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The quantum numbers $\large\frac{1}{2}$ and $-\large\frac{1}{2}$ for the electron spin represents :

$\begin{array}{1 1}(a)\;\text{Rotation of the electron in clockwise and anti clockwise direction respectively}\\(b)\;\text{Rotation of the electron in anti clockwise and clockwise direction respectively}\\(c)\;\text{Magnetic moment of the electron pointing up and down respectively}\\(d)\;\text{Two quantum mechanical states which have no classical analogue}\end{array}$

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Solution spin quantum number was derived in quantum mechanics.
Hence (d) is the correct answer.
answered Jan 15, 2014 by sreemathi.v

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