Magnitude of the intrinsic (internal) spin angular momentum

Definition

Magnitude of the intrinsic (internal) spin angular momentum is a fundamental property of particles, such as electrons, indicating the magnitude of their internal spin. It quantifies the amount of angular momentum arising from the particle's intrinsic spin characteristics.

5 Must Know Facts For Your Next Test

1. The magnitude of an electron's intrinsic spin angular momentum is given by $\sqrt{s(s+1)}\hbar$, where $s$ is the spin quantum number.
2. For an electron, which has a spin quantum number $s=\frac{1}{2}$, the magnitude is $\sqrt{3/4}\hbar = \frac{\sqrt{3}}{2}\hbar$.
3. Intrinsic spin angular momentum is distinct from orbital angular momentum, which arises from a particle's motion in space.
4. The concept of intrinsic spin was first introduced by physicists George Uhlenbeck and Samuel Goudsmit in 1925.
5. Spin quantum numbers can be half-integers (e.g., $\pm \frac{1}{2}$) or integers (e.g., $0$, $1$), depending on the type of particle.

Review Questions

Related terms

Spin Quantum Number:

A quantum number that describes the intrinsic angular momentum (spin) of a particle.

Orbital Angular Momentum: Angular momentum due to a particle's motion through space, described by quantum numbers $l$ and $m_l$.

$\hbar$: $\hbar$, known as reduced Planck's constant, is equal to Planck's constant divided by $2\pi$. It often appears in quantum mechanics equations.