objectives • Know: • Definitions of photon and Planck’s Constant. • Understand: • The manner in which the Photoelectric Effect demonstrates the particle nature of light. • Be able to: • Determine the energy of a photon based on its frequency and/or wavelength. • Determine a photon’s ‘type’ using the EM Spectrum chart. • Use/interpret a graph of photon energy vs. frequency and/or frequency vs. wavelength. • Homework – castle learning
Light as a wave electric charges electric and magnetic fields • Light is an electromagnetic wave produced by an oscillating _______________________. The vibrating charges produce alternating _________________________________which are perpendicular to the direction of the wave’s motion. This waves can travel through vacuum in vast space. • Light is a wave because • Light have wave characteristics such as _________________________________________________ • Light exhibit wave behavior such as _________________________________________________ • However, the wave model of light can not explain interactions of light with matter • amplitude, wavelength, frequency, and velocity. • diffraction, interference, and the Doppler effect.
An unusual phenomenon was discovered in the early 1900's. If a beam of light is pointed at the negative end of a pair of charged plates, a current flow is measured. A current is simply a flow of electrons in a metal, such as a wire. Thus, the beam of light must be liberating electrons from one metal plate, which are attracted to the other plate by electrostatic forces. This results in a current flow. Waves have a particle nature An unusual phenomenon was discovered in the early 1900's. Photoelectric_Effect If a beam of light is pointed at the negative end of a pair of charged plates, a current flow is measured which meansthe beam of light must be liberating electrons from one metal plate, which are attracted to the other plate by electrostatic forces. However, the observed phenomenon was that the current flow varied strongly with the frequencyof light such that there was a sharp cutoff and no current flow for smaller frequencies. Only when the frequency is above a certain point (threshold frequency), the current flow increases with light strength. Photoelectric Effect
Einstein explains photoelectric effect • ..\..\RealPlayer Downloads\Photoelectric Effect and Photoelectric Cell.flv • Einstein successful explained the photoelectric effect within the context of the new physics of the time, quantum physics developed by Max Planck. • Quantum theory assumes that electromagnetic energy is emitted from and absorbed by matter in discrete amounts of packets. Each packet carries a quantum of energy. • The quantum, or basic unit, of electromagnetic energy is called a photon. A photon is a mass-less particle of light, it carries a quantum of energy. Energy: E = h∙f
E E λ f Energy: E = h∙f • since f = c/λ E = h∙f = h∙c/λ • The amount of energy E of each photon is directly proportional to the frequency f of the electromagnetic radiation, and inversely proportional to the wavelength λ. • E is energy of a photon, in Joules, or eV, • 1 eV = 1.60x10-19 J • h is Planck’s constant, 6.63 x 10-34 J∙s • fis frequency of the photon, in hertz • c is the speed of light in vacuum, c = 3.00x108 m/s • λis wavelength, in meters Direct relationship Slope = h Inverse relationship
The Compton effect: photon-particle collision • In 1922 Arthur Compton was able to bounce an X-ray photon off an electron. The result was an electron with more kinetic energy than it started with, and an X-ray with less energy than it started with. A photon can actually interact with a particle! A photon has momentum!! - another proof that photon is a particle. • During the collision, both energy and momentum are conserved.
