M5, C4 Astrophysics and Cosmology Flashcards
the solar system astronomical distances stellar evolution stellar radiation and luminosity stellar spectra the big bang theory the evolution of the universe
what is a diffraction grating
an optical component with regularly spaced slits or lines that diffract and split light into beams of different colour, travelling in different directions
these beams can determine the wavelengths of spectral lines in the lab or from starlight
why is diffraction grating better than young’s slits
each line diffracts like a slit so produces a clearer and brighter interference pattern
what does the diffraction grating pattern depend on
path difference and phase difference of the waves from all the slits
in the equation dsinθ = nλ
what do they all mean
d is the grating spacing
θ is the angle from the incident light (normal)
λ is the wavelength of light used
n is the order of maxima eg. when n = 0 it is central maximum or n=1 is first order maxima
how do you work out diffraction grating
1 / number of lines per metre
what is the equation for the largest possible order number (n)
at the largest order, the angle can be 90
so dsin90 = nλ
sin90 = 1
d = n_max X λ
when working out the order of maxima what do you do if your answer is a decimal
ALWAYS ROUND DOWN
so if n = 5.7 the maximum order would be 5
how many maxima would you see if n = 4
9
because there is the central maxima and 4 more either side
what is the diffraction grating if it has 3000 lines per centimetre
1 / 3000 = 3.33 X 10^-4 cm
X 10^-2 to convert to metres
= 3.33 X 10^-6 m
what is the splitting of white light called
dispersion
when white light is diffracted what is observed at the central maximum
white light
then from them you get a 1st order spectrum then 2nd order and so on
when white light is diffracted and spectrums form wither side the the central maxima, what colour appears closest to the centre
violet is closer to the centre
red is furthest away
why do spectrums appear when white light is diffracted
different colours have different wavelengths so a greater value of sinθ so a greater angle
red light has the longest wavelength in the spectrum so appears at the greatest angle
what happens when white light is diffracted
zero order will be white
the other orders are split into spectra with violet nearest the zero order and red furthest away
in an atom, each level is given a number, what is n = 1
the ground state which is the lowest energy level
what happens to electrons when energy is transferred or a photon is absorbed to the substance
electrons move to higher energy levels
how do electrons move down energy levels
by emitting a photon
what does the difference between 2 energy levels in an atom equal
the energy carried by each photon emitted
an electron in the ground state of a hydrogen atom (-13.6eV) absorbs a photon and is excited to a higher enrgy level with an energy of -0.850eV. Calculate the frequency of the absorbed photon.
The electron emits a photon, and drops from the the -0.850eV energy level to an energy level with energy -3.40eV. Calculate the wavelength of the photon emitted in this transition.
E = -0.850–13.6 = 12.75 eV = 2.04 X 10^-18 J
f = E / h
=2.04 X 10^-18 / 6.63 X 10^-34 = 3.08 X 10^15 Hz
E = -0.850–3.40 = 2.55eV = 4.08 X 10^-19 J
wavelength = hc / E
=6.63X10^-34 X 3X10^8 / 4.08 X 10^-19
= 4.88 X 10^-7 m
define galaxy
clusters of stars and planets that are held together by gravity
(we are in the milky way)
define solar system
consists of a star and all the objects that orbit it
our star is the sun
define planets
large objects which orbit a star
their gravity is strong enough to have pulled in any nearby objects apart from their satellites
define dwarf planets
planet-like objects that orbit stars
too small to meet all the rules of being a planet
define planetary satellites
objects that orbit a planet
eg. moons or artificial satellites
define asteroids
chunks of rock and mineral that orbit the sun
range from 1m in diameter all the way to a dwarf planet
the asteroid belt is a disc of many asteroids that all sit in orbits between Mars and Jupiter
define comets
made of ice, dust and rock
most orbit the sun 1000X further away than Pluto
occasionally one dislodges and heads for the sun
their orbits are highly elliptical
define one astronomical unit
what is the value of 1AU?
the mean distance between the earth and the sun
1 AU = 1.5 X 10^11 m (or 150 million km)
what is the angle of parallax
if you observe the position of a star from opposite sides of earth’s orbit (6months apart), the angle of parallax is half the angle that the star appears to move in relation to the background stars.
if the angle of parallax was bigger what does that mean?
