# What is the difference between angular momentum of electron by Bohr and orbital angular momentum?

Orbital angular momentum of an electron is $$\hbar \sqrt{\ell(\ell+1)}$$ where $$\ell$$ is angular quantum number.

Angular momentum of an electron by Bohr is given by $$mvr$$ or $$\frac{nh}{2\pi}$$ (where $$v$$ is the velocity, $$n$$ is the orbit in which electron is, $$m$$ is mass of the electron, and $$r$$ is the radius of the $$n$$'th orbit).

In quantum mechanics, The eigenvalues of the total angular momentum operator $$(L^2$$) and angular momentum operator ($$L_z$$) look like $$L^2|lm\rangle =l(l+1)\hbar^2|lm\rangle$$ $$L_z|lm\rangle =m\hbar |lm\rangle$$

The second equation can be recognized as Bohr's condition, that the angular momentum is an integer multiple of ħ was later reinterpreted by de Broglie as a standing wave condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit: $$n\lambda=2\pi r$$ $$\Rightarrow l=n\hbar$$

• Though correct this answer isn't accessible to most introductory students on this material. – shai horowitz Feb 17 at 8:55