Embibe Experts Solutions for Chapter: Atomic Physics, Exercise 3: Exercise - 3

If the mass of the particle is $m=1.0 \times {10}^{–30} \mathrm{kg}$ and $a=6.6 \mathrm{nm}$, the energy of the particle in its ground state is closest to:

A diatomic molecule has moment of inertia $I$. By Bohr’s quantization condition its rotational energy in the nth level ($n=0$ is not allowed) is :

It is found that the excitation frequency from ground to the first excited state of rotation for the $\mathrm{CO}$ molecule is close to $\frac{4}{\mathrm{\pi }}\times {10}^{11} \mathrm{Hz}$. Then the moment of inertia of $\mathrm{CO}$ molecule about its centre of mass is close to (Take $\mathrm{h} = 2\mathrm{\pi } \times {10}^{–34} \mathrm{J} \mathrm{s}$)

Hydrogen ${(}^1{\mathrm{H}}_1),$ Deuterium ${(}^1{\mathrm{H}}_2),$ singly ionised Helium ${(}_2{\mathrm{He}}^4{)}^{+}$ and doubly ionised lithium ${(}_3{\mathrm{Li}}^6{)}^{++}$ all have one electron around the nucleus. Consider an electron transition from $\mathrm{n} = 2 \text{to} \mathrm{n} = 1\text{.}$ If the wavelengths of emitted radiation are ${\mathrm{\lambda }}_1, {\mathrm{\lambda }}_2, {\mathrm{\lambda }}_3, \mathrm{and} {\mathrm{\lambda }}_4$ respectively then approximately which one of the following is correct?

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $\mathrm{r} = \frac{{\mathrm{\lambda }}_1}{{\mathrm{\lambda }}_2},$is given by :

If the series limit frequency of the Lyman series is ${\nu }_L\text{,}$ then the series limit frequency of the Pfund series is:

An electron from various excited states of hydrogen atom emits radiation to come to the ground state. Let ${\mathrm{\lambda }}_{\mathrm{n}}, {\mathrm{\lambda }}_{\mathrm{g}}$ be the de-Broglie wavelength of the electron in the $n^{\mathrm{th}}$ state and the ground state respectively. Let ${\wedge }_{\mathrm{n}}$ be the wavelength of the emitted photon in transition from the $n^{\mathrm{th}}$ state to the ground state. For large $n,$$(\mathrm{A}, \mathrm{B} \mathrm{are} \mathrm{constants})$