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A star may have the spectrum of a blackbody.

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See Lecture 1, slides 19 & 20

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surface flux in J/s/m²/K⁴

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wavelength of peak intensity

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Blackbody temperature in K

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If a blackbody has a temperature of {t} K, at what wavelength (in nm) does its spectrum have its peak intensity? [[0]]

If a star radiates as a blackbody at this temperature of {t} K, what is the stellar surface flux radiated in W.m^-2? [[0]]

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A photometer is a telescope-mounted instrument that measures the photon count rate from a star. It counts the following rates for two stars.

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See Lecture 1, slides 11 & 12

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The magnitude of star A

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Star A causes a rate of {a} counts per second, star B a rate of {b} through the same filter. If star B is a star of apparent magnitude 12.5, what is the apparent magnitude of star A in that filter? [[0]]

If star B is at a distance of {d} parsecs, what is its absolute magnitude? [[0]]

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The Saha equation tells us the ratio of ions in one ionisation state to those in a different ionisation state.

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See Lecture 4, slides 10-13

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stellar temperature, in K

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Electron pressure in N/m^2

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ratio of H ionised

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What is the ratio of hydrogen that is ionised to that which is neutral if the electron pressure is {p} N.m^-2 and it is at a temperature of {temp} K? [[0]]

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Spectral lines have a natural width due to the uncertainty principle, but other broadening mechanisms often dominate.

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See Lecture 6, slides 10 to 16

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Doppler broadening FWHM in nm

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vel, km/s

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Hydrogen lines (Lyman - Pashen, alpha - delta)

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stellar temperature, in K

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line index

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line wavelength in nm

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What is the full width at half maximum in nm of the spectral line at {lambda} nm from a static pure neutral H gas at a temperature of {temp} K? [[0]]

If the gas is turbulent with a most probable velocity of {vel} km.s^-1, what is the FWHM in nm of this same spectral line? [[0]]

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It is possible to learn much about a star from its surface properties.

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See Lecture 5, slides 13 & 18

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radius of star in units of the radius of Jupiter

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stellar mass in solar units

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Log_10 stellar luminosity in solar units

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star mean density in units of density of water

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stellar temperature, in K

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A star has a surface temperature of {temp} K and a log_10 luminosity of {L} in solar luminosity units. Assuming it emits as a blackbody, what is its radius in units of the radius of the Sun (which is $6.96 \\times 10 ^8 $m)? [[0]]

The standard density of air (at sea level) is 1.225 kg.m^-3. If the star in part a of this question has a mass of {m_round} solar masses, what is its mean density in units of the standard density of air? [[0]]

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