The orbital angular momentum for an electron revolving in an...

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

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Key Concepts

Orbital Angular Momentum Quantum Number

The orbital quantum number, denoted by l, determines the magnitude of the orbital angular momentum and is related to the electron’s orbital shape. For each electron orbital, l can take any integer value from 0 up to n-1, where n is the principal quantum number. The quantum number directly affects the angular momentum and the spatial distribution or shape of the electron cloud.

Atomic Orbitals (s-orbitals)

s-orbitals are characterized by an orbital quantum number of l = 0. Because of this, the orbital angular momentum for an electron in an s-orbital is given by L = ?(0(0+1)) ? = 0, meaning that electrons in s-orbitals have zero orbital angular momentum. This distinguishes s-electrons from electrons in higher angular momentum orbitals such as p, d, or f orbitals.

Quantization of Angular Momentum

In quantum mechanics, the angular momentum of an electron in an atom is quantized, meaning it can only take on specific discrete values. This concept is typically expressed through the formula L = ?(l(l+1)) ?, where l is the orbital quantum number and ? is the reduced Planck's constant. This formulation reflects the intrinsic quantum nature of angular momentum, as opposed to a continuous classical value.

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