times 10^{-34} \ Js$)

What is the energy in joules,required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state?
The ground state electron energy is $-2.18 \times 10^{-11} \ erg$.

Calculate the wavelength for the emission transition if it starts from the orbit having radius $1.3225 \, nm$ and ends at $211.6 \, pm$. Name the series to which this transition belongs and the region of the spectrum.

For the Balmer series in the spectrum of $H$ atom,$\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$,the correct statements among $(I)$ to $(IV)$ are:
$(I)$ As wavelength decreases,the lines in the series converge.
$(II)$ The integer $n_{1}$ is equal to $2$.
$(III)$ The lines of longest wavelength corresponds to $n_{2}=3$.
$(IV)$ The ionization energy of hydrogen can be calculated from wave number of these lines.

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 energy of a photon of wavelength $(\lambda) = 1 \, m$ is (Planck's constant $= 6.626 \times 10^{-34} \, J \, s$,speed of light $= 3 \times 10^8 \, ms^{-1}$)