Question

part (a) which temperature most closely corresponds to a star whose spectrum peaks firmly in the violet region of the spectrum? 4100 k 3000 k 6000 k 4800 k 7300 k 8600 k

Explanation:

Step1: Recall Wien's displacement law

Wien's displacement law is $\lambda_{max}T = b$, where $\lambda_{max}$ is the wavelength at which the spectrum peaks, $T$ is the temperature of the black - body (in this case, the star), and $b = 2.898\times10^{-3}\ m\cdot K$. The wavelength of violet light is approximately $\lambda_{max}\approx 400\times10^{-9}\ m$.

Step2: Calculate the temperature

We can re - arrange Wien's displacement law to solve for $T$: $T=\frac{b}{\lambda_{max}}$. Substituting $b = 2.898\times10^{-3}\ m\cdot K$ and $\lambda_{max}=400\times10^{-9}\ m$ into the formula, we get $T=\frac{2.898\times10^{-3}}{400\times10^{-9}}\ K\approx7245\ K$.

Answer:

7300 K