the object is nearer to you
how do you calculate the distance from earth to a star
tan(angle of parallax) = radius of earth’s orbit (1AU) / distance of the star
so
distance of the star = radius of earth’s orbit / tan(angle of parallax)
how would you use small angle approximation for
d = r / tan(angle of parallax)
ONLY WORKING IN RADIANS
you can say tan(θ) = θ
so
d = r / θ
the angle in radians = angle in degrees X π/180
define one parsec
a star is one parsec away if the angle of parallax = 1 arcsecond = (1/3600)°
what does this equation mean?
p = 1 / d
angle of parallax in arcseconds = 1 / distance to the star in parsecs
A star has an angle of parallax of 0.77 arcseconds. Calculate the distance to the star in parsecs
d = 1 / p
= 1 / 0.77
= 1.3 pc
define light year
the distance that light travels in free space in one year
what is one arcsecond in degrees
(1/3600)°
A star is 20pc away.
Calculate this distance light years
1pc = 3.1X10^16m (in equation sheet)
20 pc = 3.1X10^16 X 10 = 62X10^16
1ly = 9.5 X 10^15m (in equation sheet)
so 20 pc = 62X10^16 / 9.5 X10^15
= 70ly
how are protostars formed
Large clouds of gas and dust contract and collapse under the force of gravity (star birth)
The clumps become more dense and heat up
What happens to protostars to form a main sequence star
1) temp increases - hydrogen nuclei fuse, forming helium (star shines)
2) temp increases - volume decreases (contracting) - gas pressure increases
3) enormous amount of EM radiation released by fusion - radiation pressure
4) gas pressure and radiation pressure are counteracted by the force of gravity
5) forces balanced - star stable
what happens to the main sequence star for it to become a red giant?
core hydrogen burning - pressure from hydrogen fusion balance gravitational force
eventually hydrogen runs out, fusion stops, core collapses under gravity. The core heats up as it contracts, outer layers expand and cool
what is solar mass
the mass of the sun
1.99 X 10^30 kg
What happens to the red giant
Shell hydrogen burning
- material surrounding the core containing hydrogen heats up, hydrogen fuses
- star expands, layers cool, gives the red glow
what happens to higher mass stars after the main sequence star? (3stages)
red super giant is formed
Shell hydrogen burning
- material surrounding the core containing hydrogen heats up, hydrogen fuses
- star expands, layers cool, gives the red glow
Core helium burning
-core continues to contract, temp and density increase: helium fuses forming oxygen and carbon
-outer layers pushed out further as energy is released
Shell helium burning
-helium in core runs out, core contracts further, heating the surrounding shell - helium fuses in shell
what happens after the red giant
most layers drift off as planetary nebula (become another star/solar system)
the core is dense and hot and is called the white dwarf
what happens during the white dwarf stage of the star cycle when it is below the Chandrasekhar limit
- no fusion, emits photons, surface temp = 30000K
- Electron degeneracy pressure - the electrons resist being squashed together so the pressure opposing the core collapses
- stars with mass up to 1.4 solar masses have enough electron degeneracy pressure to counteract gravity
- eventually the white dwarf will cool down and fade away
what is Chandrasekhar limit
the maximum mass for which electron degeneracy pressure can counteract gravitational force
what happens during the white dwarf stage of the star cycle when it is above the Chandrasekhar limit
electron degeneracy pressure can’t stop the core contracting
the core of the star continues to contract while outer layers of the star fall in and rebound off the core, setting up huge shockwaves
the shockwaves cause the star to explode in a supernova leaving the core which is either the neutron star or, if big enough, a black hole
what happens to neutron stars
- as the core of massive star contracts, electrons get squashed onto the atomic nuclei and combine with protons to form neutrons and neutrinos
- if the core is between 1.4-3 solar masses, the core suddenly collapses to become a neutron star and the outer layers create another supernova
- neutrons stars are incredibly dense but very small (20km diameter)
- the stars emit 2 beams of radio waves as they rotate, also called pulsars which we can sometimes detect
how are black holes formed
If the core of the star is more than 3 solar masses then the core will contract until neutrons are formed, but the gravitational force on the core is greater.
The neutrons can’t withstand this gravitational force so the star continues to collapse and there is nothing the stop it collapsing to an infinitely dense point - a singularity.
At this point the laws of physics break down.
what is escape velocity
The velocity an object would need to travel at to have enough kinetic energy to escape a gravitational field.
