How fast is spinning an electron ?

Question

...having mass at rest and volume too..

Answer 1

Electrons are considered point particles, that is
elcetrons do not have internal structure.
Mathematically it means that the state of electron
is fully described by its wave function which depends
only on its 3D coordinate r, and spin s: ψ(r,s).


However we can estimate 'equatorial speed' of
electron and its angualar velocity by making
some wild assumptions.

Let's assume that electron is rigid 'conductive'
ball of radius R. Its capacitance is then C = k/R, and
energy of electron carrying charge e is
E = 1/2 Ce² = ke²/2R.

Furthermore, lets assume that _all rest mass of electron
is associated with its elecrostatic energy:
mc² = E = ke²/2R
R = ke²/2mc² = 1.4e-19 m

Momentum of inertia of such ball would be
I = 2/5mR² = 1/10 1/m (ke²/c²)² ,and its angular
momentum is
L = Iω = 1/10 ω/m (ke²/c²)² which is known
to be equal to spin x hbar = hbar/2

1/10 ω/m (ke²/c²)² = hbar/2
ω = 5 hbar m (c²/ke²)² = 4.5 e+26 1/s

Equatorial speed is accordingly
v = ωr = 5/2 c (hbar c/ke²) = 5/2 1/α c,
where dimansionless α = (ke²/hbar c) = 1/37 is known as
constant of fine structure.

Finally
v = 5/2 1/α c = 2.5 x 137 c = 340 c,
which means that the assumptions stated above
cannot be true.

Answer 2

Electrons don't obey Newtonian physics, and so cannot 'spin', even although one quantum characteristic of electrons is defined as spin.