Question

The Bohr model of atoms
A: uses Einstein’s photoelectric equation
B: Predicts continuous emission spectra for atoms.
C: predicts the same emission spectra for all type of atoms
D: assumes that the angular momentum of an electron is quantised.

Answer 1

Hint:Bohr model was given by Niels Bohr and Ernest Rutherford in 1913. It explained that an atom is a system which has a dense , small and concentrated centre which is the nucleus and the electrons revolve around the nucleus. It is similar to a solar system.

Complete step by step answer:
In the Bohr’s model we have come across many facts which are very much useful in modern physics and quantum mechanics. Electrons revolve around the nucleus with definite velocities. The energy of the electron in a certain orbit is always constant. When an electron jumps from a particular orbit to a different orbit it emits spectral lines and releases energy. The orbits are known as stationary states or main energy states. The Bohr’s postulate states that the electrons revolve in discrete orbits. These postulates apply to jumps between different states characterised by discrete values of angular momentum and energy. In other words it assumes that the angular momentum of an electron is quantised. The main equations derived by these postulates are $mvr = \dfrac{{nh}}{{2\pi }}$ and $\dfrac{{kz{e^2}}}{{4\pi \varepsilon {r^2}}} = \dfrac{{m{v^2}}}{r}$
By the equation $mvr = \dfrac{{nh}}{{2\pi }}$ we can conclude the fact that the angular momentum of the electron is quantised.

Hence, option D is correct.

Additional Information:
by using the above two equations we can find the velocity, energy and radius of the orbits of an atom. $Radius = \dfrac{{{n^2}{h^2}}}{{4{\pi ^2}Kzm{e^2}}}$ , $velocity = \dfrac{{2\pi Kz{e^2}}}{{nh}}$ and $TotalEnergy = \dfrac{{ - 2{\pi ^2}{K^2}{z^2}m{e^4}}}{{{n^2}{h^2}}}$ , where $K = \dfrac{1}{{4\pi \varepsilon }}$ . The nucleus of an atom is made up of protons and neutrons. The electrons revolve around the nucleus due to the centripetal force acting on them from the protons.

Note:
The Bohr model is only applicable to the mono electron system. A system or an atom with more than one electron will not follow Bohr’s model. The radius of an orbit is inversely proportional to the atomic number.