Question

Question 3 2 pts From the previous question about the star Alnilam, how does the temperature of this star compare to the surface temperature of the Sun? The star Alnilam is hotter. The temperatures are the same. The star Alnilam is colder

Answer 1

Answer: The star Alnilam is hotter

Explanation:

The question seems to be the continuation of another question, which is written below:

Use Wien's law to calculate the surface temperature of the star Alnilam in Kelvin. The peak wavelength $\lambda_{p}$ of the star is $0.116 \mu m$

So, by using Wien's displacement law, which relates the wavelength  $\lambda_{p}$ where the intensity of the radiation is maximum with the temperature $T$ of the black body, and expresed as:

$\lambda_{p}.T=C$    (1)

Where:

$T$ is in Kelvin (K)

$\lambda_{p}=0.116 \mu m=0.116 (10)^{-6} m$ is the wavelength of the emission peak in meters (m).

$C=0.0028976 mK$ is the Wien constant

We can find Alnilam's temperature and then compare it with the Sun's temperature ($T_{Sun}=5778 K$):

$T_{Alnilam}=\frac{C}{\lambda_{p}}$    (2)

$T_{Alnilam}=\frac{0.0028976 mK}{0.116 (10)^{-6} m}$    (3)

$T_{Alnilam}=24979.310 K$    (4)

As we can see $T_{Alnilam} > T_{Sun}$, hence:

The star Alnilam is hotter