The gyromagnetic ratio of an electron in sodium atom is

Options

A. depending upon the atomic number of the atom
B. depending upon the shell number of the atom
C. independent of that orbit it is in
D. having positive value

Explanation

To find the gyromagnetic ratio of an electron in a sodium atom, we can follow these steps:

### Step 1: Understand the Gyromagnetic Ratio
The gyromagnetic ratio (γ) is defined as the ratio of the magnetic moment (μ) to the angular momentum (L) of a particle. The formula for the gyromagnetic ratio is given by:

\[ \gamma = \frac{\mu}{L} \]

### Step 2: Express Magnetic Moment and Angular Momentum
For an electron, the magnetic moment (μ) can be expressed as:

\[ \mu = \frac{N e h}{4 \pi m} \]

where:
- \(N\) is the number of electrons,
- \(e\) is the charge of the electron,
- \(h\) is Planck's constant,
- \(m\) is the mass of the electron.

The angular momentum (L) of an electron in an orbit is given by:

\[ L = \frac{N h}{2 \pi} \]

### Step 3: Substitute into the Gyromagnetic Ratio Formula
Substituting the expressions for magnetic moment and angular momentum into the gyromagnetic ratio formula gives:

\[ \gamma = \frac{\frac{N e h}{4 \pi m}}{\frac{N h}{2 \pi}} = \frac{e}{2m} \]

### Step 4: Analyze the Result
The result shows that the gyromagnetic ratio is:

\[ \gamma = \frac{e}{2m} \]

This indicates that the gyromagnetic ratio is constant and does not depend on the orbit of the electron.

### Step 5: Conclusion
Since the charge of the electron is negative, the gyromagnetic ratio is typically considered to have a negative value. Therefore, the statement that the gyromagnetic ratio of an electron in a sodium atom is independent of the orbit and has a negative value is true.

### Final Answer
The correct statement about the gyromagnetic ratio of an electron in a sodium atom is that it is independent of the orbit and has a negative value.

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