## Introductory Astronomy: Wien's Law

Wien's Law is an important formula that allows us to determine the temperature of a star. It is based on the fact that hotter objects have more energy than cooler objects and therefore emit more radiation at higher frequencies than at lower frequencies. Wien discovered that there was a direct relationship between the wavelength (or frequency) at which an object emits most of its energy and the temperature of that object. His law is shown above; in this form, wavelength must be measured in Angstroms (one Angstrom is 10^(-10) meters) and temperature in degrees Kelvin. We can understand the logic of Wien's law by looking at the following graphs: Notice that as the wavelength where the most energy is given off (maximum wavelength) goes from red to green to blue, the temperature increases. Now, we know that light with longer wavelengths has lower frequencies and therefore less energy than light with shorter wavelengths. Since the wavelength of red light is longer than green light (and green light is longer than blue), red light must have a lower frequency and less energy than green light (and green has less energy than blue). Therefore, we expect a star that emits mostly blue light to emit more energy (and thus be hotter) than a star that emits mostly red light (if they are the same size). We see from the graphs that our expectation is correct: the temperature for a star which emits most of its light at a maximum wavelength of 600 nanometers is 5000 K, the temperature for a star with a maximum wavelength at about 500 nanometers is 6000 K, and the temperature for a star with a maximum wavelength at 400 nanometers is about 7000 K. Hotter stars emit more energy per unit area than cooler stars.