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**2.5.2 The Photoelectric Effect 2.5.3 Wave-Particle Duality**

5 Quantum Mechanics G482 Electricity, Waves & Photons 2.5.1 Energy of A Photon 2.5.2 The Photoelectric Effect 2.5.3 Wave-Particle Duality 2.5.4 Energy Levels in Atoms Ks5 OCR Physics H158/H558 Index Mr Powell 2012

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Introduction.... The aim of this module is to introduce the concept of quantum behaviour. How do we know that light is a wave? The evidence for this comes from diffraction of light. However, this wave-like behaviour cannot explain how light interacts with electrons in a metal. A revolutionary model of light (photon model), developed by Max Planck and Albert Einstein, is needed to describe the interaction of light with matter. Physicists expect symmetry in nature. If light can have a dual nature, then surely particles like the electron must also have a dual nature. We study the ideas developed by de Broglie. The final section looks briefly at the idea that electrons in atoms have discrete bond energies and they move between energy levels by either absorbing or by emitting photons. There are many opportunities to discuss how theories and models develop with the history of wave-particle duality.

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**Practical Skills are assessed using OCR set tasks.**

The practical work suggested below may be carried out as part of skill development. Centres are not required to carry out all of these experiments. This module does not lend itself to many experiments carried by the students. However, it does contain many revolutionary ideas and engaging students in discussions is vital when demonstrating some of the experiments. Use a GM tube to ‘count’ gamma ray photons. Determine the wavelength of light from different LEDs Demonstrate the photoelectric effect using a photocell or a negatively charged zinc plate connected to an electroscope. Observe ‘diffraction rings’ for light passing through a tiny hole. Demonstrate the diffraction of electrons by graphite. Observe emission line spectra from different discharge tubes. (A hand-held optical spectrometer can be used to observe Fraunhofer lines in daylight. Caution: Do not look directly at the Sun.)

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**Discovery of the Electron**

Activities... Show how a GM tube clicks when detecting ‘gamma waves’ from a radioactive source. Discuss the implication of the ‘clicks’ Discuss historical ideas of light at a wave not sufficient for all phenomena. Light then to be seen as stream of particles or quanta of energy. Define a photon and give formula E = hf. Relate with c = fλ to give E = hc/λ Use eV = hc/λ for different LEDs to estimate Planck’s constant from gradient of V-1/λ graph Extend idea of W = eV to other charged particles and hence eV = ½ mv2 Define the electronvolt (eV) as a useful unit of energy on an atomic scale Resources.... Possibly show 12V bulb at different temperatures from variable supply, quickly showing red/orange/yellow/white hot and drawing spectra to illustrate black body radiation Different ‘coloured’ LEDs of given wavelength with variable supply and voltmeter. Measure minimum p.d. to just give illumination Use LHC at as an example of measuring energy in eV and use energy to calculate speed (non-relativistic) of protons Points to Note… Discuss meaning of word quantum in this context. Historical ideas could include discussion of black body radiation and cover areas of HSW Recap W = VQ from definition of p.d. in previous section Discovery of the Electron

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**2.5.1 Energy of A Photon (p172) Assessable learning outcomes....**

(a) describe the particulate nature (photon model) of electromagnetic radiation; (b) state that a photon is a quantum of energy of electromagnetic radiation; (c) select and use the equations for the energy of a photon: E = hf =hc/ (d) define and use the electronvolt (eV) as a unit of energy; (e) use the transfer equation eV = 0.5mv2 electrons and other charged particles; (f) describe an experiment using LEDs to estimate the Planck constant h using the Equation eV = hc/. (no knowledge of semiconductor theory is expected). The teacher can carry out a demonstration using a GM tube to ‘count’ gamma ray photons. Students can carry out an experiment to determine h using LEDs.

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**a/b) Which is laser light & why?**

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**a/b) Photons a General Description...**

Under the photon theory of light, a photon is a discrete bundle, packet or quantum of electromagnetic or light energy. Photons are always in motion and, in a vacuum, have a constant speed of light to all observers of c = x 108 ms-1. Photons have zero mass but carry both energy and momentum, which are also related to the frequency f and wavelength of the electromagnetic wave by E = hf = hc/ (as c = f ) They can be destroyed/created when radiation is absorbed/ emitted. They can have particle-like interactions (i.e. collisions) with electrons and other particles.

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a/b) More on Photons... The photon is an elementary particle, despite the fact that it has no mass. It cannot decay on its own, although the energy of the photon can transfer (or be created) upon interaction with other particles. Photons are electrically neutral and are one of the rare particles that are identical to their antiparticle, the antiphoton. Not needed for AS - Photons are spin-1 particles (making them bosons), which means that their energy is polarised in a direction. This feature is what allows for polarisation of light. (i.e. TV aerials) (only need to know the outcome!)

