Quantum Physics 2003 Virsion

R.I.C

QUANTUM PHYSICS & OUR UNIVERSE

Niels Bohr said, "Anyone who is not shocked by quantum theory has not understood it."

A2 level-Unit 4 | Suranjan Viraj

Quantum Physics & Our Universe  The Photon Concept  Photoelectric Effect 

Wave-Particle Duality

 De Broglie Wavelength  Energy Levels  Stationary Waves in the Hydrogen Atom  Types of Spectra  Electromagnetic Doppler Effect {Red Shift and Blue Shift}  The Expansion of The Universe and The Big Bang  The Open And Close Universe

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What is Quantum Physics? Quantum physics is a branch of science that deals with discrete, indivisible units of energy called quanta as described by the Quantum Theory. There are five main ideas represented in Quantum Theory: 1. Energy is not continuous, but comes in small but discrete units. 2. The elementary particles behave both like particles and like waves. 3. The movement of these particles is inherently random. 4. It is physically impossible to know both the position and the momentum of a particle at the same time. The more precisely one is known, the less precise the measurement of the other is. 5. The atomic world is nothing like the world we live in. While at a glance this may seem like just another strange theory, it contains many clues as to the fundamental nature of the universe and is more important then even relativity in the grand scheme of things (if any one thing at that level could be said to be more important then anything else). Furthermore, it describes the nature of the universe as being much different then the world we see. As Niels Bohr said, "Anyone who is not shocked by quantum theory has not understood it."

T HE P HOTON C ONCEPT A photon is an isolated clump of electromagnetic energy (discrete packets)

h=Planck's constant {h = 6.62 x 10-34 J.s} light{c=3 x 108 ms-1}

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c=speed of

We can now appreciate how energy and frequency or wavelength is related. Visible light is in the middle of the above picture and is of relatively moderate energy. Infrared, microwave, and radio waves are lower frequency (higher wavelength) and hence lower in energy. To the left of visible light on this graph are the higher frequency forms of electromagnetic radiation. Gamma-rays (g-rays) have extremely high frequency; photons of this type of light carry a lot of energy. X-rays are also "high energy". Ultraviolet radiation is also higher energy than visible light.

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The Photoelectric Effect If you shine light of a high enough frequency onto the surface of a metal in a vacuum, it will emit electrons, called photoelectrons. When light hits its surface the metal is bombarded by photons. If one of these photons collides with a free electron, the electron will gain enough energy equal to hf. Before an electron can leave the surface of the metal, it needs enough energy to break the bonds holding it there. This energy is called the work function energy (Ø). And its value depends on the metal. If the energy gained from the photon is greater than the work function energy, the electron is emitted [hf ≥ Ø]. If it isn’t, the electron will get excited then release the energy as another photon, the metal will heat up but no electrons will be emitted.It is reasonable to expect that a certain amount of energy is required to liberate an electron from a metal surface, since the electron is attracted to the positively charged nuclei in the metal. Thus, in order for the electron to escape, the light must supply sufficient energy to the electron to overcome this attraction.

Maximum Kinetic Energy {vmax}

1/2mv2max=

hf-Ø 1/2mv2max =eVs {stopping potential}

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The following experimental observations are found when studying the photoelectric effect. First, in order for the effect to be observed, the light must be of at least a minimum frequency which we call the threshold frequency, ν 0. This frequency is a characteristic for a given metal. That is, it is the same value for each sample of that metal, but it varies from one metal to the next. For low frequency light, photoelectrons are not observed in any number, no matter how intense the light source is. For light with frequency above ν 0, the number of photoelectrons emitted by the metal (measured by the photoelectric current, F) increases directly with the intensity of the light. These results are shown in figure 1.

Figure 1: The Photoelectric Effect. Φ is the photoelectric current, ν is the frequency of incident light, and I is the intensity of incident light. (a) For photoelectrons to be emitted, the light frequency must be greater than a threshold value. (b) If the frequency is high enough, the number of photoelectrons increases directly with the light intensity. Second, we can measure the energies of the electrons emitted by the metal. For a given metal, all photoelectrons have the same kinetic energy for a fixed frequency of light above ν 0. This fixed kinetic energy is independent of the intensity of the light source. As the frequency of the light is increased, the kinetic energy of the emitted electrons increases proportionally. These results are shown in figure 2.

