Lesson Plan and Lesson note on Physics
Duality of Matter
Subject: Physics
Theme: Energy Quantization And Duality Of Matter
Topic: Duality of Matter
Sub Topic:
Date: dd/mm/yyyy
Class: S.S 3
Average Age: 16 years and above
Duration: 40 Minutes
No of Learners: 40
At the end of the lesson, the students should be able to:
1. Explain what Duality of Matter is.
Duality of matter is the state of matter having two natures which is often applied in physics. The classic example is wave-particle duality. The elementary constituents of nature electrons, quarks, photons, gravitons etc. which behaves in some aspects like particles and in others like waves.Observing a light is one of the easiest ways to prove the duality between a particle and a wave. Since light is similar to waves, it can diffract, refract, interface, etc.
There are therefore two theories of matter;
a. The wave theory (Electron Diffraction).
b. The particle theory (Photoelectric Effect).
Experiment like electron diffraction shows that matter behaves like a wave but other phenomena such as photo-electric effect and Compton effect shows that matter behaves like a stream of particle or photons. This behavior of matter having two identity in different circumstances shows the duality of matter. This is referred to as the wave-particle duality or the wave-particle paradox. As in matter, so it is light. Some observable phenomenon in the nature of light such as reflection, refraction, diffraction, interference and polarization can be interpreted or explained by assuming that light (or matter) behaves like waves. But other observable phenomena such as emission and absorption of light, photo-electricity, radiation of energy from heated bodies, thermionic emission.
2. Defined Wave-Particle Duality.
Wave-Particle Duality is a principle that matter (light and all other electromagnetic radiation may be considered a particle or a wave nature) have properties typical of both waves and particles. Depending on conditions, light could be viewed as either a wave or a particle.3. State/explain Theories of Wave Particle Duality
Many physicists have derived theories that summarize the existence of wave-particle matter duality. Further, it has been depicted that the larger the wave amplitude the larger is the probability of finding the particle.-
The probability of looking for the electron is smaller in the case of smaller wave amplitude. Thus, when electron emission takes place then the kinetic energy gets released. The greater is the intensity; the greater is the release of energy. This also raises that wave is proportional to amplitude.
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The interference pattern for electrons passing through very closely spaced slits demonstrates that quantum particles such as electrons can exhibit wavelike behavior.
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The experimental results illustrated here demonstrate the wave–particle duality in electrons. The electrons pass through very closely spaced slits, forming an interference pattern, with increasing numbers of electrons being recorded from the left image to the right. With only a few electrons recorded, it is clear that the electrons arrive as individual localized “particles,” but in a seemingly random pattern. As more electrons arrive, a wavelike interference pattern begins to emerge. Note that the probability of the final electron location is still governed by the wave-type distribution, even for a single electron, but it can be observed more easily if many electron collisions have been recorded.
(a) De Broglie Wavelength
In 1923 physicists Louis De Broglie proposed that any particle of matter having momentum (p) has an associated wavelength (λ).
i.e λ α 1/p
De Broglie Wavelength formula is given by λ = h/p
Where, h is the Planck constant h = 6.63 x 10-34 Js
for a particle of momentum mv, the wavelength is given by
λ = h/mv
This equation is also applicable for photons too.
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Albert Einstein’s theory of photoelectric effect significantly contributed to De Broglie’s Theory and acted as proof that particles and waves could overlap. Light can also be observed in the form of a particle called a photon. When light is seen on certain objects, electrons are released. A certain amount of energy is needed to eliminate an electron from the surface of an object. So, an electron will be emitted when a photon of greater energy than an electron hits a solid.
When the electrons are emitted, they also release kinetic energy. According to classical wave theory, the greater the intensity, the greater the energy. Because the energy of a wave is directly proportional to its amplitude, it was complex for scientists to find high-intensity lights that did not affect its overall kinetic energy.
(b) Newton’s Corpuscular theory
Newton said that light composes of corpuscles. These corpuscles travel in straight lines. The law of reflection justifies the wave feature of light if it bounces off from a planar surface after reflection. However, in the case of refraction, the light moves slowly in dense material that tells about the particle-like nature of light.
(c) Huygens Wave theory
It was proposed by Huygens in 1678. The theory states that every point of the light waveform is a source of a spherical wave. It greatly supports the theory by physicists like Kirchhoff and Fresnel.
(d) Quantum view of the light
The light depicting particle properties on a quantum atoms scale is proven by the photoelectric effect. Moreover, the theory said that there will be particle treatment of light refraction by obtaining adequate localization of energy for the ejection of electrons from the surface.
