The orbital angular momentum for an electron re volving in...

The orbital angular momentum for an electron re volving in an orbit is given by $\sqrt{\ell} /(l+1) \mathrm{h} / 2 \pi$. This momentum for an s electron will be given by
(a) $+1 / 2 . \mathrm{h} / 2 \pi$
(b) zero
(c) $h / 2 \pi$
(d) $\sqrt{2} \cdot \mathrm{h} / 2 \pi$

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Key Concepts

Orbital Angular Momentum in Quantum Mechanics

Orbital angular momentum in quantum mechanics is quantized and is determined by the azimuthal quantum number, l. It is typically expressed using the formula involving the reduced Planck constant, where the angular momentum takes discrete values, and each value corresponds to a particular orbital characteristic of the electron in an atom.

Azimuthal Quantum Number (l)

The azimuthal quantum number, l, defines the orbital shape and directly influences the magnitude of the orbital angular momentum. It takes integer values starting from 0, with specific formulas relating it to the quantized angular momentum of the electron.

s Orbital

An s orbital is characterized by an azimuthal quantum number l equal to zero. Because the orbital angular momentum is proportional to l (or functions of l), an electron in an s orbital effectively has zero orbital angular momentum, highlighting a special case in the quantization of angular momentum.

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