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The spin magnetic moment of an electron, based on the Bohr magneton, is a central concept in Quantum Physics, particularly in quantum mechanics and atomic physics. It describes the magnetic moment associated with the intrinsic 'spin' of the electron, giving rise to a magnetic dipole moment with a particular value measured in Bohr magnetons. This tutorial breaks down the formula, its creators, its real-life applications, key contributors, and interesting facts about this fundamental concept.

Spin Magnetic Moment = |

The formula for the spin magnetic moment (µ) of an electron based on the Bohr magneton (µ_{B}) is:

μ = g × µ_{B}

Where:

**μ**: Spin magnetic moment of an electron.**g**: The electron spin g-factor, which is approximately 2 for an electron.**µ**: The Bohr magneton, a physical constant named after Niels Bohr. Its value is approximately 5.788 × 10_{B}^{-5}eV/T (electron-volt per tesla).

The spin magnetic moment was first introduced by George Uhlenbeck and Samuel Goudsmit in 1925. The Bohr magneton was introduced by Niels Bohr in 1913. The concept of the electron spin magnetic moment plays a pivotal role not only in quantum physics but also in fields like condensed matter physics, particularly in the study of materials with magnetic properties, and in the design of electronic devices and sensors that work based on magnetic fields.

In real life, the spin magnetic moment and the Bohr magneton find application in magnetic resonance imaging (MRI). An MRI scanner works by creating a strong magnetic field which causes the magnetic moments of the electrons in the body to align with the field. When this field is altered, the magnetic moments of the electrons precess to realign with the new field, emitting a radio signal in the process. This signal is used to construct an image of the body.

Niels Bohr, George Uhlenbeck, and Samuel Goudsmit are key individuals associated with the spin magnetic moment of an electron. Bohr, a Danish physicist, introduced the concept of the Bohr magneton. Uhlenbeck and Goudsmit, Dutch-American and Dutch physicists respectively, first proposed the concept of electron spin. These ideas have revolutionized our understanding of quantum physics.

- The Bohr magneton is used as the basic unit for expressing electron magnetic moment. Its value is derived from fundamental constants, including the electron charge and Planck's constant.
- The discovery of electron spin led to a more accurate explanation of the Zeeman effect, the phenomenon of splitting a spectral line into several components in the presence of a static magnetic field.
- Quantum computing, a new and powerful form of computing, utilizes electron spin in quantum bits or qubits. This technology could potentially revolutionize how we process information in the future.

Understanding the spin magnetic moment of an electron and the Bohr magneton is fundamental to quantum physics and has wide-reaching implications. From MRI scanners to the potential of quantum computing, the impacts of these concepts on science and technology are vast and enduring.

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