The ratio of the velocity of an electron in the second orbit of $He^{+}$ to the third orbit of $B^{4+}$ is:

The radius (in $\mathring{A}$) of the $3^{rd}$ Bohr orbit in $Li^{2+}$ ion is closest to $......$ [Given: Atomic number of $Li = 3$]

In a mixture of $H$ and $He^{+}$ gases,all $H$ atoms and $He^{+}$ ions are excited to their first excited states. Subsequently,on de-excitation in $H$ atoms,energy is transferred to the excited $He^{+}$ ion. The quantum number $n$ of the $He^{+}$ ion after the energy is transferred is:

In a photoelectric effect experiment, the kinetic energy of an emitted electron is $1.986 \times 10^{-19} \ J$, when a radiation of frequency $1.0 \times 10^{15} \ s^{-1}$ hits the metal. What is the threshold frequency of the metal (in $s^{-1}$)? (Planck's constant $= 6.62 \times 10^{-34} \ J \ s$)

Angular momentum of an electron in the $n^{th}$ orbit of a hydrogen atom is given by

Which of the following was $NOT$ proposed by Rutherford in his atomic model?