Presentation on theme: "Lecture 5: Light and the EMR Spectrum (Ch )"— Presentation transcript:
1Lecture 5: Light and the EMR Spectrum (Ch 4.4-4.9) Dr HarrisSuggested HW: (Ch 4) 13, 19, 20, 21, 22, 28, 29, 31, 37
2Our present understanding of the electronic structure of atoms has come from the light that is absorbed and emitted by substancesFor example, what happens when you switch on aNeon lights are glass chambers pressurized with Neon or other noble gasesWhen a voltage is applied, the gas is ionized. This ionization causes a “glow”.Why does this phenomena occur?What further information can this provide us about the electronic structure of atoms?Over the course of the next two class periods, we will be able to understand exactly what’s happening, and what it meansNeon light ?
3EMR: Light and EnergyThe applied voltage cause the electrons to become excited, or “bumped up” in energyWhen the electron drops back down to its original, lower energy state, the excess energy is released as light. This is called emission.But what exactly is light?The light that we see with our eyes is a type of electromagnetic radiation (EMR)When we use the term radiation, we are referring to energy that is propagated (moves and spreads outward) through space as wavesLight, like that which emits from a lamp, is comprised of visible wavesRadio waves from a radio are another type of EMRInvisible UV and Infrared rays from the sun are also EMR
4Propagation of WavesThe waves created in water when an external force is applied are an example of propagation.The energy transferred to the spot of impact is spread and transmitted throughout the water.EMR propagates through the universe as oscillating, perpendicular electric and magnetic fields
5Wavelength and Frequency The distance between local maxima, or crests, is the wavelength λ (units of meters)If we picture these waves moving across the page, the number of crests that pass a given point per second is the frequency, ν (units of s-1)The speed of a wave is given by the product of ν and λ:λν = cc is the speed of light, 3.0 x 108 m/s. All EMR moves at this speed through vacuum
6Different Types of EMR Have Different Wavelengths The electromagnetic spectrum below shows EMR listed by increasing wavelengthWavelengths vary from the size of an atomic nucleus to the length of a football field
7The Visible SpectrumROY G. BIV (increasing Energy)
8Examples What is the frequency of orange (~650 nm) light? A certain type of radiation has a frequency of 1015 s-1. What is the wavelength, in nm, of this radiation? What kind of radiation is it?
9Continuous SpectraWhite light is comprised of all wavelengths of the visible spectrum. Because the spectrum of white light has no gaps, it is a continuous spectrum.Sunlight, for example, is continuous over a long range of wavelengths. The spectrum of sunlight is shown.
10Line (Discontinuous) Spectra Light emitted from chemical samples exhibits a discontinuous spectrum. The radiation consists of spectral lines at particular wavelengths. This type of spectrum is a line spectrum, or atomic emission spectraSodium burns very brightly and emits an orangish-yellow color: Discontinuous spectrum
11Max PlanckThe observation of spectral lines indicates that certain elements can only emit certain wavelengthsHow can this be? Why can’t any element emit at any wavelength?Max Planck first began to answer this question with his interpretation of a phenomena known as blackbody radiation.
12Blackbody Radiation And The End Of Classical Physics All solid objects, when heated, emit thermal radiation.Just when an object is hot enough to glow, it appears red. As you continue to heat the material, it becomes “white hot”Classical physics predicts that continuous heating would produce higher and higher frequencies at increasing intensityThis means that light bulbs would give off UV, gamma, X-rays, and so on. Of course, this doesn’t happen
13The Birth Of Quantum Physics The failure of Classical Physics to explain blackbody radiation lead to the creation of Quantum Physics by Planck, Einstein, and others.Planck explained blackbody radiation by asserting that light (radiation) can only be emitted in small, exact amounts called photons (or quanta)He then derived the amount of energy absorbed or released in a single event is equal to:En = nhνwhere En is the total energy in J, n is the number of photons, and h is Planck’s constant, x J•s
14ExamplesCalculate the energy contained in a single photon of blue light (~400 nm)Calculate the energy of contained in 10 photons of green light (~520 nm)
15Einstein and the Photon Like Planck, Einstein envisioned light as a beam of particles.Borrowing from Planck’s theory, he asserted that each photon in the beam is a little packet of energy E = hνUsing this theory, Einstein sought to understand a phenomena that had defied physics for many years prior… the Photoelectric effect
16The Photoelectric Effect The photoelectric effect is the ejection of electrons from metal surface under illumination following the absorption of a photon’s energy.Photons too low in frequency (energy), no matter how intense the beam, will not eject an electron from a metal surface.It is not until some minimum frequency (threshold frequency, νT) is reached, that a photon is just energetic enough to loosen an electron.At energies beyond the threshold energy (ET = hvT), the electron converts the excess energy of the photon into kinetic energy and is ejected.
