Suppose the visible surface of a star has a temperature of 5,478 K. Determine th

Question

Suppose the visible surface of a star has a temperature of 5,478 K. Determine the wavelength in nm at which the star's blackbody radiation has a peak intensity, nm The position of an electron is determined to within 2.35 nm. What is the minimum uncertainty in the electron's speed? m/s 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

Explanation / Answer

1) T=5478 K

Lambdapeak*T=2.898x10^-3m*k

Solving for lambdapeak....lambdapeak=2.898x10^-3m*k/5478K

wavelength lambda = 529.025 nm

2) Uncertainty in velocity can be calculated according to the fllowing expression v=h/4*pi*m*lambda; where h=Plank's constant=6.625×10^-34 J · s. and m=electron mass 9.11 x 10-31 kg

lambda=2.35x10^-9m

therefore v=(6.625×10^-34 kg*m^2/s) /9.11 x 10-31 kg*2.35x10^-9m*4*pi=2.463x10^3 m/s

3) Lambdapeak*T=2.898x10^-3m*k

T=2.898x10^-3m*k/970x10^-9m=2987.63K for Betelgeuse and

T=2.898x10^-3m*k/145x10^-9m=19986.21 K for Rigel

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