Question

The angular momentum of an electron depends on:
a.) principal quantum number
b.) azimuthal quantum number
c.) magnetic quantum number
d.) all of the above

Answer 1

Hint: Angular momentum of an electron was given by Bohr. This is the result of applying quantum theory to the orbit of the electron. The solution of the Schrodinger equation yields the angular momentum quantum number.

Complete step by step solution: According to Bohr’s atomic model, the angular momentum of electron orbiting around the nucleus is quantized, which can be given by

\[mvr=\dfrac{nh}{2\pi }\]

where, m = mass of the electron
      n = integer 1,2,3,4……
      V = velocity
 h = Planck’s constant
 R = radius
He also added that electrons move only in those orbits where angular momentum of an electron is an integral multiple of h/2. His postulate regarding the quantization of angular momentum of an electron was later explained by deBroglie.
Now, Orbital angular momentum is the component of angular momentum. It is the value of angular momentum of the electron revolving around the orbit and the fact that the electron is spinning around its own axis is neglected i.e. the spin is constant.
Orbital angular momentum is given as \[L=\sqrt{l(l+1)\hbar }\], where l is azimuthal quantum number.
The azimuthal quantum number (l) is the quantum number associated with the angular momentum of an atomic electron. It is also known as the angular momentum quantum number or the second quantum number.

So, from the above statements we can conclude that the angular momentum of the electrons depends on the azimuthal quantum number, thus, the correct option is (a).

Note: \[\dfrac{nh}{2\pi }\] gives angular momentum of an electron revolving in a circular orbit, for example an electron is present in the 5th orbit. However orbital angular momentum of electrons in a given orbital, for example an electron is present in d orbital.