Question

The bright star Betelgeuse in the constellation Orion emits the greatest intensity of radiation at a wavelength of 808 nm. Calculate the surface temperature of the star.

Answer 1

Given :

Wavelength corresponding to greatest intensity of

radiation $\dpi{150} \bg_white \lambda$ _p = 808 nm = 808* 10^-9 m

Surface temperature T =?

Surface temperature can be calculated using 'Wein's displacement law' :

$\dpi{150} \bg_white \lambda$p* T = b

( where b = 2.898 * 10^{-3​​​​}​​​​​​ m- K , called as Wein's displacement constant and temperature in Kelvin)

$\dpi{150} \bg_white \lambda$_p T = 2.898* 10^-3

808* 10^-9 * T = 2.898 * ^{​​​​​​}10^-3

^{T = 3586.63 K}

Hence surface temperature of the star = T = 3586.63 K