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Figure 2: KE is the photoelectron kinetic energy, ν is the frequency of incident light, and I is the intensity of incident light. (a) If the frequency is high enough, the energy of the electrons increases directly with the frequency. (b) However, the energy of the photoelectrons does not depend on the light intensity. Reasoning from this analogy, we must conclude that the energy of the light is supplied in "bundles" or "packets" of constant energy, which we will call photons. We have already concluded that the light supplies energy to the electron which is proportional to the light frequency. Now we can say that the energy of each photon is proportional to the frequency of the light. The intensity of the light is proportional to the number of these packets. This now accounts for the threshold frequency in a straightforward way. For a photon to dislodge a photoelectron, it must have sufficient energy, by itself, to supply to the electron to overcome its attraction to the metal. Although increasing the intensity of the light does increase the total energy of the light, it does not increase the energy of an individual photon. Therefore, if the frequency of the light is too low, the photon energy is too low to eject an electron. Referring back to the analogy, we can say that a single bowling bowl can accomplish what many ping-pong balls cannot, and a single high frequency photon can accomplish what many low frequency photons cannot. The remarkable aspects of the photoelectric effect when it was first observed were: 1. The electrons were emitted immediately - no time lag! 2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! 3. Red light will not cause the ejection of electrons, no matter what the intensity! 4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths!

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Wave-Particle Duality Does light consist of particles or waves? When one focuses upon the different types of phenomena observed with light, a strong case can be built for a wave picture:

Interference

Diffraction

Polarization

By the turn of the 20th century, most physicists were convinced by phenomena like the above that light could be fully described by a wave, with no necessity for invoking a particle nature. But the story was not over.

Phenomen on

Can be explained in terms of waves.

Can be explained in terms of particles.

Reflection Refraction Interferenc e Diffraction Polarizatio n Photoelect ric effect

Most commonly observed phenomena with light can be explained by waves. But the photoelectric effect suggested a particle nature for light. Then electrons too were found to exhibit dual natures.

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De Broglie

If “wave-like” light showed particle properties (photons), “particles” like electrons should be expected to show wave-like properties. The de Broglie equation relates a wave property to a moving particle property.

λ =h/mv (mv, momentum) h=Planck's constant {h = 6.62 x 10-34 J.s}

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The Two-Slit Experiment/Electrons If we fire a beam of electrons through a double slit onto a detector, and the slits made small enough and close enough together, we actually observe the following:

This means that the electrons are diffracting through the slits and interfering with each other just like waves. This means that the electrons have wave-particle duality, just like photons. In this case, they must have properties like wavelength and frequency. We can deduce the properties from the behavior of the electrons as they pass through our diffraction grating.

Recall the property relating wavelength to diffraction fringe spacing that we found:

Where: S is the fringe spacing

λ is the wavelength

L is the distance from slits to screen spacing

d is the grating

If we can get electrons to diffract through a known grating, we can obtain a wavelength for the electron. Practically, it turns out that electrons have an extremely short wavelength, so we [Type text]

cannot make gratings fine enough to diffract those significantly using traditional methods. However, we can use crystals as they are essentially extremely regular gratings with spacing on the order of nanometers. If we use an electron gun to produce our electrons, and fire these electrons though a crystal with a known atomic structure, we can work out the wavelength of the electron experimentally. This leads to a description of the electron as a wave.

