Quiz 1, Astro 1140, AU15, Pradhan – Curve: +10%

AB

CD

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Einstein’s Theory of Relativity

• Is there a maximum velocity in nature ?• If no, then one can travel or convey

information over infinite distances in infinitesimally short time – Action at a distance as presupposed by Newton

• But, do not observe instantaneous action implying infinite speed

• But if yes, then what is the limiting velocity?

The Two Postulates of Relativity1. Speed of light is the maximum speed in

nature, and is constant regardless of the speed of the source or the observer

2. All physical laws are the same everywhere, and should have the same form (equations) when describing the same phenomenon (first proposed by Galileo) Principle of Relativity

Changes our concept of space and time

Consequences of Relativity• Special Theory of relativity constant velocities• Can not simply add velocities v1 + v2

v = (v1 + v2) / (1 + v1v2 / c2)• E = m c2 Energy and mass are equivalent

(example: atomic energy, A- and H-bombs)• No object with mass can attain the speed of light;

its inertial mass becomes infinite

m = m(rest) / (1 – v2/c2)1/2

• Light is bent by gravity of a massive object such as the Sun

Relativity (Contd.)

• General Theory of Relativity Accelerating objects and gravity• Why are astronauts in the orbiting space

shuttle weightless ?• They are continuously falling towards the

Earth at the same rate as the floor of the space shuttle (e.g. like a freely falling elevator)

• Gravity Acceleration (equivalent)• Basic idea: F = ma W = mg

Relativity (Contd.)• Space and time are equivalent

(simultaneity is relative, not absolute)• Example: Two observers, one on a

moving train and the other stationary on the ground observe “simultaneous” flashes of light at different times difference in space due to motion is “converted” to difference in time

• Time ‘flows’ slower in a moving frame of reference (astronauts live slightly longer!), or near a massive object such as a black hole

Time Dilation and Space Contraction

• A time interval in a moving frame of reference (platform moving with velocity v) gets longer as

t’ = t / [ 1 – (v/c)2]1/2

• But the space interval gets shorter as

x’ = x [ 1 – (v/c)2]1/2

Light and Matter• Light is electromagnetic energy, due to

interaction of electrical charges• Matter is made of atoms – equal number

of positive and negative particles• An atom is the smallest particle of an

element; natural element H to U• Atom Nucleus (protons + neutrons),

with ‘orbiting’ electrons• No. of protons in nucleus = Atomic

Number• Science of light Spectroscopy

Why is the sky blue ?

The atmosphere scatters the blue light more than red light

Spectrum

Prism

WhiteLight

Prisms disperse light into its component colors: Red-Violet

Light is electromagnetic wave;Does not require a medium to propagate,

unlike water or sound

Wavelength is the distance between successive crests or troughs

Wavelength ()

Speed (c)

Frequency (f) (# waves/second)

Speed = wavelength x frequency c = fFrequency ‘f’ is the number of waves passing a point per second

WAVES: Frequency, Wavelength, Speed

Visible Light

• Forms a narrow band within the electromagnetic spectrum ranging from gamma rays to radio waves

• Human eye is most sensitive to which color?

• Yellow. Why?

Units of wavelength and frequency

• Frequency is the number of cycles per second• Since speed of light is constant, higher the

frequency the shorter the wavelength and vice-versa

• Wavelengths are measured in Angstroms: 1A = 1/100,000,000 cm = 1/10 nanometer (nm)

• The higher the frequency the more energetic the wave

• Wavelength (or frequency) defines radiation or color

Visible light spectrum: Each color is defined by its wavelength, frequency or energy

Red - Blue 7000 - 4000 Angstroms ( 1 nm = 10 A, 1 A = 10-8 cm)Blue light is more energetic than red light

Light also behaves like ‘particles’ called photons Photon energy, frequency, wavelength: E = h f = hc/ Planck’s Law (‘h’ is a number known as Planck’s constant)

Spectroscopy: Science of Light Analysis of the color of light from a source

Light: Electromagnetic SpectrumFrom Gamma Rays to Radio Waves

Gamma rays are the most energetic (highest frequency, shortest wavelength),Radio waves are the least energetic.

