Question

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

Explanation:

Step1: Recall Wien's displacement law

Wien's displacement law is $\lambda_{max}T = 2.898\times10^{-3}\text{ m}\cdot\text{K}$, where $\lambda_{max}$ is the wavelength at which the spectrum peaks and $T$ is the temperature of the black - body (a good approximation for stars). Red light has a relatively long wavelength, around $\lambda_{max}\approx 650\times10^{-9}\text{ m}$.

Step2: Calculate the temperature

We can re - arrange Wien's displacement law to $T=\frac{2.898\times10^{-3}\text{ m}\cdot\text{K}}{\lambda_{max}}$. Substituting $\lambda_{max} = 650\times10^{-9}\text{ m}$ into the formula, we get $T=\frac{2.898\times10^{-3}\text{ m}\cdot\text{K}}{650\times10^{-9}\text{ m}}\approx4460\text{ K}$.

Step3: Select the closest value

Among the given values $8600\text{ K},4800\text{ K},7300\text{ K},4100\text{ K},6000\text{ K},3000\text{ K}$, the value closest to $4460\text{ K}$ is $4100\text{ K}$.

Answer:

$4100\text{ K}$