Bohr Magneton is unit of: 

Explanation:

Bohr Magneton:

Definition: The Bohr Magneton (denoted by μ_B) is a physical constant that represents the natural unit for expressing the magnetic moment of an electron due to its orbital or spin angular momentum. It is named after the Danish physicist Niels Bohr and is a fundamental parameter in quantum mechanics and atomic physics.

The formula for the Bohr Magneton is:

μ_B = (eħ) / (2m_e)

Where:

• e: Elementary charge (1.602 × 10^-19 C)
• ħ: Reduced Planck's constant (1.055 × 10^-34 J·s)
• m_e: Mass of an electron (9.109 × 10^-31 kg)

In SI units, the Bohr Magneton has the value:

μ_B = 9.274 × 10^-24 J/T

Physical Interpretation: The Bohr Magneton is the quantum of magnetic moment associated with the intrinsic spin or orbital angular momentum of an electron. It plays a crucial role in determining the magnetic properties of atoms and molecules, as well as in the study of phenomena such as electron spin resonance and atomic magnetic dipole moments.

Correct Option Analysis:

The correct option is:

Option 2: Permanent dipole moment due to spin

This is the correct answer because the Bohr Magneton represents the magnetic dipole moment of an electron due to its spin or orbital angular momentum. This quantum mechanical property arises from the intrinsic spin of the electron and its orbital motion around the nucleus. The Bohr Magneton quantifies the strength of this magnetic moment, making it a fundamental unit in atomic and quantum physics.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Magnetic energy

This option is incorrect because the Bohr Magneton is not a unit of magnetic energy. While it is related to the magnetic properties of electrons, it quantifies the magnetic moment rather than energy. Magnetic energy, on the other hand, depends on the interaction of magnetic moments with external magnetic fields and is expressed in terms of joules (J).

Option 3: Polarisability

This option is incorrect because polarisability refers to the tendency of an atom or molecule to become polarized (i.e., to have its electron cloud distorted) in response to an external electric field. It is a measure of electric dipole moment and has no direct relation to the Bohr Magneton, which deals with magnetic moments.

Option 4: Hysteresis

This option is incorrect because hysteresis refers to the lag between the magnetization of a material and the applied magnetic field, typically observed in ferromagnetic materials. The Bohr Magneton is not a measure of hysteresis but rather a fundamental unit of magnetic moment at the quantum level.

Conclusion:

The Bohr Magneton (μ_B) is a fundamental physical constant that quantifies the magnetic dipole moment of an electron due to its spin or orbital angular momentum. It is an essential concept in quantum mechanics and atomic physics, providing a natural unit for describing the magnetic properties of subatomic particles. Among the given options, only "Permanent dipole moment due to spin" correctly identifies the property described by the Bohr Magneton. The other options pertain to different physical phenomena and are unrelated to the concept of the Bohr Magneton.