The momentum of a photon • A photon, although mass-less, it has momentum as well as energy. All photons travel at the speed of light, c. The momentum of photon is p = h/λ = h∙f/c Where p is momentum, h is plank’s constant, λis the wavelength • Momentum p is directly proportional to the frequency light, and inversely proportional to the wavelength. p = h/λ = h∙f/c E = hc/λ = h∙f
wavelength, frequency, crests, troughs, amplitude … • In conclusion, light has both wave and particle nature. • Wave nature: • Exhibit wave characteristics: _______________________________________________________ • Exhibit wave behavior: • _______________________________________________ • Particle nature: • ________________________________________ • _________________________________ • _________________________________ interference, diffract, Doppler effect, refract, reflect … • Photoelectric effect Interact with electron – has momentum Reflect like a particle
Particles have wave nature • Just as radiation has both wave and particle characteristics, matter in motion has wave as well as particle characteristics. • The wavelengths of the waves associated with the motion of ordinary object is too small to be detected. • The waves associated with the motion of particles of atomic or subatomic size, such as electrons, can produce diffraction and interference patterns that can be observed. • ..\..\RealPlayer Downloads\Double Slit Experiment - The Strangeness Of Quantum Mechanics.flv
All Matters have wave nature • All matters have wave nature. • Louis de Broglie (Frenchphysicist and a Nobel laureate)assumed that any particle--an electron, an atom, a bowling ball, whatever--had a "wavelength" that was equal to Planck's constant divided by its momentum... λ = h / p ..\..\RealPlayer Downloads\Matter Wave - De Broglie Wavelength.flv
In summary • Waves has particle nature, it has momentum just like a particle: • Particle has wave nature, it has a wavelength just like a wave: p = h / λ λ = h / p
Class work – today’s date Which graph best represents the relationship between the intensity of light that falls on a photo-emissive surface and the number of photoelectrons that the surface emits? a b c d Note: this only happens when the frequency of the light beam is above a certain point
When the source of a dim orange light shines on a photosensitive metal, no photoelectrons are ejected from its surface. What could be done to increase the likelihood of producing photoelectrons? • Replace the orange light source with a red light source. • Replace the orange light source with a higher frequency light source. • Increase the brightness of the orange light source. • Increase the angle at which the photons of orange light strike the metal. • Which characteristic of electromagnetic radiation is directly proportional to the energy of a photon? • wavelength c. period • frequency d. path
A beam of monochromatic light incident on a metal surface causes the emission of photoelectrons. The length of time that the surface is illuminated by this beam is varied, but the intensity of the beam is kept constant. Which graph below best represents the relationship between the total number of photoelectrons emitted and the length of time of illumination? a b c d
The energy of a photon is 2.11 electronvolts • Determine the energy of the photon in Joules • Determine the frequency of the photon • Determine the color of light associated with the photon. • The threshold frequency of a photo emissive surface is 7.1 x 1014 hertz. Which electromagnetic radiation, incident upon the surface, will produce the greatest amount of current? • low-intensity infrared radiation • high-intensity infrared radiation • low-intensity ultraviolet radiation • high-intensity ultraviolet radiation
The slope of a graph of photon energy versus photon frequency represents • Planck’s constant • the mass of a photon • the speed of light • the speed of light squared • A photon of light carries • energy, but not momentum • momentum, but not energy • both energy and momentum • neither energy nor momentum • All photons in a vacuum have the same • speed c. wavelength • energy d. frequency
Models of an atom • Describe Thompson’s model • Explain the strengths and weaknesses of Rutherford’s model of the atom • Describe Bohr model of an atom • Describe cloud model • Explain why only certain energy levels are permitted in atoms.
About 440BC, a Greek scientist named Democritus came up with the idea that eventually, all objects could be reduces to a single particle that could not be reduced any further.He called this particle an atom, from the Greek word atomos which meant “not able to be divided.”From this, the idea of the atom – the basic building block of all matter – was born. • Around 1700, scientists understanding of molecular composition of matter had grown considerably. They had figured out that elements combine together in specific ratios to form compounds. In 1803, British chemist John Dalton came up with a theory about atoms: • All substances are made of small particles that can’t be created, divided, or destroyed called atoms. • Atoms of the same element are exactly alike, and atoms of different elements are different from each other. (So, atoms of gold are exactly like gold atoms, but different than aluminum atoms). • Atoms join with other atoms to make new substances.
Thompson’s model • In 1897, a British scientist named JJ Thomson discovered that electrons are relatively low-mass, negatively charged particles present in atoms. • Because atoms are neutral, he proposed a model - the "atom" was made of negatively-charged particles (electrons) dispersed among positively-charged particles (protons) like raisins in "plums in a pudding". • In 1909, British scientist Ernest Rutherford decided to test the Thomson theory, and designed an experiment to examine the parts of an atom.
