Question

suppose you observed three stars and obtained the following spectra, shown below. arrange the spectra in order of surface temperature, from hottest to coolest. grade summary deductions 0% potential 100% submissions attempt(s) remaining: 999 2% deduction per attempt detailed view hints: 0% deduction per hint. hints remaining: 1 feedback: 0% deduction per feedback.

Explanation:

Step1: Recall Wien's displacement law

According to Wien's displacement law, $\lambda_{max}T = b$, where $\lambda_{max}$ is the wavelength at which the intensity of the radiation is maximum, $T$ is the temperature of the black - body (stars can be approximated as black - bodies), and $b$ is Wien's displacement constant. A higher temperature corresponds to a shorter $\lambda_{max}$.

Step2: Identify $\lambda_{max}$ for each spectrum

For the first spectrum, $\lambda_{max}\approx1500$ nm. For the second spectrum, $\lambda_{max}\approx500$ nm. For the third spectrum, $\lambda_{max}\approx1000$ nm.

Step3: Order stars by temperature

Since $T=\frac{b}{\lambda_{max}}$, the star with the shortest $\lambda_{max}$ has the highest temperature. So the order from hottest to coolest is: the spectrum with $\lambda_{max}\approx500$ nm, the spectrum with $\lambda_{max}\approx1000$ nm, the spectrum with $\lambda_{max}\approx1500$ nm.

Answer:

The spectrum with the shortest $\lambda_{max}$ (around 500 nm), the spectrum with $\lambda_{max}$ around 1000 nm, the spectrum with $\lambda_{max}$ around 1500 nm.