Final answer:
Using Wien's Law, the peak wavelength of a star with a temperature of 7,945 K is calculated to be 365 nanometers, which is in the ultraviolet region and indicates that the star is hotter than our Sun and appears blue.
Step-by-step explanation:
To determine the peak wavelength of a star with a temperature of 7,945 K, we use Wien's Law, which states that the blackbody radiation curve for an object of a constant temperature will peak at a wavelength inversely proportional to the temperature. Wien's Law is mathematically expressed as λmax = b / T, where λmax is the peak wavelength in meters, T is the temperature in kelvins, and b is a constant of proportionality known as Wien's displacement constant, approximately equal to 2.897 x 10⁻³ m*K.
Using this formula, we calculate the peak wavelength of the star:
λmax = (2.897 x 10⁻³ m*K) / 7,945 K = 0.365 x 10⁻⁶ meters or 365 nanometers (nm).
This peak wavelength is in the ultraviolet region of the electromagnetic spectrum, indicating that the star is much hotter than our Sun and appears blue.