Rutherford’s model • In his experiment, He fired alpha particles (2 positive charges) beam at extremely thin gold foil. • He expected alpha particles travel in straight line unaffected because the net electric force on the alpha particle would be relatively small. • However, he found a small number of particles were scattered at large angles. • Rutherford explained this phenomenon by assuming the following: • Most particles were not affected due to the vast empty space inside the atom • Only a few particles were scattered due to the repulsive force between the concentrated positive charge inside the atom and the particle. • Rutherford’s model of the atom • most of the mass was concentrated into a compact nucleus (holding all of the positive charge), with electrons occupying the bulk of the atom's space and orbiting the nucleus at a distance.
In Rutherford’s model of the atom, electrons orbit the nucleusin a manner similar to planets orbiting the sun.
Limitation of Rutherford model • According to Rutherford, electrons accelerate due to centripetal force, and the accelerating charges radiate electromagnetic waves, losing energy. So the radius of electron’s orbit would steadily decrease. • This model would lead a rapid collapse of the atom as the electron plunged into the nucleus.
Spectral Lines • At the end of 19th century, physicists knew there were electrons inside atoms, and that the wiggling of these electrons gave off light and other electromagnetic radiation. Physicists would heat up different elements until they glowed, and then direct the light through a prism. But when scientists looked at the light coming off of just one element, hydrogen for instance, they didn't see the whole rainbow. Instead they just got bright lines of certain colors.
The Bohr Model of the hydrogen atom • Danish physicistNiels Bohr attempted to explain the problems in Rutherford’s model. He proposed in 1913 that electrons move around the nucleus of an atom in specific paths, on different levels of energy. • All forms of energy are quantized. • The electron in an atom can occupy only certain specific orbits and no other. • Electrons can jump from one orbit to another by emitting or absorbing a quantum of energy in the form of photon. • Each allowed orbit in the atom corresponds to a specific energy level. The orbit nearest the nucleus represents the smallest amount of energy that the electron can have. The electron can remain in this orbit with out losing energy even though it is being accelerated.
When electron is in any particular orbit, it is said to be in a stationary state. Each stationary state represents an energy level. The successive energy levels of an atom are assigned integral numbers, denoted by n=1, 2, 3… • When the electron is in the lowest level (n=1), it is said to be in the ground state. • For a hydrogen atom, an electron in any level above the ground state is said to be in an excited state.
When electron goes up from lower to higher level, the atom absorbs a quantum of energy in the form of a photon. • When electron goes down from higher to lower level, the atom emits a quantum of energy in the form of a photon.
If the energy of the photon of light is just right, it will cause the electron to jump to a higher level. • When the electron jumps back down, a photon is emitted for each jump down. • A photon without the right amount of energy (the pink one) passes through the atom with no effect. • Photons with too much energy will cause the electron to be ejected which ionizes the atom
Energy levels • excitation: any process that raises the energy level of electrons in an atom. • Excitation can be the result of absorbing the energy of colliding particles of matter, such as electrons, or of photons of electromagnetic radiation. • A photon’s energy is absorbed by an electron in an atom only if the photon’s energy corresponds exactly to an energy-level difference possible for the electron. • Excitation energies are different for different atoms.
Atoms rapidly lose the energy of their various excited states as their electrons return to the ground state. This lost energy is in the form of photons of specific frequencies, which appear as the spectrum lines in the characteristic spectrum of each element. • A spectrum line is a particular frequency of absorbed or emitted energy characteristic of an atom. Absorption Spectrum Emission Spectrum
Ionization potential • An atom can absorb sufficient energy to raise an electron to an energy level such that the electron is removed from the atom’s bound and an ion is formed. • The energy required to remove an electron from an atom to form an ion is called the atom’s ionization potential. • An atom in an excited state requires a smaller amount of energy to become an ion than does an atom in the ground state.
Energy level diagram ionization • The energy level of an electron that has been completely removed from the atom is defined to be 0.00 eV. All other energy levels have negative values. • The electron in the ground state has the lowest energy, with largest negative value. Ground state
Energy level is explained by Louis de Broglie’s particle-wave theory • ..\..\RealPlayer Downloads\Matter Wave - De Broglie Wavelength.flv • According to de Broglie, particles have wave nature: λ = h / p • If we begin to think of electrons as waves, we'll have to change our whole concept of what an "orbit" is. Instead of having a little particle whizzing around the nucleus in a circular path, we'd have a wave sort of strung out around the whole circle. Now, the only way such a wave could exist is if a whole number of its wavelengths fit exactly around the circle. • If the circumference is exactly as long as two wavelengths, say, or three or four or five, that's great, but two and a half won't cut it.
