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"Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. Even if the electron radius were as large as 14 nm (classical electron radius) then it would have to be rotating at 2.3×10^11 m/s. The speed of rotation would be in excess of the speed of light, 2.998×10^8 m/s, and is thus impossible.[2] Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon."

This quote implies a calculation to relate the radius and speed, what is the formula that is used in this calculation to get the rotation speed? TIA