Magnitude of the intrinsic (internal) spin angular momentum
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College Physics I – Introduction
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.
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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.
For an electron, which has a spin quantum number $s=\frac{1}{2}$, the magnitude is $\sqrt{3/4}\hbar = \frac{\sqrt{3}}{2}\hbar$.
Intrinsic spin angular momentum is distinct from orbital angular momentum, which arises from a particle's motion in space.
The concept of intrinsic spin was first introduced by physicists George Uhlenbeck and Samuel Goudsmit in 1925.
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
What formula is used to calculate the magnitude of an electron's intrinsic spin angular momentum?
How does intrinsic spin differ from orbital angular momentum?
Who introduced the concept of intrinsic spin and when?
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.
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