Limitations of Bohr’s model • It can not predict or explain the electron orbits of elements having many electrons • ..\..\RealPlayer Downloads\Quantum Mechanics.flv
The cloud model (Schrödinger model) • In this model, electrons are not confined to specific orbits, instead, they are spread out in space in a form called an electron cloud. • The electron cloud is densest in regions where the probability of finding the electron is highest. The cloud model represents a sort of history of where the electron has probably been and where it is likely to be going.
example • The diagram represents alpha particleA approaching a gold nucleus. D is the distance between the path of the alpha particle and the path for a head-on collision. If D is decreased, the angle of deflection θ of the alpha particle would • decrease • increase • remain the same
example • Which diagram shows a possible path of an alpha particle as it passes very near the nucleus of a gold atom? • 1 • 2 • 3 • 4
example • In Rutherford's model of the atom, the positive charge • is distributed throughout the atom's volume • revolves about the nucleus in specific orbits • is concentrated at the center of the atom • occupies most of the space of the atom
example • White light is passed through a cloud of cool hydrogen gas and then examined with a spectroscope. What is the cause of dark lines observed on a bright background?
example • The term "electron cloud" refers to the • electron plasma surrounding a hot wire • cathode rays in a gas discharge tube • high-probability region for an electron in an atom • negatively charged cloud that can produce a lightning strike
Atomic spectra • Explain atomic spectra using Bohr’s model of the atom. • Recognize that each element has a unique emission and absorption spectrum.
Atomic spectra • According to Bohr’s model, electrons in atoms can be found in only certain discrete energy states.
Atomic spectra • When electrons jump from the lower to the higher number orbits, they absorb a particular amount of energy and we can observe the absorption spectrum. • When they fall back again they release the same amount of energy and we can observe the emission (bright-line) spectrum. The amount of energy absorbed or released in this way can be directly related to the wavelength at which we see the absorption and emission lines on the spectrum.
Each element has a characteristic spectrum that differs from that of every other element. • The emission spectrum can be used to identify the element, even when the element is mixed with other elements. Hydrogen spectrum Helium spectrum
Emission (bright-line, atomic) spectra • In a hot gas, when an electron in an atom in an excited state falls to a lower energy level, the energy of the emitted photon is equal to the difference between the energies of the initial and final states. Ephoton = Ei – Ef = hf • Ei isthe initial energy of the electron in its excited state and Ef is the final energy of the electron in the lower energy level.
Each energy difference between two energy levels corresponds to a photon having a specific frequency. For example: An electron in a hydrogen atom drops from the n = 3 energy level to the n = 2 energy level. The energy of the emitted photon is Ephoton = E3 – E2 = (-1.51 eV) – (-3.40 eV) = 1.89 eV Ephoton = 1.89 eV x 1.60 x 10-19 J/eV = 3.02 x 10-19 J Using Ephoton = hf, we can find the frequency of the emitted photon: f = 3.02 x 10-19 J / (6.63x10-34 J∙s) = 4.56 x 1014 Hz which corresponding to red light
A specific series of frequencies, characteristic of the element, is produced when the electrons of its atoms in excited states fall back to lower states or to the ground state. When these emitted frequencies appear as a series of bright lines against a dark background, they are called a bright-line spectrum or an emission spectrum.
Absorption spectra • In a cold gas, an atom can absorb only photons having energies equal to specific differences in its energy levels. • The frequencies and wavelengths of these absorbed photons are exactly the same as those of the photons emitted when electrons lose energy and fall between the same energy levels.
Class work – today’s date • An electron in a hydrogen atom drops from the n = 4 energy level to the n = 2 energy level. The energy of the emitted photon is Ephoton =Ei – Ef Ephoton =(-0.85eV)–(-3.40eV) Ephoton =2.55 eV Ephoton =4.08 x 10-19 J