Question

Spin of electron is: (a) Rotation of electron about it's own axis. (b) Clock wise and anticlock wise rotation of electron. (c) An intrinsic characteristics of electron connect with its magnetic field. (d) A quantum number which depend upon direction and speed of rotation of electron.

Short answer

The correct answer is option (c): An intrinsic characteristic of electron connected with its magnetic field.

Step-by-step solution

Understanding Spin

The spin of an electron is a fundamental property in quantum mechanics that describes a type of intrinsic angular momentum that electrons possess. Unlike orbital angular momentum, which is due to the electron's path around the nucleus, spin is an inherent characteristic independent of motion.

Analyzing Option (a)

Option (a) suggests that spin is the rotation of the electron about its own axis, similar to how a spinning top rotates. However, in quantum mechanics, electron spin does not involve actual physical rotation. It is not a classical concept of rotation but rather a quantum property.

Analyzing Option (b)

Option (b) implies spin involves clockwise and anticlockwise rotation of the electron. While spin is represented in terms of 'up' and 'down' (akin to two directions of rotation), these are quantum states, not literal rotations.

Analyzing Option (c)

Option (c) states that spin is an intrinsic characteristic of electrons connected with their magnetic field. This is true because electron spin generates a magnetic moment that interacts with external magnetic fields, contributing to its intrinsic magnetic properties.

Analyzing Option (d)

Option (d) suggests that spin is a quantum number depending on the direction and speed of electron rotation. Although spin is represented by the spin quantum number, it does not depend on speed or classical direction of rotation.

Conclusion

Based on the analyses, option (c), stating that electron spin is an intrinsic characteristic linked to its magnetic field, is the correct understanding of what electron spin signifies.

Key concepts

Quantum Mechanics

Quantum mechanics is a branch of physics that explores the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It provides the foundation for understanding complex phenomena that classical physics cannot explain. One of the most intriguing aspects of quantum mechanics is the concept of quantization. In this framework, many properties like energy, position, and momentum of particles come in discrete units, known as quanta. This is a pivotal shift from classical mechanics, where such quantities are continuous.

• Particles are viewed as both waves and particles, a concept known as wave-particle duality.
• The principle of superposition allows particles to exist in multiple states simultaneously until measurement.
• Heisenberg's Uncertainty Principle posits that certain pairs of properties, like position and momentum, cannot be measured with absolute precision.

Understanding these principles helps clarify why concepts like electron spin do not conform to classical physical intuition. Instead of visualizing an electron spinning like a top, quantum mechanics describes spin as an intrinsic property akin to charge or mass.

Magnetic Moment

The magnetic moment is a vector quantity that represents the magnetic strength and orientation of a magnetic object. For electrons, it is intimately connected to the phenomenon of spin. When an electron has a spin, it creates a magnetic moment, which essentially means it behaves like a tiny bar magnet that can align itself with an external magnetic field.
Through this behavior, electrons exhibit properties that are exploited in technologies like MRI machines and electron spin resonance spectroscopy.

• The magnetic moment due to spin is described by the equation: \( \mu = g \cdot \frac{e}{2m} \cdot S \), where \( \mu \) is the magnetic moment, \( g \) is the g-factor, \( e \) is the electron charge, \( m \) is the electron mass, and \( S \) is the spin angular momentum.
• This relationship shows how intrinsic properties lead to measurable magnetic effects.
• Magnetic moment is not only due to spin but also arises from the electron's motion around the nucleus, though spin contributes a significant part for electrons in many contexts.

Understanding the magnetic moment allows for deeper insights into how electron spins interact with external magnetic fields, a crucial aspect in atomic and molecular physics.

Spin Quantum Number

The spin quantum number is a vital identifier in the quantum realm, describing the intrinsic spin angular momentum of electrons. Unlike classical spin, it doesn't represent a real rotation, but rather an intrinsic attribute that defines how an electron behaves in quantum systems.

• The spin quantum number, denoted as \( s \), can take on values of \( +\frac{1}{2} \) or \( -\frac{1}{2} \). These are often termed "spin-up" and "spin-down" states.
• This quantum number plays a critical role in the Pauli Exclusion Principle, which states that no two electrons in an atom can have identical quantum numbers. Therefore, the spin quantum number is essential for determining electron configurations and chemical properties.
• The physical implications of the spin quantum number are profound, affecting everything from the stability of atomic structures to the magnetic properties of materials.

By conceptualizing the spin quantum number, scientists can predict and explain behaviors that are crucial in technologies like quantum computing and magnetic storage.