(e) Duality of Photons
A single photon can showcase a distinctive interference fringe. This property is visible when light is in a very weak state due to an extremely high brightness index. Thus, when light projects on a large screen in this state, it creates a scattering towards the border. We refer to this phenomenon as the Duality of Photons.
(f) Heisenberg uncertainty principle
The Heisenberg uncertainty principle is one of the best principles that agree with the wave-particle duality as well as De Broglie’s equation.
It states that measured value cannot assign to the position (x) and momentum (p) of a particle simultaneously with the unlimited precision
Mathematically, ∆x∆px ≥ h/4π
or ∆x(m∆vx) ≥ h/4π
or ∆x∆vx ≥ h/4πm
Where,
∆x is the uncertainty in the position of the particle,
∆p is the uncertainty in the momentum of the particle,
∆v is the uncertainty in the velocity of the particle,
m is the mass of the particle,
h is Plank’s constant.
In the Heisenberg Uncertainty principle, it states that momentum and position cannot be predicted at a time, which is based on the particle assumption. So, there should be a wave nature associated with this, which is discussed in quantum mechanics.
4. Calculate the Wavelength of a Particle
EXAMPLE 1.
If an electron travels at a velocity of 1.0 × 107 m/s and has a mass of 9.109 × 10–28 g, what is its wavelength?
[h= 6.63 x 10-38 Js]
SOLUTION
λ = ?
v = 1.0 × 107 m/s
m = 9.109 × 10–28 = 9.109 ÷ 1000–28
m = 9.109 × 10–25 kg
h = 6.63 x 10-34
λ = h/mv
λ = 6.63 x 10-34 ÷ (9.109 × 10–25 x 1.0 × 107)
λ = 7.278 x 10-17 m
EXAMPLE 2.
Calculate the wavelength of a softball with a mass of 100 g traveling at a velocity of 35 m/s, assuming that it can be modeled as a single particle.
[h= 6.63 x 10-38 Js]
SOLUTION
m = 100g = 0.1 kg
v = 35 m/s
h= 6.63 x 10-38 Js
λ = h/mv
λ = 6.63 x 10-34 ÷ (0.1 x 35)
λ = 1.9 × 10–34 m
5. List and explain Application of wave nature of the article
1. Electron microscope
An electron microscope offers an important and interesting example of the dual nature of electrons. An electron beam can be used to form an image of an object much similar to that of light. So here, the wave nature of the electron comes into the picture for image formation, which is an application of De Broglie’s theory.
2. Atomic spectra
Every neutral atom consists of at least one electron. So when a material is heated, it emits light and different materials have different types of light. This is because of the dual nature of the matter again, which is proved by De Broglie’s theory.
3. Bohr’s atomic model
According to Bohr’s atomic model, the angular momentum of the electron is quantized.
Rationale:
Matter sometimes behaves as a wave and at other times as particles.
There are therefore two theories of matter;
a. The wave theory.
b. The particle theory.
Wave Nature of Matter (Electron Diffraction).
In the Davisson and Germer experiment, a beam of electrons emitted froma heated filament was made to impinge on a layer of a thin metal film orcrystal at C. The electrons were diffracted and the diffraction rings wereproduced on a photographic plate placed behind the thin metal film. If thevoltage V on the anode was increased, the velocity, V, of the electrons wasincreased. The rings were then seen to become narrower. The wavelength,λ, of the electron waves decreases with increasing electron velocity.
λ = h/mv
mv = momentum of the object
h = planck’s constant
Experiments showed that protons, neutrons and other particles have the wave property of diffraction.
Prerequisite/ Previous knowledge:
Photoelectric Effect.
Learning Resources:
Flash cards, an audio and video youtube examples, Available useful objects.
Reference Materials:
1. New system physics for secondary school by Dr. Charles chew etal
2. New school physics by M. W Anyakoha
3. Internet facility
Lesson Development:
STAGE |
TEACHER'S ACTIVITY |
LEARNER'S ACTIVITY |
LEARNING POINTS |
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| STEP 1: INTRODUCTION Individual Student |
The teacher asks the students the following questions: Draw and label the modern X-ray tube. |
The students expected answers:
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Identification of Prior Ideas and revising previous lesson |
| STEP 2: Development and Grouping |
The teacher asks students to form groups and choose their leaders and secretaries.
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The students form groups and choose their leaders and secretaries. The students write down what the teacher explains and listen attentively. |
Inculcating leadership skills, competitive spirit, cooperation, teamwork and a sense of responsibility among learners. Concept of Duality of matter |
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| STEP 3: EXPLORATION Entire Class |
The teacher’s leads the students to understand from the PARTICLE NATURE OF MATTER (Photoelectric Effect) and the THE COMPTON EFFECT (Particle Nature of matter) that the wave-particle duality refers to the idea that light and
matter (such as electrons) have both wave and particle properties, that is, light behaves either as wave or as a particle but not as both
simultaneously.
