The wavelength of a particle having an Einstein energy of $1.995 \times 10^{12} \ erg \ mol^{-1} \ photon^{-1}$ is .......... $\mathring{A}$.

What is the ratio of the time period of revolution of an electron in the second orbit of a hydrogen atom to that in the third orbit of a $He^{+}$ ion?

The wave number of the first Lyman transition in $H$ atom spectrum is equal to the wave number of the second Balmer transition in the spectrum of

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 $h = 6.625 \times 10^{-34} \ Js$)

The energy of an electron in an excited hydrogen atom is $-3.4 \, eV$. According to Bohr's theory,the angular momentum of this electron in $J \cdot s$ is:

$(i)$ The energy associated with the first orbit in the hydrogen atom is $-2.18 \times 10^{-18} \, J \, atom^{-1}$. What is the energy associated with the fifth orbit?
$(ii)$ Calculate the radius of Bohr's fifth orbit for the hydrogen atom.