At a singularity there is such a strong gravitational field that the escape velocity is greater than the speed of light, hence why light can’t escape a black hole.
what is the event horizon
the boundary of the escape velocity
at the event horizon the escape velocity is equal the speed of light so light has just enough kinetic energy to escape the black hole’s gravitational pull
the event horizon is considered as the boundary of the black hole
sketch the Hertzsprung-Russell diagram showing stellar evolution
what do the x and y axis represent
look it up
x axis: temperature (hot->cold)
y axis: luminosity (relative to sun)
What does it mean when it says electrons can only exist in one of a discrete set of energies called energy levels?
An electron can’t have a quantity of energy between 2 levels.
Energy levels are negative - indicates that electrons are trapped within the atom, bound to positive nucleus - shows external energy is required to remove electron from the atom.
An electron with 0 energy is free from the atom.
Energy level with most negative value is ground level (n=1)
do energy levels have positive or negative values
negative
what is happening in atom shells when an electron is being excited
Electron moves from a lower level to a higher level (eg, n=1 to n=2)
Requires external energy e.g. electric field, heating or photons of specific frequency are absorbed.
Energy required= difference between levels
what is happening in atom shells when an electron is being de-excited
Electron moves from higher energy level to a lower one (eg. n=3 to n=2), emitting a photon, with particular energy= difference between the two levels
what is emission line spectra
Produced when excited elements of gas drop to lower energy levels, emitting photons of specific discrete frequencies, unique to that gas.
Produces a coloured line corresponding to photon’s wavelength
Each element produces a unique line spectra due to its unique energy levels.
what is continuous spectra
All visible frequencies or wavelengths are present
The atoms of a heated solid metal e.g. lamp filament produce this spectrum
what is absorption line spectra
Occurs when light of continuous spectrum of energy (white light) passes through a cool gas
At low temperatures, most electrons of gas in ground state
Photons of specific wavelength are absorbed by electrons of gas, exciting them to higher levels
These absorbed wavelengths are missing from the spectrum as it exits the gas
how are absorption line spectra and emission line spectra related
Absorption line spectra are USUALLY negative of emission line spectra
BUT a few lines MAY be missing in emission as excited electrons may return to ground state in stages e.g n=3 to n=2 then n=1
Absorption is nearly always from ground state
how does the double slit experiment differ to the diffracting experiment in terms of fringes and angles
Double slit experiment – fringes are equally spaced and angles are very small.
Diffraction grating experiment – angles are much greater and fringes are not equally spaced.
what is a black body
an idealised object that absorbs all the EM radiation that shines on it
when in thermal equilibrium, it emits a characteristic distribution of wavelengths at a specific temp
what is Wien’s displacement law?
The hotter the black body, the shorter the peak wavelength of the curve
λmax α 1/T
relating to Wien’s displacement law, what happens when the temperature of the object changes
as temp increases, maximum wavelength decreases and intensity increases, peak is sharper
what is Stefan’s law
the total power (luminosity) radiated per unit surface area of a black body is directly proportional to the fourth power of the absolute temp of the black body
what does Stefan’s law show us
L is directly proportional to r^2
L is directly proportional to T^4
L is directly proportional to surface area (4pi(r^2)
The doppler equation is ∆λ/λ ≈ ∆f/f ≈ v/c
what do all the symbols mean
∆λ - different between the observed and emitted wavelengths
λ - the emitted wavelength
∆f - difference between the observed and emitted frequencies
f - the emitted frequency
v - speed of the source relative to the observer
c - speed of light
define the doppler effect
the change in frequency or wavelength of a wave in relation to observer
when does the doppler equation NOT work
when the speed of the source is near the value of the speed of light
The wavelength of an emitted source is 617nm. It was doppler shifted by 5nm. The frequency of the wave was 4.86X10^14 Hz.
What is the difference between the observed and emitted frequencies?
∆λ/λ ≈ ∆f/f
∆f = (5X10^-9 / 617X10^-9) X 4.86X10^14
= 3.94X10^12 Hz
what does Hubble’s law state
the speed of recession of a galaxy is proportional to the distance to the galaxy from the earth
what is Hubble’s constant in kms^-1Mpc^-1 approx.
convert this to base units (s^-1)
hubble’s constant = 70 kms^-1Mpc^-1
1kms^-1 = 1000ms^-1 1Mpc = 1X10^6 X (3.1X10^16) (get given pc in equation sheet)
(70 X 1000) / (1X10^6 X 3.1 X 10^16)
= 2.3 X 10^-18 s^-1
the km and Mpc cancel out because they are both distances
what does the equation v=H_0 d mean?
