Other / Mixed: Atoms & Bohr Links

The gyromagnetic ratio and Bohr magneton are given respectively by [Given $e =$ charge on electron, $m =$ mass of electron, $h =$ Planck's constant]

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $10.2\text{ V}$. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc $= 1245\text{ eV nm},\ e = 1.6 \times 10^{-19}\text{ C}$).

An atom absorbs a photon of wavelength $500\text{ nm}$ and emits another photon of wavelength $600\text{ nm}$. The net energy absorbed by the atom in this process is $n \times 10^{-4}\text{ eV}$. The value of n is __________. [Assume the atom to be stationary during the absorption and emission process] (Take $h = 6.6 \times 10^{-34}\text{ Js}$ and $c = 3 \times 10^{8}\text{ m/s}$)

The wave number of the last line of the Balmer series in the hydrogen spectrum will be $($ Rydberg's cons $\text{tant}, R = \frac{10^{7}}{\text{m}})$

A free electron of 2.6 eV energy collides with a H+ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 $\times$ 10$-$34 Js)

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000$\text{\AA}$. What is the maximum kinetic energy of the emitted photoelectron?

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be:

In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to:

Formation of covalent bonds in compounds exhibits

The $21\text{ cm}$ radio wave emitted by hydrogen in interstellar space is due to the interaction called the hyperfine interaction in atomic hydrogen. The energy of the emitted wave is nearly

An electron with (rest mass $m_0$) moves with a speed of $0.8\,c$. Its mass when it moves with this speed is