Question

Who gave the quantum model of a hydrogen atom?
(A) S.N. Bose
(B) Niels Bohr
(C) James Clerk Maxwell
(D) R.A. Millikan

Answer 1

The Bohr Theory of the atom was explained using the structure of the hydrogen atom. He obtained four postulates for this model, each clearing up the orbit of an electron, energy of an electron, energy absorbed/emitted during electronic transitions, and the angular momentum of an electron respectively.

Formula used:
$v = \dfrac{{\Delta E}}{h} = \dfrac{{{E_2} - {E_1}}}{h}$
Where $v$ is the frequency of radiation, $h$ is the Planck’s constant, ${E_1}$ and ${E_2}$ are the energies of the lower and higher allowed energy states respectively.

Complete answer:
Bohr used the structure of the hydrogen atom to explain what he thought could be the structure of all atoms.
His first postulate described what an orbit of an electron is. It is as follows:
-The electron in the hydrogen atom can travel around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states, or permitted energy states. These orbits are set concentrically around the nucleus.
In the next postulate, he references the energy of the electron in its orbit, and about transitions between different orbits.
-The energy of an electron in the orbit does not vary with time. While the electron can move from a lower stationary state to a higher stationary state if an essential amount of energy is absorbed by the electron or energy can be released when the electron moves from a higher stationary state to a lower stationary state. This energy variation does not continuously take place.
The third postulate is one of the most important, as it gives us the relation between the frequency of emitted/absorbed radiations during the transition and talks about the energy difference between two orbits.
-The frequency of radiation absorbed or emitted when the transition occurs between two stationary states that vary in energy by $\Delta E$ is given by:
$v = \dfrac{{\Delta E}}{h} = \dfrac{{{E_2} - {E_1}}}{h}$
Where $v$ is the frequency of radiation, $h$ is the Planck’s constant, ${E_1}$ and ${E_2}$ are the energies of the lower and higher allowed energy states respectively.
-The last postulate measures the angular momentum of an electron. That is, he provided a mathematical expression for the momentum of an electron in each orbit.
-An electron can move only in those orbits for which its angular momentum is an integral multiple of $\dfrac{h}{{2\pi }}$ , and that is why only certain fixed orbits are allowed. Expressed as an equation, we get:
${m_e}vr = n\dfrac{h}{{2\pi }}$ ,
Where $n = 1,2,3............$
${m_e}$ is the mass of an electron, $v$ is the velocity of the electron, $r$ is the radius of the orbit, and $h$ is Planck’s constant.
Hence the correct answer is option (B) Niels Bohr.

Note:
Although the Bohr model of the atom could explain the stability and line spectra of the hydrogen atom and another hydrogen-like species, it was unable to explain the spectrum of other elements. Also, it failed to explain the splitting of spectral lines in the presence of magnetic fields,