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.