QJEEM24Ph760d: JEE Main 2024 Physics - Class 12 JEEM24Ph760d Solution: An electron revolving in n th  Bohr orbit has magnetic…

To determine the relationship between the magnetic moment and the principal quantum number $n$ , we need to understand the formula for the magnetic moment of an electron in a Bohr orbit.

The magnetic moment ( $\mu_n$ ) of an electron in the nth Bohr orbit is given by:

$${\mu }_n=\frac{n\cdot e}{2m}\cdot \frac{e\cdot Z\cdot h}{2\pi m}$$

Where:

• $e$ is the charge of the electron
• $m$ is the mass of the electron
• $Z$ is the atomic number (for a hydrogen atom, $Z = 1$ )
• $h$ is Planck's constant

Since the Bohr's magneton ( $\mu_B$ ) is defined as:

$${\mu }_B=\frac{e\hslash }{2m}$$

The magnetic moment for the nth orbit can be written as:

$${\mu }_n=n\cdot {\mu }_B$$

From the above formula, it is clear that the magnetic moment $\mu_n$ is directly proportional to the principal quantum number $n$ . Mathematically, this relationship can be expressed as:

$${\mu }_n\propto n^1$$

Therefore, the value of $x$ is 1.

Answer: Option D (1)