Lecture 6: Light and the Electromagnetic Spectrum

1. Lecture 6: Light and the Electromagnetic Spectrum Dr Harris 9/5/12 HW: Ch 4: 21, 22, 27-30

2. The vast majority of our present understanding of the electronic structure of atoms has come from the light that is absorbed and emitted by substances • For example, what happens when you switch on a • Neon lights are glass chambers pressurized with Neon or other noble gases • When a voltage is applied, the gas is ionized. This ionization causes a “glow”. • Whydoes this phenomena occur? • What further information can this provide us about the electronic structure of atoms? • Over the course of the next two lectures, we will be able to understand exactly what’s happening, and what it means Neon light ?

3. EMR: Light and Energy • The electric current that flows through the lights causes the gases electrons to become excited, or “bumped up” in energy • When 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 waves • Light, such as that which emits from a lamp is comprised of visible waves • Radio waves from a radio are another • Invisible UV and Infrared rays from the sun are also EMR

4. Propagation of Waves • The waves created in water when an external force is applied are an example of propagation. • The energy transferred to the spot of impact when the droplet strikes the surface is spread and transmitted throughout the water. • EMR propagates through the universe as oscillating, perpendicular electric and magnetic fields

5. Wavelength 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 = c c is the speed of light, 3.0 x 108 m/s. All EMR moves at this speed through vacuum

6. Different Types of EMR Have Different Wavelengths • The electromagnetic spectrum below shows EMR listed by increasing wavelength • Wavelengths vary from the size of an atomic nucleus to the length of a football field

7. The Visible Spectrum ROY G. BIV (increasing Energy)

8. Examples • 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?

9. Continuous Spectra • White 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. • Just something to know: Sunlight is actually white, but absorption and scattering of light by the atmosphere causes the sky to appear blue and the sun to appear yellow.

10. Line (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 spectra • Sodium burns very brightly and emits an orangish-yellow color: Discontinuous spectrum

12. Max Planck • The observation of spectral lines indicates that certain elements can only emit certain wavelengths • How 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.

13. Blackbody 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” • The old laws of physics (Classical physics) would predict that if you continued to heat a body, you would produce higher and higher frequencies at increasing intensity • This means that light bulbs would give off UV, gamma, X-rays, and so on. Of course, this doesn’t happen

14. The 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 radiation can only be emitted in small, exact amounts called quanta • He then derived the amount of energy absorbed or released in a single event is equal to: E = nhν where E is the total energy in J, n is the number of quanta, and h is Planck’s constant, 6.626 x 10-34Js

15. Examples • Calculate the energy contained in a single quanta of blue light (~400 nm) • Calculate the energy of contained in 10 quanta of green light (~520 nm) • A laser beam of yellowish light (~550 nm) emits 1018quanta per minute. How much energy is emitted per hour?

16. Einstein and the Photon • Like Planck, Einstein envisioned light as a beam of particles, each consisting of equal energy. He called these particles photons. • Borrowing from Planck’s theory, he asserted that each photon in the beam is a little packet of energy E = hν • Using this theory, Einstein sought to understand a phenomena that had defied physics for many years prior… the Photoelectric effect

17. The Photoelectric Effect • The photoelectric effect is the ejection of electrons from metal surface under illumination. • Photons of low frequency, no matter how intense the beam, will not eject an electron from a metal surface. • It is not until the 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 is ejected at higher and higher velocities.

18. Excess Energy is Converted to Kinetic Energy Plot of Ek vs. νfor sodium • The 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 is the velocity (speed) in meters per second (m/s). The units of energy are Joules (J). slope of line = h 5.51 x 1014 s-1 • Einstein found that as you increase the energy of the photons striking the metal, the energy beyond the threshold energy (excess) is converted intokinetic energy. Thus,

19. http://phet.colorado.edu/en/simulation/photoelectric

20. Example • Given that the threshold frequency of copper is 1.076 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 = 1.076 x 1015 s-1 νphoton= substitute:

21. Example Continued. • From the example on the previous page, calculate the velocity of the electron? • Mass of electron = 9.109 x 10-31 kg. Joule

22. Section 2. Wave-Particle Duality

23. Intro • Planck 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

24. Many years prior to Einstein’s photoelectric effect experiment, it had been proposed that light was comprised of waves • Thomas Young was the first physicist to propose that light was of wave-like character, not particle like as proposed by Issac Newton • To test his hypothesis, Young conducted the ‘slit experiment’

25. Light 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 slit • What Young observed, however, was a series of light and dark fringes • This was the first indication of the wave-like character of light

26. Constructive and Destructive Interference • The observed diffraction patternof 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 color • amplitude dictates brightness

27. Double 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.

28. Real Example

29. Back 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 electron • When 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 EXACTLYenough energy to separate an electron from the metal atom. However, there is no energy left for the electron to move. Motion REQUIRESkinetic energy • The photon has EXCESS energy. The excess energy is converted to kinetic energy, and the electron moves away at some velocity (speed) v.

30. Schematic E = hνphoton Ek

31. Compton Scattering • Einstein’s Photoelectric effect suggested that photons had momentum, a property of particles • Compton 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 energy • This further supported particle-like behavior λ’ λ

32. What now? • Young’s slit experiments did not mean that Newton was wrong about the particle nature of EMR • Einstein’s and Compton’s work did not prove that Newton was correct • What these experiments DIDprove, was that physicists had to develop a new theory that fused both the wave and particle-like aspects of EMR into a single theory

33. DeBroglie’s Approach • DeBroglie combined Einstein’s special theory of relativity with Planck’s quantum theory to create the DeBroglierelation. In short, he summates that if waves are particle-like, then particles, and hence, mass, is wave-like. Einstein (particle like): E = pc (p is momentum, p= m) Planck (wave like) : E = hν DeBroglie (both) : pc = hν pc = p = pλ = h λD = h/p • The value, λD is the DeBroglie wavelength, or the wavelength of any mass m with momentum p. Louis DeBroglie (1892-1987)

34. DeBroglie’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 manner Both exhibit the wave-like ability of diffraction

35. Examples • Calculate 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 second • DeBroglie wavelength of large objects is negligible

36. Quantum Condition • Recall 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.

37. Quantum Condition • Therefore: n = 1,2,3…. • We define n as the principle quantum number. Bohr showed that an electron in a given orbit can ONLY have the following energy: • We 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 =3 n =2 n =1

38. Transitions • The lowest energy state is called the groundstate. When an electron is transitioned to a higher state, the electron is said to be excited, or in an excitedstate. • 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 nucleus • Thus, 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:

39. Example • What 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? E n=4 n=2 n=1 λ

40. Atomic Emission Spectra of Hydrogen There it is!!!

41. Transitions for a Hydrogen Atom Emission in the visible region.

42. Conclusions • The 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 hydrogen • We 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