If the sunlight from a star peaks at a wavelength of $0.55 \mu \mathrm { m }$, what temperature does this imply for the surface of that star? The constant in Wien's law is $0.00290 \mathrm {~m} \cdot \mathrm { K }$.
A) $9500 \mathrm {~K}$
B) $25,000 \mathrm {~K}$
C) $5300 \mathrm {~K}$
D) $15,000 \mathrm {~K}$
E) $2500 \mathrm {~K}$

Question

Quizplus · Accepted Answer

Wien's law is given by $\lambda_{\text{max}} T = b$, where $\lambda_{\text{max}}$ is the peak wavelength, $T$ is the temperature in Kelvin, and $b$ is Wien's displacement constant ($0.00290 \, \text{m} \cdot \text{K}$). Rearranging for $T$, we get $T = \frac{b}{\lambda_{\text{max}}}$. Substituting $\lambda_{\text{max}} = 0.55 \times 10^{-6} \, \text{m}$ and $b = 0.00290 \, \text{m} \cdot \text{K}$, we find $T = \frac{0.00290}{0.55 \times 10^{-6}} = 5272.73 \, \text{K}$, which rounds to $5300 \, \text{K}$.

If the Sunlight from a Star Peaks at a Wavelength 0.55μm0.55 \mu \mathrm { m }0.55μm

If the Sunlight from a Star Peaks at a Wavelength $0.55 \mu \mathrm { m }$