In a multi-electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields?

(i) $\mathrm{n}=1, \mathrm{l}=0, \mathrm{m}=0$

(ii) $\mathrm{n}=2, \mathrm{l}=0, \mathrm{m}=0$

(iii) $\mathrm{n}=2, \mathrm{l}=1, \mathrm{m}=1$

(iv) $\mathrm{n}=3, \mathrm{l}=2, \mathrm{m}=1$

(v) $\mathrm{n}=3, \mathrm{l}=2, \mathrm{m}=0$

The electrons identified by the quantum numbers $\mathrm{n}$ and $\mathrm{l}$

($\mathrm{i}$) $\mathrm{n}=4, \mathrm{l}=1$

($\mathrm{ii}$) $\mathrm{n}=4, \mathrm{l}=0$

($\mathrm{iii}$) $\mathrm{n}=3, \mathrm{l}=2$

($\mathrm{iv}$) $\mathrm{n}=3, \mathrm{l}=1$ can be placed in the order of increasing energy from the lowest to highest as

The paramagnetic character follows the order

The five $\mathrm{d}-$orbitals are designated as ${\mathrm{d}}_{\mathrm{xy}}, {\mathrm{d}}_{\mathrm{yz}}, {\mathrm{d}}_{\mathrm{xz}}, {\mathrm{d}}_{{\mathrm{x}}^2-{\mathrm{y}}^2}$ and ${\mathrm{d}}_{{\mathrm{z}}^2}$. Choose the correct statement.

When an electron of charge $\text{'}\mathrm{e}\text{'}$ and mass $\text{'}\mathrm{m}\text{'}$ moves with a velocity $\text{'}\mathrm{v}\text{'}$ towards the nuclear charge $\text{'}\mathrm{Ze}\text{'}$ in a circular orbit of radius $\text{'}\mathrm{r}\text{'}$. The potential energy of the electron is given by

A certain metal when irradiated by light $\left(\mathrm{\nu }=3.2\times {10}^{16} \mathrm{Hz}\right)$ emits photoelectrons with twice kinetic energy as did photoelectrons when the same metal is irradiated by light $\left(\mathrm{\nu }=2.0\times {10}^{16} \mathrm{Hz}\right)$. The ${\mathrm{\nu }}_0$ of metal is

The frequency of radiation emitted when electron falls from $\mathrm{n}=4$ to $\mathrm{n}=1$ in a hydrogen atom will be

(Given: Ionization energy of $\mathrm{H}=2.18\times {10}^{-18} \mathrm{J} {\mathrm{atom}}^{-1}$ and $\mathrm{h}=6.625\times {10}^{-34} \mathrm{J} \mathrm{s}$)