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**Lecture 5: Light and the EMR Spectrum (Ch 4.4-4.9)**

Dr Harris Suggested HW: (Ch 4) 13, 19, 20, 21, 22, 28, 29, 31, 37

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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”. 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 means Neon light ?

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EMR: Light and Energy The applied voltage cause the 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, like that which emits from a lamp, is comprised of visible waves Radio waves from a radio are another type of EMR Invisible UV and Infrared rays from the sun are also EMR

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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 is spread and transmitted throughout the water. EMR propagates through the universe as oscillating, perpendicular electric and magnetic fields

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**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

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**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

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The Visible Spectrum ROY G. BIV (increasing Energy)

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**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?

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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.

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**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

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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.

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**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” Classical physics predicts that continuous heating 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

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**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 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 = nhν where En is the total energy in J, n is the number of photons, and h is Planck’s constant, x J•s

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Examples Calculate 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)

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**Einstein 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 = hν Using this theory, Einstein sought to understand a phenomena that had defied physics for many years prior… the Photoelectric effect

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**The 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.

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**Excess Energy is Converted to Kinetic Energy**

Plot of Ek vs. ν for 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 𝑉 is the velocity (speed) in meters per second (m/s). The units of energy are Joules (J). slope of line = h 𝑬 𝒌 = 𝟏 𝟐 𝒎 𝑽 𝟐 5.51 x 1014 s-1 Einstein 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

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Example Given 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-1 νphoton = 𝑐 λ = 3.0 𝑥 𝑚 𝑠 − 𝑥 1 0 −7 𝑚 =1.428 𝑥 𝑠 −1 𝑬 𝒌 = 𝑬 𝒑𝒉𝒐𝒕𝒐𝒏 − 𝑬 𝑻 substitute: 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

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Example Continued. From the example on the previous page, calculate the velocity of the electron? Mass of electron = x kg Joule = 𝒌𝒈 𝒎 𝟐 𝒔 𝟐 𝑬 𝒌 = 𝟏 𝟐 𝒎 𝑽 𝟐 𝑆𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝑉: 𝑉= 𝐸 𝑘 𝑚 𝑉= 2 (2.33 𝑥 1 0 −19 𝑘𝑔 𝑚 2 𝑠 −2 ) (9.109 𝑥 1 0 −31 𝑘𝑔) =7.15 𝑥 𝑚/𝑠

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**Section 2. Wave-Particle Duality**

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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

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A New Wave of Thought 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’

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**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

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**Constructive 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 color amplitude dictates brightness

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**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.

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Real Example

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**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 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 energy The photon has EXCESS energy. The excess energy is converted to kinetic energy, and the electron moves away at some velocity (speed) v.

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Schematic Ep = hνp Ek Electrons bound by energy E= hvT

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**Compton Scattering λ’ λ**

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

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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 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

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DeBroglie’s Approach DeBroglie 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 = hν DeBroglie (both) : pc = hν pc = ℎ𝑐 λ p = ℎ λ pλ = h λD = h/p The value, λD is the DeBroglie wavelength, or the wavelength of any mass m with momentum p. Louis DeBroglie ( )

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**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

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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 λ 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 𝑚 𝑉 = 120 𝑚𝑖 ℎ𝑟 𝑥 5280 𝑓𝑡 𝑚𝑖 𝑥 𝑚 𝑓𝑡 𝑥 ℎ𝑟 3600 𝑠 =53.6 m/s λ 𝐷 = ℎ 𝑝 = 𝑥 1 0 −34 𝐽 𝑠 𝑘𝑔 𝑚 𝑠 −1 =2.69 x 1 0 −34 𝑚 DeBroglie wavelength of large objects is negligible

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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.

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**Quantum 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 2 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

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**Transitions 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 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: 𝐸 𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸 𝐼 − 𝐸 𝐹

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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 𝐸 𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸 𝐼 − 𝐸 𝐹 n=4 n=2 = 𝐸 4 − 𝐸 2 = − 𝑎𝐽 − − 𝑎𝐽 2 2 n=1 =𝟎.𝟒𝟎𝟖𝟖 𝒂𝑱 λ = 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

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**Atomic Emission Spectra of Hydrogen**

There it is!!!

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**Transitions for a Hydrogen Atom**

Emission in the visible region.

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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

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Section 5.3 Physics and the Quantum Mechanical Model

Section 5.3 Physics and the Quantum Mechanical Model

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