Question

The angular momentum of electron of Hydrogen atom in ground state is:
A. $\dfrac{h}{\pi }$
B. $\dfrac{h}{2\pi }$
C. $\dfrac{2h}{\pi }$
D. $\dfrac{3h}{2\pi }$

Answer 1

Hint: We will mention the three postulates given by Niels Bohr in 1913 which combined the concepts of classical physics and early concepts of quantum mechanics to predict the nature of motion of electrons in mono-electronic atom species. Then we will use these postulates to find the angular momentum of the electron in the ground state inside the Hydrogen atom.

Complete answer:
Let us first give the three postulates given by Niels Bohr.

A.)The first postulates states that electrons can move in certain special orbits around the nucleus without emitting and electromagnetic radiation as is done by charged particles under acceleration. These are called the energy states of the atom and they all have a definite total energy.

B.)The second postulates states that for these definite orbits in which the electron revolves, the angular momentum of the electron must be an integral multiple of $\dfrac{h}{2\pi }$. Where h is the Planck’s constant. This means that the angular momentum of electrons in atom is quantized

C.)The third postulate states that an electron can go from one of its specified orbits to another orbit of lower energy. When this happens, a photon is emitted which has energy equal to the energy difference between the initial and final states.

The first orbit is called the ground state and according to the second postulate the angular momentum must be single multiple of $\dfrac{h}{2\pi }$.Hence, the correct option is $\dfrac{h}{2\pi }$.

So, the correct answer is “Option B”.

Note:
One must take care when using these postulates, they only provide a very basic insight on the motion and nature of electrons inside the atom, the reality as explained by modern quantum physics is very different. Also, these are only valid for atoms which have only one electron. Even the interactions between two electrons require a very high level of understanding of quantum mechanics.