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**They are like little squiggles of energy! **

(b) state that a photon is a quantum of energy of electromagnetic radiation; All EM radiation can be thought of “photons” or “packets” or a “quantum” of energy. They are like little squiggles of energy! If we take a photo like this shown using a photon sensor the results are strange. Instead of a dim pattern getting stronger we have dots which add to the image. This experiment is evidence that light is a stream of some type of particle-like object. (in certain conditions) In fact many experiments convincingly lead to the surprising result that electromagnetic waves, although they are waves, have a particle-like nature. These particle-like components of electromagnetic waves are called photons.

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**(a) describe the particulate nature (photon model) of electromagnetic radiation;**

The photon model of electromagnetic waves consists of three basic postulates: Electromagnetic waves consist of discrete, massless units called photons. A photon travels in vacuum at the speed of light, “c = 3 x 108ms-1 Each photon has energy E = hf where f is the frequency of the wave and h is a universal constant called Planck’s constant. The value of Planck’s constant is In other words, the electromagnetic waves come in discrete “chunks” of Energy. The superposition of a sufficiently large number of photons has the characteristics of a continuous electromagnetic wave.

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**(c) select and use the equations for the energy of a photon: E = hf =hc/**

The known constants for these calculations are always; h=6.63 x10-34Js c=3.00 x 108 ms-1 Using our formulae of E = hf or since c=f , f= c/ we could say for neatness and simplicity that; E = hc/ Try working out the energies for different frequencies of visible light to test out your skills. You should get a range of answers i.e. 3 x 10-19J. Try 350nm, 590nm, 700nm 350nm = 5.68 x 10-19J 590nm = 3.37 x 10-19J 700nm = 2.84 x 10-19J High Energy Low Energy

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**(c) select and use the equations for the energy of a photon: E = hf =hc/**

The known constants for these calculations are always; h=6.63 x10-34Js c=3.00 x 108 ms-1 Using our formulae of E = hf or since c=f , f= c/ we could say for neatness and simplicity that; E = hc/ Try working out the energies for different frequencies of visible light to test out your skills. You should get a range of answers i.e. 3 x 10-19J. Try 350nm, 590nm, 700nm 350nm = 590nm = 700nm = High Energy Low Energy

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**(d) define and use the electronvolt (eV) as a unit of energy; (recap)**

Charge on the electron is 1e = 1.6x10-19 C (eq1) But we also know from electrical circuits; 1V = 1 JC-1 So by multiplying equation 1 by 1V on each side we get: 1e x 1V = 1V x 1.6x10-19 C (eq2) Then sub in 1JC-1 for the voltage part on the RHS of (eq2) gives us; 1e x 1V = 1JC-1 x 1.6x10-19 C This leaves us with definition: 1eV = 1.6x10-19 J 1MeV = 1x 106 x 1eV We can use this a smaller version of the joule (not a smaller version of the volt!) Convert these photon energies from Joules to eV 5.68 x 10-19J = eV 3.37 x 10-19J = eV 2.84 x 10-19J = eV

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**(d) define and use the electronvolt (eV) as a unit of energy; (recap)**

Charge on the electron is 1e = 1.6x10-19 C (eq1) But we also know from electrical circuits; So by multiplying equation 1 by 1V on each side we get: Then sub in 1JC-1 for the voltage part on the RHS of (eq2) gives us; This leaves us with definition: We can use this a smaller version of the joule (not a smaller version of the volt!) Convert these photon energies from Joules to eV 5.68 x 10-19J = eV 3.37 x 10-19J = eV 2.84 x 10-19J = eV

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**(e) use the transfer equation eV = 0**

(e) use the transfer equation eV = 0.5mv2 for electrons and other charged particles;

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**(e) use the transfer equation eV = 0**

(e) use the transfer equation eV = 0.5mv2 for electrons and other charged particles; If we imagine that we have two oppositely charged metal plates in a vacuum with a PD of 5000V between them. A charged particle such as an electron -1.6 x 10-19C is accelerated by the field from one plate to another. Electron has a rest mass of 1/1840 of an a.m.u. Or 9.11 × 10–31 kg. We can find the velocity or Kinetic energy that it gains as..... Units: (Jkg-1 )0.5 = kgm2s-2kg-1)0.5

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**(e) use the transfer equation eV = 0**

(e) use the transfer equation eV = 0.5mv2 for electrons and other charged particles; If we imagine that we have two oppositely charged metal plates in a vacuum with a PD of 5000V between them. A charged particle such as an electron -1.6 x 10-19C is accelerated by the field from one plate to another. Electron has a rest mass of 1/1840 of an a.m.u. Or 9.11 × 10–31 kg. We can find the velocity or Kinetic energy that it gains as..... Units: (Jkg-1 )0.5 = kgm2s-2kg-1)0.5