17Excess Energy is Converted to Kinetic Energy Plot of Ek vs. ν for sodiumThe energy of motion is called kinetic energy (Ek)The kinetic energy of a body of mass is given by:m is the mass in kg, and 𝑉 is the velocity (speed) in meters per second (m/s). The units of energy are Joules (J).slope of line = h𝑬 𝒌 = 𝟏 𝟐 𝒎 𝑽 𝟐5.51 x 1014 s-1Einstein found that as you increase the energy of the incident photon striking, the velocity of the ejected electron increases proportionally:𝑬 𝒌 = 𝑬 𝒑𝒉𝒐𝒕𝒐𝒏 − 𝑬 𝑻
19ExampleGiven that the threshold frequency of copper is x 1015 s-1, calculate the kinetic energy of an electron that will be ejected when a 210 nm photon strikes the surface?What do we know?νT = x 1015 s-1νphoton = 𝑐 λ = 3.0 𝑥 𝑚 𝑠 − 𝑥 1 0 −7 𝑚 =1.428 𝑥 𝑠 −1𝑬 𝒌 = 𝑬 𝒑𝒉𝒐𝒕𝒐𝒏 − 𝑬 𝑻substitute:𝐸 𝑘 =ℎ 𝑣 𝑝ℎ𝑜𝑡𝑜𝑛 −ℎ 𝑣 𝑇 =ℎ( 𝑣 𝑝ℎ𝑜𝑡𝑜𝑛− 𝑣 𝑇 )𝐸 𝑘 =(6.626 𝑥 1 0 −34 𝐽𝑠)(3.52 𝑥 𝑠 −1 )𝑬 𝒌 =𝟐.𝟑𝟑 𝐱 𝟏 𝟎 −𝟏𝟗 𝑱
20Example Continued.From the example on the previous page, calculate the velocity of the electron?Mass of electron = x kg Joule = 𝒌𝒈 𝒎 𝟐 𝒔 𝟐𝑬 𝒌 = 𝟏 𝟐 𝒎 𝑽 𝟐𝑆𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝑉: 𝑉= 𝐸 𝑘 𝑚𝑉= 2 (2.33 𝑥 1 0 −19 𝑘𝑔 𝑚 2 𝑠 −2 ) (9.109 𝑥 1 0 −31 𝑘𝑔) =7.15 𝑥 𝑚/𝑠
22IntroPlanck and Einstein were able to determine that energy transferred to or from an electron must be quantized.However, the question yet to be answered is: What determines the allowed energies of emission of a given element?The physical nature of photons and electrons needed to be understood before this issue could be addressed
23A New Wave of ThoughtMany years prior to Einstein’s photoelectric effect experiment, it had been proposed that light was comprised of wavesThomas Young was the first physicist to propose that light was of wave-like character, not particle like as proposed by Issac NewtonTo test his hypothesis, Young conducted the ‘slit experiment’
24Light As Waves? Young’s Slit Experiment (1799) If light were made of only particles, then light passing through a slight of height X would appear on a screen with the size and shape of the slitWhat Young observed, however, was a series of light and dark fringesThis was the first indication of the wave-like character of light
25Constructive and Destructive Interference The observed diffraction pattern of light can be explained by treating light as waves with certain wavelengths and amplitudes.Waves of light that are in phase, can interact, forming a single wave of larger amplitude. This is called constructive interference (a).Waves that are out of phase will deconstruct (b), yielding a lower amplitude (destructive interference).Remember:wavelength determines coloramplitude dictates brightness
26Double Slit Experiment To confirm his hypothesis and prove his idea of constructive interference, Young repeated the experiment using two slits.If light were indeed composed of waves, and the fringes due to constructive interference, then the light fringes should be twice as bright. The dark ones should be more defined. He was correct.Young’s sketch of the interference, 1807.
28Back To the Photoelectric Effect In class yesterday, we described the photoelectric effect (Einstein, 1905)Electrons are bound to the metal atoms. The energy of this bond is the threshold energy. In other words, it takes this much energy to ‘loosen’ the electronWhen photons strike a metal surface, one of three scenarios can occur:The photon has an energy which is less than the threshold energy. So, the photon is not absorbed and nothing happens.The photon has EXACTLY enough energy to separate an electron from the metal atom. However, there is no energy left for the electron to move. Motion REQUIRES kinetic energyThe photon has EXCESS energy. The excess energy is converted to kinetic energy, and the electron moves away at some velocity (speed) v.
