// Numbas version: exam_results_page_options {"name": "PA2601 exam version 2", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], []], "questions": [{"name": "Blackbody v2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julian Osborne", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1416/"}, {"name": "Martin Barstow", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5191/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

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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The Bohr model of an atom is a simplified view in which the quantised orbital angular momentum of an electron causes electrons of different energies to orbit at different radii.

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See Lecture 2, slides 13 to 25

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part a: initial quantum state

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part b: initial quantum state

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part a: photon energy in eV

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part a: final quantum state

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series name of initial state

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part b: final quantum state

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set of line names

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part b: change in quantum number

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part b

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Line name associated with change in state

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If an electron in a hydrogen atom makes a transition from principle quantum number {n1} to number {n2}, what is the energy of the photon emitted in eV? [[0]]

What are the principle quantum numbers of the initial and final states in a {series} {line} photon absorption transition? [[0]] [[1]]

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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 line-of-sight velocity of a light source affects the observed wavelengths of the photons; this is the Doppler effect.

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See Lecture 2, slide 13

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photon energy in eV

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initial quantum state

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emitted photon wavelength, nm

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final quantum state

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Observed wavelength of photon, nm

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star's recessional velocity, km/s

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energy to 3 decimal places

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If the atoms in the surface of a star are making a quantum state change and thus are absorbing photons of energy {energy_3dp} eV, and the star is moving away from us at a speed of {v} km.s^-1,what would be the observed wavelength (in nm) of the spectral line due to these transitions? [[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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A gas in thermal equilibrium will have a Maxwell-Boltzmann distribution of velocities.

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See Lecture 3, slides 18 to 21.

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RMS particle velocity in km/s

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element list

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part b: mean velocity

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Element

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mass of nucleus in 10^-27 kg

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part b: lower velocity limit, km/s

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fraction of atoms between v1 & v2

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part b: temperature of the cloud of H, in K

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part b: upper velocity limit in km/s

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Numbers of neutrons for each element_no

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Number of neutrons

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gas temperature in K

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If the atoms in a pure {element} neutral gas have a root-mean-squared velocity of {vel} km.s^-1, taking account of the number of protons, neutrons and electrons (and ignoring the effect of nuclear binding energy); what is the temperature of the gas in kelvin? [[0]]

A cloud of neutral H has a temperature of {t_cloud} K, what fraction of the atoms in the cloud have velocities between {v1} and {v2} km.s^-1? [[0]]

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The Boltzmann equation gives the ratio of the number atoms in one state of excitation to the number in another.

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See Lecture 3, slides 22-26

part b: temperature of the cloud of H, in K

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number of atoms in 1st excited state

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number of atoms in ground state x 10^-7

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If a cloud of neutral H atoms are mostly in the ground state, what temperature is the cloud is there are {n} atoms in the first excited state for every {m}x10⁷ in the ground state? [[0]]

Hint: work in units of eV, where k = 8.62x10^-5 eV.K^-1

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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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The main sequence is a region of the Hertzsprung-Russell diagram occupied by stars that are burning hydrogen in their core.

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See Lecture 5, slide 23

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Luminosity (solar units)

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stellar mass index number

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stellar mass in solar units

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list of masses (solar units)

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set of luminosities

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If a star has a mass {m} solar masses when it joins the main sequence, what is it's luminosity in solar units when it leaves the main sequence? [[0]]

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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