Respuesta :
The wavelength of the radiation emitted by the star is 183 nm.
Explanation:
As per Wien's displacement law, the product of emitted wavelength and temperature of the star will be equal to 2.898 × 10⁻³ mK.
[tex]T*wavelength = 2.898 * 10^{-3}[/tex]
So if the wavelength of the emitted radiation by Sun is given as 550 nm, then the temperature of the Sun will be
[tex]Temperature of Sun = \frac{2.898*10^{-3} }{wavelength}[/tex]
[tex]Temperature of Sun = \frac{2.898*10^{-3} }{550 * 10^{-9} } = 5.27 * 10^{3} K[/tex]
Then if the temperature of star is said to be 3.5 times hotter than Sun, then the temperature of Star = 3.5×5.27×10³ = 15.81×10³ K.
With this temperature, the wavelength of the emitted radiation can be found as follows:
[tex]Wavelength = \frac{2.898 * 10^{-3} }{15.81 * 10^{3} } =183 nm[/tex]
So, the wavelength of the radiation emitted by the star is 183 nm.
The star will emit most of its radiation at a wavelength of [tex]157.14nm[/tex]
Wavelength of radiation :
The temperature is inversely proportional to wavelength.
Let us consider that temperature of sun is T.
Given that, the star is [tex]3.50[/tex] times hotter than our Sun.
- So that, Temperature of star [tex]T'=3.5T[/tex]
- Wavelength of sun [tex]\lambda=550nm[/tex]
[tex]\frac{T}{T'}=\frac{\lambda'}{\lambda} \\\\\frac{T}{3.5T}=\frac{\lambda'}{550} \\\\\lambda'=\frac{550}{3.5}=157.14nm[/tex]
The star will emit most of its radiation at a wavelength of [tex]157.14nm[/tex]
Learn more about the wavelength here:
https://brainly.com/question/26637292
