Question

Use Wien’s Law to calculate the peak wavelength of Betelgeuse, based on the temperature found in Question #8. Note: 1 nanometer (nm) = .0000001 centimeters (cm) 208nm 400nm 828nm 1800nm

Answer 1

The peak wavelength of Betelgeuse is 828 nm

Explanation:

The relationship between surface temperature and peak wavelength of a star is given by Wien's displacement law:

$\lambda=\frac{b}{T}$

where

$\lambda$ is the peak wavelength

T is the surface temperature

$b=2.898\cdot 10^{-3} m\cdot K$ is Wien's constant

For Betelgeuse, the surface temperature is approximately

T = 3500 K

Therefore, its peak wavelength is:

$\lambda=\frac{2.898\cdot 10^{-3}}{3500}=8.28\cdot 10^{-7} m = 828 nm$

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