29SchematicEp = hνpEkElectrons bound by energy E= hvT
30Compton Scattering λ’ λ Einstein’s Photoelectric effect suggested that photons had momentum, a property of particlesCompton asserted… “If EMR is made of particles, lets hit something with it”This lead to the discovery of the ‘Compton Scattering’X-rays were found to ‘bounce’ off of electrons at calculated angles, like pool balls, and with an energy lower than the initial energyThis further supported particle-like behaviorλ’λ
31What now?Young’s slit experiments did not mean that Newton was wrong about the particle nature of EMREinstein’s and Compton’s work did not prove that Newton was correctWhat these experiments DID prove, was that physicists had to develop a new theory that fused both the wave and particle-like aspects of EMR into a single theory
32DeBroglie’s ApproachDeBroglie combined Einstein’s special theory of relativity with Planck’s quantum theory to create the DeBroglie relation. In short, he summates that if waves are particle-like, then particles, and hence, mass, are wave-like.Einstein (particle like): E = pc (p is momentum, p= m 𝑉 )Planck (wave like) : E = hνDeBroglie (both) : pc = hνpc = ℎ𝑐 λ p = ℎ λ pλ = hλD = h/pThe value, λD is the DeBroglie wavelength, or the wavelength of any mass m with momentum p.Louis DeBroglie ( )
33DeBroglie’s Hypothesis Confirmed Below are diffraction patterns of Aluminum foil. The left image is formed by bombarding Al atoms with X-rays. The right image is formed with an electron beam.As shown, both the EMR and electrons behave in the same wave-like mannerBoth exhibit the wave-like ability of diffraction
34ExamplesCalculate the DeBroglie wavelength of an electron travelling at 1.00% of the speed of light.What is the DeBroglie wavelength of a golf ball which weighs 45.9 g and is traveling at a velocity of 120 miles per hour?First, convert velocity to meters per secondλ 𝐷 = ℎ 𝑝 = 𝑥 1 0 −34 𝐽 𝑠 𝑥 1 0 −31 𝑘𝑔 𝟑.𝟎𝟎 𝒙𝟏 𝟎 𝟔 𝒎 𝒔 −𝟏 =2.43 x 1 0 −10 𝑚𝑉 = 120 𝑚𝑖 ℎ𝑟 𝑥 5280 𝑓𝑡 𝑚𝑖 𝑥 𝑚 𝑓𝑡 𝑥 ℎ𝑟 3600 𝑠 =53.6 m/sλ 𝐷 = ℎ 𝑝 = 𝑥 1 0 −34 𝐽 𝑠 𝑘𝑔 𝑚 𝑠 −1 =2.69 x 1 0 −34 𝑚DeBroglie wavelength of large objects is negligible
35Quantum ConditionRecall the Bohr model of the atom. Bohr used DeBroglie’s theory to justify why electrons are restricted to certain orbits around the nucleus.As shown above, if the waves of the electron do not match after a revolution, you will have progressive destructive interference, and the waves will cancel.Thus, the orbits will only be stable if some whole number of orbits, n, around the nucleus fit the circumference (2πr) of the orbit.
36Quantum Condition Therefore: We define n as the principle quantum number. Bohr showed that an electron in a given orbit can ONLY have the following energy:𝐸 𝑛 = − 𝑎𝐽 𝑛 2We say that the energy of the electrons in each level is quantized.Each orbit represents an allowed state, or energy level in which an electron can reside.n =3n =2n =1
37Transitions 𝐸 𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸 𝐼 − 𝐸 𝐹 The lowest energy state is called the ground state. When an electron is transitioned to a higher state, the electron is said to be excited, or in an excited state.Now, we can understand why certain elements can only emit at certain wavelengths….because only certain transitions exist depending on the circumference of the orbits around the nucleusThus, when atoms absorb energy, electrons move to an excited state. When they return to the ground state, the atom emits a photon to release the energy. The energy of the photon is the difference in energy between the initial and final states:𝐸 𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸 𝐼 − 𝐸 𝐹
38ExampleWhat would the wavelength of emitted light be, in nm, if an excited hydrogen electron in the n=4 state relaxes back to the n=2 state?E𝐸 𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸 𝐼 − 𝐸 𝐹n=4n=2= 𝐸 4 − 𝐸 2= − 𝑎𝐽 − − 𝑎𝐽 2 2n=1=𝟎.𝟒𝟎𝟖𝟖 𝒂𝑱λ = ℎ𝑐 𝐸 = (6.626 𝑥 1 0 −34 𝐽𝑠)(3.0 𝑥1 0 8 𝑚 𝑠 −1 ) (.4088 𝑥 1 0 −18 𝐽) =486 𝑛𝑚
39Atomic Emission Spectra of Hydrogen There it is!!!
40Transitions for a Hydrogen Atom Emission in the visible region.
41ConclusionsThe work of Planck, Einstein, DeBroglie and Bohr has provided much information into the relationship between EMR and electronic structure.From the understanding that energies are quantized, and that photons and electrons are both wave and particle like, the Bohr model of the atom was able to explain the line spectra of hydrogenWe now know that emission is the result of transitions from quantized energy states. Different atoms have different allowed transitions.The allowed wavelengths of light that can be absorbed and emitted by an atom give insight into the energy states involved in a given process in an atom