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Black-body radiation and spectral classes questions
A star's colour is a thermometer and its spectrum is a fingerprint. Two short laws turn the shape of starlight into a temperature and a power output, and the missing wavelengths sort every star in the sky into seven lettered classes.
19 original questions · 57 marks · the black-body radiation and spectral classes notes · Astrophysics
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State Stefan's law and Wien's displacement law, defining each symbol and giving the unit of Wien's constant.
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Stefan: P = σAT4, with A the surface area and T the surface temperature in kelvin (1). Wien: λmaxT = 2.9 × 10−3 m K, the constant carrying the product unit metre kelvin (1).Write the spectral classes in order from hottest to coolest, and state the class of the Sun.
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O B A F G K M, hottest to coolest (1). The Sun, at about 5800 K, is a class G star (1).State the two assumptions made when a star's temperature, power and radius are deduced from its measured spectrum.
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The star radiates as a black body (1), and the light travels to the telescope without absorption on the way, by dust or by atmosphere (1).State what is meant by a black body.
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A body that absorbs all the electromagnetic radiation incident on it (1). It is therefore also the best possible emitter, radiating a spectrum that depends only on its temperature (1).State the colour of a class O star and of a class M star, and name the molecule prominent in class M absorption spectra.
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Class O stars are blue; class M stars are red (1). Class M spectra show molecular absorption by titanium oxide, TiO (1).A star's surface temperature rises. Describe two changes to its black-body radiation curve.
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The peak moves to a shorter wavelength (Wien's law) (1), and the curve rises at every wavelength, so the total power radiated (the area under the curve) increases (1).Calculate the peak wavelength of the radiation from a star with a surface temperature of 10 000 K, and state the region of the spectrum in which it lies.
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λmax = 2.9 × 10−3/10 000 (1)
λmax = 2.9 × 10−7 m (1)
In the ultraviolet, so the star looks blue-white (1)A star's spectrum peaks at 9.7 × 10−7 m. Calculate its surface temperature and suggest its spectral class.
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T = 2.9 × 10−3/(9.7 × 10−7) (1)
T = 2990 K (1)
Just below 3500 K, so a red class M star (1)A star has twice the Sun's radius (take the Sun's radius as 6.96 × 108 m) and a surface temperature of 9000 K. Calculate its power output.
Explain why the hydrogen Balmer absorption lines are strongest in class A stars, weaker in cooler stars, and weak again in the hottest stars.
A star's surface temperature triples while its radius stays the same. State the factor by which its power output increases.
Two stars have equal radii. One has its spectral peak at 400 nm, the other at 800 nm. Calculate the ratio of their power outputs.
A white dwarf of radius 7.0 × 106 m radiates a total power of 1.1 × 1024 W. Calculate its surface temperature. σ = 5.67 × 10−8 W m−2 K−4.
Calculate the power radiated by each square metre of the Sun's surface, taking the surface temperature as 5800 K and σ = 5.67 × 10−8 W m−2 K−4.
A red giant radiates 3.9 × 1028 W, one hundred times the Sun's output, from a surface at 3480 K. Calculate its radius, and express it in solar radii (Sun's radius 6.96 × 108 m).
Two stars have the same radius. Star X is class M and star Y is class A. Compare, with reasons, their colours and their power outputs.
A student says a star's colour tells you its temperature. State what measurement makes this precise, and the law that converts it.
An astronomer must decide which of two stars is the larger. Star J radiates 4.6 × 1026 W with its spectral peak at 690 nm; star K radiates 1.5 × 1027 W with its peak at 230 nm. Deduce which star has the larger radius. σ = 5.67 × 10−8 W m−2 K−4; Wien constant 2.9 × 10−3 m K.
Describe fully how astronomers determine the radius of a distant star from its spectrum and its measured brightness, naming each law used and stating the assumptions involved.
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