Question

Antares is a star with a temperature of roughly 3,000 kelvin. At what wavelength does Antares give off the most energy? Option a) Ultraviolet Option b) Infrared Option c) X-ray Option d) Visible light

Answer 1

Infrared.

Step-by-step explanation:

The peak wavelength of a star can be found from its surface temperature using Wien's displacement law:

`\displaystyle \lambda_\text{peak} = (b)/(T)`,

Where:

• 
  `\lambda_{\text{peak}}` is the wavelength where energy is maximized,
• 
  `b \approx 2.89778 * 10^(-3) \; {\rm m\cdot K}` is Wien's displacement constant, and
• 
  `T` is the surface temperature of this star.

Given that
`T = 3000\; {\rm K}`, apply this equation to find
`\lambda_{\text{peak}}`:

`\begin{aligned}\lambda_\text{peak} &= (b)/(T) \\ &= \frac{2.89778 * 10^(-3)\; {\rm m\cdot K}}{3000\; {\rm K}} \\ &\approx 9.659 * 10^(-7)\; {\rm m} \\ &\approx 965.9\; {\rm nm}\end{aligned}`.

The wavelength of visible light ranges between
`380\; {\rm nm}` and
`700\; {\rm nm}`. The peak wavelength
`965.9\; {\rm nm}` is not in the range of visible light, but in the range of infrared between
`700\; {\rm nm}` and
`1\; {\rm mm}`.