The gyromagnetic ratio and Bohr magneton are given respectively by | PGMN Solutions

The gyromagnetic ratio and Bohr magneton are given respectively by [Given : e= charge on electron, m= mass of electron, h= Planck's constant]
(A) e/(2" " m),eh/(4π" " m)
(B) eh/(4π" " m),e/(2" " m)
(C) (2" " m)/e,(4π" " m)/eh
(D) (4π" " m)/eh,(2" " m)/e



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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Magnetic Material
📌 Topic: Gyromagnetic Ratio & Bohr Magneton

🔹 Step 1: Understand what gyromagnetic ratio means
The gyromagnetic ratio represents how the magnetic moment of a particle relates to its angular momentum. It tells us how efficiently a moving charge (like an electron) creates a magnetic effect.

🔹 Step 2: Know the definition of Bohr magneton
The Bohr magneton is a constant value representing the smallest unit of magnetic moment that an electron can have due to its motion in an orbit. It depends on fundamental constants like the electron's charge and Planck’s constant.

🔹 Step 3: Apply conceptual knowledge

Gyromagnetic ratio is directly related to charge and mass of the electron.

Bohr magneton involves Planck's constant along with charge and mass.

These quantities are derived by analyzing the circular motion of an electron and how it creates a magnetic field.

🔹 Step 4: Match the correct pair based on concept
From the options:

The gyromagnetic ratio is correctly given as a simple ratio involving charge and mass.

The Bohr magneton includes Planck’s constant, showing it deals with quantization of magnetic moment.

✅ Final Answer: (A) e/(2m), eh/(4πm) 🚀

🔥 Pro Tip:
To remember easily:

If there’s no Planck’s constant → it's likely gyromagnetic ratio

If there is Planck’s constant → it's Bohr magneton


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