physics-dual

Do electron spin like a ball? you have heard that electron have spin and magnitude of that spin is $\dfrac{1}{2}$. well it's actually $\dfrac{1}{2}\hbar$ we just take $\hbar = 1$  and we all know that $\hbar$ is reduced plank constant. but is electron really spinning like ball and having angular momentum of $\dfrac{1}{2}\hbar$ ? hmmm... what is velocity of the electron then? let's try to calculate that , let's assume electron is solid sphere and it's radius is $r_e = 2.81×10^{-15}$ meters. (check this https://en.m.wikipedia.org/wiki/Classical_electron_radius) from high-school physics you can calculate moment of inertia of the solid sphere. and it's turn out to be $I = \dfrac{2}{5}mr^2$. and angular velocity $\omega = \dfrac{v}{r}$  so we have all the equipment. now we know that angular momentum $L = I\omega$  also $L = \dfrac{1}{2}\hbar$  so we have $I\omega = \dfrac{1}{2}\hbar$ putting Value of $I$ and $\omega$ $\dfrac{2}{5}mr^{2}\dfrac{v}{r} = \dfrac{1}{2}\hba...