Here's how to determine the surface temperature of Antares using its peak wavelength:

Wien's Displacement Law

Wien's Displacement Law relates the peak wavelength of radiation emitted by a blackbody (like a star) to its temperature. The law is:

* λ_max * T = b

Where:

* λ_max is the peak wavelength (in meters)

* T is the temperature (in Kelvin)

* b is Wien's displacement constant (approximately 2.898 x 10^-3 m·K)

Calculations

1. Convert wavelength to meters:

700 nm = 700 x 10^-9 m

2. Rearrange the formula to solve for temperature:

T = b / λ_max

3. Plug in the values:

T = (2.898 x 10^-3 m·K) / (700 x 10^-9 m)

4. Calculate the temperature:

T ≈ 4140 K

Therefore, the surface temperature of Antares is approximately 4140 Kelvin.