Question

a. What information is given by the spin quantum number? b. What are the possible values for this quantum number?

Short answer

a. It describes the intrinsic angular momentum (spin) of an electron. b. The possible values are +1/2 and -1/2.

Step-by-step solution

Identify the Spin Quantum Number

The spin quantum number is one of the four quantum numbers used to describe the state of an electron in an atom. It specifically describes the intrinsic angular momentum, or spin, of the electron.

Possible Values of Spin Quantum Number

The spin quantum number can take on one of two possible values. These values are +1/2 and -1/2. These values indicate the two possible orientations of the electron's spin, which can be thought of as 'spin-up' and 'spin-down'.

Key concepts

Quantum Numbers

Quantum numbers are essential values that describe the unique quantum state of an electron in an atom.
These numbers come in four types:

• Principal quantum number (n)
• Angular momentum quantum number (l)
• Magnetic quantum number (m_l)
• Spin quantum number (m_s)

Each number provides a different piece of information about the electron:

• The principal quantum number (n) indicates the electron's energy level.
• The angular momentum quantum number (l) describes the shape of the electron's orbital.
• The magnetic quantum number (m_l) reveals the orientation of the orbital in space.
• The spin quantum number (m_s) specifies the intrinsic angular momentum or 'spin' of the electron.

Understanding these four quantum numbers is crucial for comprehending the arrangement of electrons in atoms, which in turn influences an element’s chemical properties.

Electron Spin

Electron spin is a fundamental property of electrons.
It is represented by the spin quantum number (m_s).
The spin describes an electron's intrinsic form of angular momentum.
Here are key points about electron spin:

• Spin is quantized and can only take on certain discrete values.
• For electrons, these values are +1/2 and -1/2, often depicted as 'spin-up' and 'spin-down'.
• Electron spin is not an actual spinning motion, but a quantum property analogous to angular momentum.

Understanding electron spin helps in concepts like Pauli's exclusion principle, which states that no two electrons can have the same set of all four quantum numbers within a single atom.

Intrinsic Angular Momentum

Intrinsic angular momentum, commonly known as spin, is a distinct type of angular momentum found in quantum particles such as electrons.
Unlike classical angular momentum, intrinsic angular momentum:

• Is an inherent property of particles, not due to physical spinning.
• Quantum mechanically defined.

In formulas, intrinsic angular momentum for electrons is given by the spin quantum number (m_s).
When we say an electron has a spin of +1/2 or -1/2, we are referring to its intrinsic angular momentum.
This quantum property affects how electrons interact with magnetic fields and each other.
It also plays a crucial role in the structure of atoms and molecules through the Pauli exclusion principle and other quantum mechanical phenomena.