If a T star has a surface temperature of 1460 K, at what wavelength will it be brightest?
 
The star is brightest at a wavelength of  *λ*max =  nm.

To determine the wavelength at which the T star is brightest, we can use **Wien's Displacement Law**. This law states that the wavelength of peak emission \(\lambda_{\text{max}}\) is inversely proportional to the surface temperature of the star. Mathematically, it is expressed as:

\[
\lambda_{\text{max}} = \frac{b}{T}
\]

where:

- \(\lambda_{\text{max}}\) is the peak wavelength in meters,
- \(T\) is the surface temperature of the star in Kelvin (K),
- \(b\) is Wien's constant, approximately \(2.898 \times 10^{-3}\) meters Kelvin (m·K).

### Given:
- \(T = 1460 \, \text{K}\)

Now, using Wien's constant:

\[
\lambda_{\text{max}} = \frac{2.898 \times 10^{-3} \, \text{m·K}}{1460 \, \text{K}} 
\]

\[
\lambda_{\text{max}} \approx 1.984 \times 10^{-6} \, \text{m} = 1984 \, \text{nm}
\]

So, the star is brightest at a wavelength of approximately **1984 nm**.

### Would you like more details or further clarification?

Here are some questions that expand on the topic:

1. What is Wien's law used for in astrophysics?
2. How does the surface temperature of a star affect its color?
3. Can Wien's Law be used for all types of stars?
4. What is the relationship between wavelength and frequency for electromagnetic waves?
5. How does Wien's constant relate to Planck's law?

**Tip:** As temperature increases, the peak wavelength shifts towards shorter (bluer) wavelengths.

If a T star has a surface temperature of 1460 K, at what wavelength will it be brightest?

Learn how to calculate the peak wavelength for a star with a surface temperature of 1460 K using Wien's Displacement Law. This step-by-step guide covers essential astrophysics and thermodynamic concepts and is suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation