Hydrogen atoms can be ionized by light with a wavelength of 9.12 × 10^-8 m or shorter. What approximate temperature would a star need in order to have the PEAK of its spectrum at this wavelength?

Question

Quizplus · Accepted Answer

To find the temperature that corresponds to the peak of the spectrum at a given wavelength, we can use Wien's displacement law, which states that the product of the peak wavelength (in meters) and the temperature (in Kelvin) is a constant, approximately $2.898 \times 10^{-3}$ m·K. Rearranging this to solve for temperature (T), we get $T = \frac{2.898 \times 10^{-3}}{\lambda}$, where $\lambda$ is the wavelength in meters. Plugging in the given wavelength of $9.12 \times 10^{-8}$ meters, we find that the temperature is approximately 32,000 K.

Hydrogen Atoms Can Be Ionized by Light with a Wavelength