Question

The surface temperature of our sun is 5800 K, and the peak of its intensity curve is in the middle of the visible spectrum. A star that appears violet in color could have a surface temperature of:

Answer 1

The value is
`T_2 = 7975 \ K`

Step-by-step explanation:

From the question we are told that

The surface temperature of sun is
`T_1 = 5800 \ K`

Generally the wavelength that fall in the middle of the visible spectrum is

`\lambda_1 = 550 nm = 550*10^(-9) \ m`

This means that the peak of the intensity curve of our sun is at a wavelength
`\lambda_1 = 550 nm = 550*10^(-9) \ m`

Generally wavelength of violent in the visible spectrum is
`\lambda_2 = 400 nm = 400 *10^(-9) \ m`

This means that the peak of the intensity curve of the star that appears violet is at a wavelength
`\lambda_2 = 400 nm = 400 *10^(-9) \ m`

Generally wavelength varies inversely with, which can be mathematically represented at

`T \ \ \alpha \ \ (1)/(\lambda)`

=>
`T = k * (1)/(\lambda)`

=>
`T \lambda = k`

=>
`T_1 \lambda _1 = T_2 \lambda _2`

=>
`(T_1)/(T_2) = (\lambda_2)/( \lambda _1)`

=>
`(5800)/(T_2) = (400 *10^(-9))/( 550 *10^(-9))`

=>
`T_2 = 7975 \ K`