speed of recession of a galaxy = Hubble’s constant X distance to galaxy from earth
if the distance to a galaxy is 2.28X10^24m and hubble’s constant is 71.9 kms^-1Mpc^-1
what speed is it receding
put 71.9 kms^-1Mpc^-1 into s^-1
(71.9 X 1000) / (3.1 X 10^16 X 1X10^6)
=2.32 X 10^-18
v=H_0 d
= 2.32X10^-18 X 2.28 X 10^24
= 5.3 X 10^6 ms^-1
what is the cosmological principle
the laws of physics are universal (same everywhere)
the universe is homogenous (every part is the same as every part)
the universe is isotropic ( everything looks the same in every direction and there’s no edge or centre)
what is the theory of the expanding universe
space and time are expanding in all directions
any point is moving away from every other point in the universe
the further apart point are from each other, the faster their relative motion eg. most distant star is most red shifted
what does this equation mean
t = H_0 ^-1
age of the universe = 1 / Hubble’s constant
estimate the age of the universe in seconds when Hubble’s constant is 75kms^-1Mpc^-1
t=1/H_0
(75X1000) / (3.1X10^16 X 1X10^6)
= 2.42X10^-18
1 / 2.42X10^-18
= 4.13 X 10^17 s
what is the big bang theory
the universe started off very hot and very dense (perhaps infinitely hot and dense) and has been expanding ever since
what did cosmic microwave background radiation come from
The big bang theory predicts gamma radiation was produced at the beginning of the universe.
Because the universe has expanded, the wavelengths of this cosmic background radiation have been stretched and are now in the microwave region.
what did the satellite COBE detect when looking at radiation in space
saw a continuous spectrum of a temperature of 2.7K
radiation was largely the same everywhere (homogeneous) and in all directions (isotropic)
there are tiny fluctuations which are due to tiny energy-density variations in the early universe, and are needed of initial star/galaxy formation
what happened immediately after the big bang
- Time and space created
- One grand unified force
- Universe expands and cools
- Gravity, strong nuclear, weak nuclear and electromagnetic forces formed
- Rapid expansion - inflation
- There is a sea of quarks, antiquarks, leptons and photons but they aren’t bound together because there is too much energy
- There is slightly more matter than antimatter
what happened about 10^-4s after the big bang
- Temperature = 10^12 K
- Quarks join up to from protons and neutrons
- Matter and antimatter annihilate each other leaving a small excess of matter and huge number of photons (gamma radiation which we now detect as CMBR)
what happened about 100s after the big bang
- Temperature = 10^9 K
- Protons are cool enough to fuse to form helium nuclei
what happened about 300,000 years after the big bang
- Temp = 3000K
- Electrons combine with helium and hydrogen nuclei to form atoms
- Universe becomes transparent as there are no free charges for the photons to interact with
what happened about 14 billion years after the big bang (present)
what is the present temp of the universe?
- Temperature = 2.7K
- Slight density fluctuations
- Clumps of matter have been condensed by gravity into clusters, galaxies and stars
Why do scientists believe there is a thing called dark matter?
A Swiss astronomer calculated the mass of a cluster of galaxies based on the velocity of it’s outer galaxies and compared this figure to the mass of the cluster as estimated from its luminosity.
The mass from the velocity calculation was much bigger suggesting there’s an extra mass in the cluster that can’t be seen.
Also Rubin observed stars at the edge of galaxies were moving faster than they should given the mass and distribution of stars. For Newton’s laws to hold, there needs to be extra matter.
what percentage of the universe do scientists predict is made of dark matter
25%
what are some of scientists theories into what dark matter could be?
(MACHOs, WIMPs, mistake?)
MACHOs (Massive Compact Halo Objects) - objects made of normal matter in a very dense form so are hard to detect. But if it were true then there would have to be lots more protons and neutrons which isn’t compatible with the big bang theory
WIMPs (Weakly interacting Massive Particles) - particles that don’t interact with the electromagnetic force but do interact with gravity. This is purely theoretical (hasn’t been detected)
Or dark matter doesn’t exist at all and is an illusion caused by mistakes in other theories
what is dark energy
a type of energy that fills the whole of space
thought to make up 70% of the universe
astronomers are trying to explain how the universe is accelerating by using dark energy
but like dark matter, dark energy is a mystery
why does the colour of a star change with temperature
as it gets hotter:
- the intensity of the radiation emitted at each wavelength increases
- the wavelength at which the peak occurs decreases