Electron Energy Levels Electrons in an atom can only exist in certain well-defined energy levels. Each level is given a number (called the principle quantum number of the electron en that state), with n=1 representing the electrons lowest possible energy – its ground state. When excited by electromagnetic waves, with enough energy (absorbed photons) the electrons will climb up the energy levels. Electrons can move down an energy level by emitting a photon. Since these transitions are between definite energy levels, the energy of each photon emitted can only take certain values. [Type text]

∆ E=E2-E1=hf=hc/ λ

An electron (the An redelectron one) absorbs emits aa photon and photon (the orange jumps one) toand a lower jumps orbit. to a higher orbit (the green one)

The Balmer series of spectral lines at visible wavelengths are emitted when the electrons fall from all higher atomic energy levels to the first [Type text]

excited level, n = 2. In so doing, it emits a photon with energy equal to the energy difference of the initial and final states. Other series indicated on figure above illustrate the other series of lines found by Theodore Lyman and Louis Paschen. This type of diagram is called an energy level diagram because it illustrates the discrete, allowed energy levels and the permissible transitions for the orbiting electron.

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Stationary waves in the Hydrogen Atom Since light has particle and wave characteristics, electrons should have wave-like character. Specifically when they’re in orbit around a nucleus they ought to behave like the standing waves. Exist ay certain well defined frequencies, for the circular orbits suggested by Bohr, the wavelength of the electron waves should fit the circumference a whole number times. The principle quantum number is equal to the number of complete waves that fit the circumference.

“Orbiting” electron as standing wave around the nucleus, (a) two cycles per orbit, (b) three cycles per orbit. Electrons only could exist in certain, definite “orbits” around the nucleus because those were the only distances where the wave ends would match. In any other radius, the wave should destructively interfere with itself and thus cease to exist.

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Types of spectra {CONTINUOUS, EMISSION, AND ADSORPTION} Spectroscopy is a tool used by scientists to determine the elemental composition of objects. Spectroscopes are tools that break down the light emitted or absorbed by chemical elements into specific lines of color. Each element is individual in the type of light that it emits. Therefore, each element has its own spectral “fingerprint” that makes it unique and therefore easy to identify. There are three basic types of spectra used by scientists. They are continuous spectra, absorption spectra, and emission spectra.

Continuous spectra can be identified by all the colors of the rainbow blended next to each other in a band. Superheated solids and liquids will emit light of all colors.

Emission spectra can be identified by bright lines of color on top of a black background. Atoms that are excited only emit certain colors of light. Because of this characteristic, we can use the bright bands of color to identify the atom.

Absorption spectra can be identified by black bands on top of a [Type text]

continuous spectrum. When atoms are present as a gas, they will absorb only certain colors of light. When viewed through a spectroscope, some colors will be missing. The missing colors are the colors that were absorbed by the gas as the light passed through it.

Single observed frequency in the hydrogen atom spectrum. As shown in the following image the frequencies observed in the visible range of the spectrum are all due to n = 2. This series is called the Balmer series (acc. to the Swiss spectroscopist Johann Balmer).

The conditions needed to produce line spectra Emission and absorption lines can tell us a great deal about a distant celestial source, but they only occur under certain conditions. Emission lines from an element will appear if • • •

there are atoms of the element present the atoms are in a low-density gas the atoms are excited into a particular high energy level by some external source

Absorption lines from an element will appear if • • • •

there are atoms of the element present the atoms are in a low-density gas the atoms spend most of their time in a particular low-energy level the gas lies between us and a source of continuous light (of all wavelengths)

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Electromagnetic Doppler Effect {red shift and Blue Shift}

When the source of a waveform—such as sound or light—is moving, the detected frequency or wavelength is different than what was emitted. This change is called the Doppler Effect. The wavelength appears shorter when the source is moving toward you and appears longer when the source is moving away. The star is pulled toward or away from Earth as the planet orbits around it. As the star moves toward Earth its light is shifted to a shorter wavelength, known as a blue shift. If the star is moving away from Earth we see the light as red shifted because the light from the star has been shifted to longer wavelengths. Astronomers can measure how much the light from the star has shifted. This is not a dramatic shift, like from blue light to red light, but it is enough for astronomers to measure. From the measurements, it can be calculated how fast the galaxies are moving away from us. It also shows that the Universe is expanding.