Gamma

X-Ray

UV

Visible

DecreasingWavelength ORIncreasingFrequency

Matter and Particles of Light: Quantum Theory

• Light (energy) and matter in motion behave both as waves and particles

• Wave-Particle Duality - Quantum Theory • Particles of light are called photons: E = hf = hc/• Photons of a specific wavelength may be absorbed

or emitted by atoms in matter• Matter is made of different natural elements: lightest

Hydrogen (1 proton), heaviest Uranium (92 protons)• Smallest particle of an element is atom, made up of a

nucleus (protons and neutrons), and orbiting electrons• Electrons and protons attract as opposite electrical

charges, NOT gravitationally like planets and Sun

The simplest atom: Ordinary Hydrogen

One proton in the center (nucleus) and one electron in orbits of definite energy;Ordinary H has no neutrons, but ‘heavy hydrogen’ has one neutron in the nucleus

p – positively chargede – negatively “

Resemblance toplanets orbitingthe Sun issuperficial !

Electrons alsomove bothas particlesand waves

Energy, Frequency, Wavelength• Light particles ‘photons’ have a unique

wavelength• The more ‘energetic’ a wave, the higher its

frequency, or lower its wavelength• Planck’s Law: Photon energy (‘quantum’) is E = h f = h / ‘h’ is the Planck’s constant This ‘quantum’ of energy must be equal to

the difference in energies between two electron orbits, for either absorption or emission by an atom

Absorption and emission of photons by H-atom

Energy of the photon must be exactly equal to the energy difference between the two ‘orbits’

An electron may absorb or emit light photons at specific wavelength

Wavelength (n = 3 n = 2): 6562 Angstroms (RED Color)

file:///E:/Univ7e/content/ch05/0503002.html

n=1 (Ground State)

n=3 (2nd excited state)

n=2 (1st excited state)

n=4n=5

Energy Level Diagram of 1H

Continuum

n=

n=1 (Ground State)

n=3 (2nd excited state)

n=2 (1st excited state)

n=4n=5

Photons of all other energies (wavelengths) are ignored and pass on by unabsorbed.

n=2326 25 24n=6

n=1 (Ground State)

n=3 (2nd excited state)

n=2 (1st excited state)

n=4n=5

n=3262 52 42

Larger Jump = More Energy = Bluer Wavelength

n=6

Series of spectral lines of Hydrogen

Wavelengths of series of lines from Hydrogen

Spectrum of a Fluorescent Light

Mercury

Characteristic spectra of elements

Observations of spectra of different elements in a source (planet, star, galaxy etc.) yields its chemical composition

Each elementhas a uniqueset of spectrallines, thusenabling itsidentification inthe source.

Continuous, Absorption, and Emission spectra of a source

Continuous spectrum covers wavelengths in a given range; absorption or emission spectrum consists of dark or bright lines respectively at definite wavelengths

Color Indicates Temperature and Energy of the Source

Objects generally emit radiation at all wavelengths, but mostly at one peak Wavelength depending on their temperature (e.g. blue – hot, red – cool)

Surface T (Sun) = 5600 K “ (Mercury) = 800 K

Blackbody: Perfectabsorber and emitterOf radiation at a givenTemperature T

TEMPERATURE SCALES

Room Temp = 300 K = 27 C = 81 F

Astronomers usually use the Kelvin Scale

K = C + 273 C = (F - 32) x 5/9 ~ (F - 30) / 2 F = (C x 9/5) + 32 ~ C x 2 + 30

d=1

d=2

d=3

B=1

B=1/9

B=1/4

Brightness decreases inversely as the square of the distance

Brightness and Temperature

• Brightness is related to the total energy emitted, or the luminosity of an object

• The energy emitted is related to the temperature of the object

• B = T4 is a constant)

Stefan-Boltzmann Law

The Doppler Effect

• Why does the “pitch” of a police siren differ when, say, a police car is approaching you, or when you are running away from the police (not recommended) ?

• The frequency (the number of sound waves per second) is higher when approaching, and smaller when receding from the source

Doppler Effect in Sound

High Pitch(short waves)

Low Pitch(long waves)

The Doppler Effect

Velocity c = frequency (f) x wavelength (

Doppler Shift of Wavelengths

• What about the wavelength?• What about light?• Shorter wavelength Blue-shift, • Longer wavelength Red-shift• We can determine the velocity of

astronomical objects, moving away or towards the Earth, by measuring the wavelength of light from the object

• Observed red-shift of galaxies all over the sky shows that galaxies are moving away from one another the Universe is expanding (Hubble’s Law)