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

Answer:

The value  is   $T_2 = 7975 \ K$

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

             $T \ \ \alpha \ \ \frac{1}{\lambda}$

=>          $T = k * \frac{1}{\lambda}$

=>          $T \lambda = k$

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

=>       $\frac{T_1}{T_2} = \frac{\lambda_2}{ \lambda _1}$

=>     $\frac{5800}{T_2} = \frac{400 *10^{-9}}{ 550 *10^{-9}}$

=>     $T_2 = 7975 \ K$