Z=Δλ/λ=v/c v<
if

The amount red shift or blue shift is determined by the following formula:

Z-is the red shift Δλ-difference between the observed wavelength and the emitted wave length

λ-is the emitted wavelength v-is the velocity of the source in the direction of the observer and c is the speed of light

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The expansion of the Universe and the Big Bang In the Big Bang theory the universe started billions of years ago.....

While many people believe that the big bang theory refers to an explosion, it actually refers to the expansion of the universe.

According to the Big bang theory, the universe originated in an extremely dense singularity. Space has expanded with time, and galaxies have been moved further away from each other. It is these particles that were made in the Big Bang, eventually forming galaxies billions of years later. Such was the violence of that event that galaxies, or cluster of galaxies, are still rushing apart in an everexpanding universe. The Birth of Atoms Immediately after the start of the Big Bang, space rapidly expanded for a very short time. This process which lasted for the minutest fraction of second in called inflation. After that, expansion began to slow down and different kinds of particles including quarks and electrons made their appearance. Just one millionth of a second after the birth of the universe, the quarks had clumped together to form new particles called protons and neutrons. After a hundred seconds some of the protons and nearly all neutrons gathered into bunches consisting of 2 protons and neutrons. Eventually each bunch or atomic nucleus captured 2 electrons to form a helium atom and each remaining proton captured a single electron to form a hydrogen atom. The first building blocks of matter had been born. The Birth of Galaxies By the time atoms of hydrogen and helium had formed, the searing heat of the Big Bang had cooled down and the dense gas of earlier times was [Type text]

becoming more thinly spread out as the space continued to expand. Gradually though perhaps a billion years later huge clouds of gas held together by gravity began to collapse to form galaxies and clusters of galaxies. As time went on stars began to be formed in the galaxies and the galaxies began to form familiar elliptical and spiral shapes. About 5 billion years ago, in our own Milky Way Galaxy the Sun was born. Planets began to form around the Sun, and one of them was our home the Earth. Hubble’s Law Edwin Hubble was able to show that the velocity of a distance galaxy, measured from Earth, was directly proportional to the distance of the galaxy from Earth. Hubble only had a few points to work with at first. Later evidence was able to support this proportionality between velocity and distance. The direct proportionality between velocity and distance can be expressed as : v=Hd where v = velocity of a distant galaxy from Earth. H = Hubble's constant.

H= (2 ±1) x 10-18 s-1

d = distance between the galaxy and Earth (in our galaxy). Astronomical distances measured in light years (ly).A light year is the distance travelled by light in one year =9.46 x 10-15 m Consider the distance (d) between two galaxies we observe today. Let this be a time T after the Big Bang. Using v = d / T we can then state that the age of the Universe is given by T = d/v And Hubble’s equation states that v = Hd ,

H= (2 ±1 ) x 10-18 s-1

So substituting for v gives

The Age of the Universe 1/H

T=

Age of the universe=5 x 1017 s ≈1010 years Therefore knowledge of the Hubble constant is important in our calculation of the age of the universe. Unfortunately, there appears to be a large disagreement between scientists on the value to be taken for the Hubble constant. The main reasons for the differences arise from the errors (uncertainties) in the measurements of v and d, and the methods [Type text]

used to determine these values. To make things more complicated, Hubble constant will change with time, if the universe is decelerating in is expansion, as a result of gravitational attraction.

The Open and Close Universe The Big Crunch –

Universe Open OR Closed

Big crunch

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The closed universes correspond to the bottom curve. Open universes correspond to the top curve. The flat universe (the critical universe) separates things into closed and open universes. Flat universes ---> expanding universe and will stop expanding after an infinite amount of time; the flat universe is the dividing line between open and closed universes. Closed universes ---> expanding, but will reach a maximum size and then collapse Open universes ---> expanding universe which will expand forever and is infinite in spatial extent The expansion of the universe is gradually slowing down. Galaxies may continue to move apart forever. However, gravity a force of attraction between bodies in the universe – may eventually halt the expansion. Then, the galaxies will start to fall together until everything collides in a ‘Big Crunch’. No one can tell whether the universe is open (ever expanding) or closed (destined eventually to collapse upon itself).

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