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**(e) use the transfer equation eV = 0**

(e) use the transfer equation eV = 0.5mv2 for electrons and other charged particles; What would be the velocity of the following particles for a similar PD of 5000V? Proton (mass of × 10–27 kg) Alpha Particle (mass of × 10–27 kg)

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**(e) use the transfer equation eV = 0**

(e) use the transfer equation eV = 0.5mv2 for electrons and other charged particles; What would be the velocity of the following particles for a similar PD of 5000V? Proton (mass of × 10–27 kg) Alpha Particle (mass of × 10–27 kg)

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(f) describe an experiment using LEDs to estimate the Planck constant h using the Equation eV = hc/. (no knowledge of semiconductor theory is expected).

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**This is because it is connected to the positive terminal on the PSU.**

LED.... e- A photodiode is a circuit component which can be used to convert a light signal into an electrical one. Light incident on the thin transparent conducting surface layer of the diode passes through it to be absorbed in the insulating layer. The energy of each photon is sufficient to release one electron in the insulating layer. It is a “quantum” effect based on the idea that that the light behaves as a “quantum” or “photon” The potential difference V applied across the insulating layer causes these electrons to move upwards to the upper conducting layer. This is because it is connected to the positive terminal on the PSU. 3 x incident photons To the circuit

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**Emin =1.78 eV Emax = 3.11 eV Visible Light.... (Recap)**

The energy E, frequency f, and wavelength λ of a photon are related by the formula; where h is Planck's constant and c is the speed of light. For example, the spectrum of visible light consists of wavelengths ranging from 400 nm to 700 nm. Photons of visible light therefore have energies ranging from Emin =1.78 eV Emax = 3.11 eV An electronvolt is also the energy of an infrared photon with a wavelength of approximately 1240 nm. Similarly, 10eV would correspond to ultraviolet of wavelength 124 nm, and so on…… h = 6.63 x Js

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**Using a ICT Spectrometer**

Your teacher will show you some examples of laser light. Can you use E=hf or hc/ to work out the energies of the light involved in Joules and eV? Lastly can you predict an energy that a UV photon might have with a of 253.7nm Source / 1x 10-9m Joules / J x10-19 eV Red 656 Green 532 UV h = 6.63 x Js & c = 3 x 108ms-1

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**Source / 1x 10-9m Joules / J x10-19 eV**

Using a Spectrometer Your teacher will show you some examples of laser light. Can you use E=hf or hc/ to work out the energies of the light involved in Joules and eV? Lastly can you predict an energy that a UV photon might have with a of 253.7nm Source / 1x 10-9m Joules / J x10-19 eV Red 656 3.0 1.9 ± 0.003 Green 532 3.7 2.3 ± 0.002 UV 254 7.8 4.89 ± 0.01 h = 6.63 x Js & c = 3 x 108ms-1

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Revision Question 13. Show that the wavelength of a photon of energy 3.9 eV is 320 nm.

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Revision Question On average, a student uses a computer of power rating 110 W for 4.0 hours every day. The computer draws a current of 0.48 A and its screen emits visible light of average wavelength 5.5 x 10-7m. 1. Calculate the energy of each photon of wavelength 5.5 x 10–7 m emitted from the computer screen. energy = J [3]

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Revision Question

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Revision Question 13. Show that the wavelength of a photon of energy 3.9 eV is 320 nm.

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Revision Question On average, a student uses a computer of power rating 110 W for 4.0 hours every day. The computer draws a current of 0.48 A and its screen emits visible light of average wavelength 5.5 x 10-7m. 1. Calculate the energy of each photon of wavelength 5.5 x 10–7 m emitted from the computer screen. energy = J [3]

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Revision Question

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Connection Connect your learning to the content of the lesson Share the process by which the learning will actually take place Explore the outcomes of the learning, emphasising why this will be beneficial for the learner Demonstration Use formative feedback – Assessment for Learning Vary the groupings within the classroom for the purpose of learning – individual; pair; group/team; friendship; teacher selected; single sex; mixed sex Offer different ways for the students to demonstrate their understanding Allow the students to “show off” their learning Consolidation Structure active reflection on the lesson content and the process of learning Seek transfer between “subjects” Review the learning from this lesson and preview the learning for the next Promote ways in which the students will remember A “news broadcast” approach to learning Activation Construct problem-solving challenges for the students Use a multi-sensory approach – VAK Promote a language of learning to enable the students to talk about their progress or obstacles to it Learning as an active process, so the students aren’t passive receptors

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