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Answer the following. (a) What is the surface temperature of Betelgeuse, a red giant star in the constellation of Orion, which radiates with a peak wavelength of about 970 nm? K (b) Rigel, a bluish-white star in Orion, radiates with a peak wavelength of 145 nm. Find the temperature of Rigel's surface. K

Sagot :

hamzaahmeds

Answer:

(a) T = 2987.6 k

(b) T = 19986.2 k

Explanation:

The temperature of a star in terms of peak wavelength can be given by Wein's Displacement Law, which is as follows:

[tex]T = \frac{0.2898\ x\ 10^{-2}\ m.k}{\lambda_{max}}[/tex]

where,

T = Radiated surface temperature

[tex]\lambda_{max}[/tex] = peak wavelength

(a)

here,

[tex]\lambda_{max}[/tex] = 970 nm = 9.7 x 10⁻⁷ m

Therefore,

[tex]T = \frac{0.2898\ x\ 10^{-2}\ m.k}{9.7\ x\ 10^{-7}\ m}[/tex]

T = 2987.6 k

(b)

here,

[tex]\lambda_{max}[/tex] = 145 nm = 1.45 x 10⁻⁷ m

Therefore,

[tex]T = \frac{0.2898\ x\ 10^{-2}\ m.k}{1.45\ x\ 10^{-7}\ m}[/tex]

T = 19986.2 k

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