Embibe Experts Solutions for Chapter: Atoms, Exercise 1: Uttar Pradesh Board-2020

In an electron current, the velocity of electron is $2.0\times {10}^7 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$. Electron is deflected by $3.4 \mathrm{mm}$ in moving $10 \mathrm{cm}$ perpendicular direction to electrostatic field of $1.6\times {10}^3 \raisebox{1ex}{$\mathrm{volt}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.$. Calculate $\raisebox{1ex}{$\mathrm{e}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.$ of the electron.

The wavelength of the first line of Lyman series of hydrogen atom is equal to the wavelength of the second line of Balmer series of $\mathrm{n}$ hydrogen like atom $\mathrm{X}$. Find out energies of the ground state and second excited state of $\mathrm{X}$. Also find the ionisation potential of the atom $\mathrm{X}$. given Energy of hydrogen atom in ground state$=-13.6 \mathrm{eV}$.

Write the Bohr's postulates for the hydrogen atom. Derive the formula for the orbital frequency of electron moving in the ${\mathrm{n}}^{\mathrm{th}}$ orbit of hydrogen atom, using Bohr's postulates.