We will see that the quantum numbers discussed in this section are valid for a broad range of particles and other systems, such as nuclei. Some quantum numbers, such as intrinsic spin, are related to fundamental classifications of subatomic particles, and they obey laws that will give us further insight into the substructure of matter and its interactions.
Phet explorations: stern-gerlach experiment
The classic Stern-Gerlach Experiment shows that atoms have a property called spin. Spin is a kind of intrinsic angular momentum, which has no classical counterpart. When the z-component of the spin is measured, one always gets one of two values: spin up or spin down.
Section summary
Quantum numbers are used to express the allowed values of quantized entities. The principal quantum number
labels the basic states of a system and is given by
The magnitude of angular momentum is given by
where
is the angular momentum quantum number. The direction of angular momentum is quantized, in that its component along an axis defined by a magnetic field, called the
-axis is given by
where
is the
-component of the angular momentum and
is the angular momentum projection quantum number. Similarly, the electron’s intrinsic spin angular momentum
is given by
is defined to be the spin quantum number. Finally, the direction of the electron’s spin along the
-axis is given by
where
is the
-component of spin angular momentum and
is the spin projection quantum number. Spin projection
is referred to as spin up, whereas
is called spin down.
[link] summarizes the atomic quantum numbers and their allowed values.
(a) What is the magnitude of the angular momentum for an
electron? (b) Calculate the magnitude of the electron’s spin angular momentum. (c) What is the ratio of these angular momenta?
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