The ratio of the radius of the first orbit in hydrogen to the radius of the first orbit in deuterium is .......

The energy associated with the electron in the first orbit of a hydrogen atom is $-2.18 \times 10^{-18} \ J$. The frequency of the light required (in $Hz$) to excite the electron to the fifth orbit is $(h = 6.6 \times 10^{-34} \ Js)$

State whether the following statements are true or false:
$(i)$ The $Bohr$ model cannot explain how atoms form molecules.
$(ii)$ The $Bohr$ model is accepted as the planetary model.
$(iii)$ Electrons in an atom do not absorb or emit energy while moving in a stationary orbit.
$(iv)$ The spectral lines of the $Brackett$ series are found in the ultraviolet region.

What is the work function of the metal if the light of wavelength $4000 \, \mathring{A}$ generates photoelectrons of velocity $6 \times 10^5 \, ms^{-1}$ from it? ............. $eV$ (Mass of electron $= 9 \times 10^{-31} \, kg$; Velocity of light $= 3 \times 10^8 \, ms^{-1}$; Planck's constant $= 6.626 \times 10^{-34} \, Js$; Charge of electron $= 1.6 \times 10^{-19} \, C \, eV^{-1}$)

The shortest wavelength of $He^{+}$ ion in Balmer series is $x$. Then,the longest wavelength in the Paschen series of $Li^{2+}$ is:

The energy required for the ionization of an excited hydrogen atom would be (in $eV$)-