How is the temperature of stars determined by

Options

A. Planck's law
B. Wien's displacement law
C. Rayleigh - jeans law
D. Kirchhoff's law

Answer

To determine the temperature of stars, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Stellar Radiation**:
- Stars emit radiation across a spectrum of wavelengths. The intensity of this radiation varies with wavelength.

2. **Analyze the Energy Distribution**:
- By analyzing the radiation emitted by a star, we can obtain a graph of energy distribution over different wavelengths. This graph helps us identify the wavelength at which the radiation is most intense.

3. **Identify the Wavelength of Maximum Energy**:
- The wavelength corresponding to the maximum energy emitted by the star is crucial for determining its temperature. This is the peak of the energy distribution curve.

4. **Apply Wien's Displacement Law**:
- Wien's Displacement Law states that the wavelength of maximum emission (λ_max) is inversely proportional to the temperature (T) of the radiating body. The law can be mathematically expressed as:
\[ \lambda_{\text{max}} \cdot T = b \]
where \( b \) is Wien's constant (approximately \( 2.898 \times 10^{-3} \, \text{m K} \)).

5. **Calculate the Temperature**:
- Rearranging the formula gives us:
\[ T = \frac{b}{\lambda_{\text{max}}} \]
- By measuring the wavelength of maximum intensity from the star's radiation, we can calculate its temperature using the above formula.

6. **Conclusion**:
- Therefore, the temperature of stars is determined by analyzing their emitted radiation and applying Wien's Displacement Law.

### Final Answer:
The temperature of stars is determined by Wien's Displacement Law, which relates the wavelength of maximum emission to the temperature of the star.