PARTICLE NATURE OF MATTER (Photoelectric Effect)When light falls on a metal surface, electros are emitted from the surface. Similarly, when X-ray is allowed to fall on the surface of a thin sheet of metal like gold, the X-ray not only produces diffraction pattern but also acting like particles they may collide with the atoms of the metal and eject electrons as in the photoelectric effect.THE COMPTON EFFECT (Particle Nature of matter)When a single X-ray photo collides with a free electron, the electron recoils off as though it were a perfectly elastic sphere. This is the Compton effect. The scattered photon has a slightly lower frequency than the incident X-ray photon. Here matter inform of X-rays behave as a particle. The recoiling photon and electron are able to conserve energy and momentum. |
The students write down what the teacher explains and listen attentively. | Definition of wave-particle duality. |
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| STEP 3: DISCUSSION Entire class |
The teacher state/explain theories of wave particle duality with the students.
1. Heisenberg uncertainty principleHeisenberg uncertainty principle states that it is impossible to know accurately the exact position and momentum of a particle simultaneously. The uncertainty in the momentum multiplied by the uncertainty in the position approximately equals the planck’s constant, h.The process of making a measurement tends to alter the quantity being measured. It is impossible in principle to make precise measurement of both the position (x) and momentum (ρ) of a particle simultaneously. The more precisely the location of the particle has to be specified, the more uncertainty is introduced into the determination of its momentum. Any such measurements have inbuilt uncertainties; Δx in position and Δρ in the momentum. 2. De Broglie Wavelength
In 1923 physicists Louis De Broglie proposed that any particle of matter having momentum (p) has an associated wavelength (λ). |
The students copied the worked examples. | Better understanding of of wave particle duality. |
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| The teacher guides the students to calculate the wavelength of an electron. EXAMPLE 1. If an electron travels at a velocity of 1.0 × 107 m/s and has a mass of 9.109 × 10–28 g, what is its wavelength? [h= 6.63 x 10-38 Js] SOLUTION λ = ? velosity (v) = 1.0 × 107 m/s m = 9.109 × 10–28 g = 9.109 ÷ 1000–28 m = 9.109 × 10–25 kg h = 6.63 x 10-34 λ = h/mv λ = 6.63 x 10-34 ÷ (9.109 × 10–25 x 1.0 × 107) λ = 7.278 x 10-17 m EXAMPLE 2. If electrons are accelerated from rest through a potential difference of 10kv, what is the wavelength of the associated electrons? (me = 9.1 × 10-31 kg, e = 1.6× 10-19 C, h = 6.6× 10-34 JS) SOLUTION accelerating potential difference v = 10kv = 10 x 103 v potential difference (v) = 10000v Wavelength λ = h/√(2eVme) λ = 6.6×10-34 ÷ √(2×1.6×10-19 × 10000 ×9.1×1031) λ = 1.22 × 10-11 m |
The students write down the questions and listen attentively to teacher. | Worked examples | |
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| STEP 4: APPLICATION Entire class |
The teacher ask the students to read through all they have copied and give more discussion/explanation as directed by the teacher. They take corrections where they are wrong. | The students did what the teacher ask them to do. | Better understanding of Wave Particle Duality. |
| STEP 5: EVALUATION Individual students |
The teacher asks the students questions to test them. 1. Who invented the Wave Particle Duality? 2. How is light both a wave and a particle? 3. Why is wave particle duality important? 4. State the De Broglie Wavelength formula. 5. What is wave-particle duality? 6. Who explained the photo-electric effect? 7. List the process which proves the wave nature of light? 8. Which process describes the particle nature of light? 9. What is the wavelength of a falling grain of sand? If the grain’s mass is 5×10-10 kg and its diameter is 0.07mm, it fall in the air with a terminal speed of about 0.4 m/s? |
The students respond to the questions correctly. SOLUTION 1. In the year 1924, a French physicist by the name of Louis de Broglie postulated the theory that electrons and other components of matter have a distinctive wavelength and frequency. 2. Albert Einstein stated in his theory of light that photons, one of the primary components of light, flow in the form of waves. However, using Einstein’s own Quantum theory of Light he was also able to justify that light energy is directly relatable to its own Oscillating frequency. 3. The behavioural analysis of light and matter can simultaneously solve by using the differential equation of wave function. Moreover, this was the most significant derivative of Wave Particle Duality developed using the Schrodinger equation. 4. De Broglie Wavelength formula is given by λ = h/p 5. Wave-particle duality is the main concept of quantum mechanics, which explains how light behaves as particles and waves. 6. Albert Einstein explained the photo-electric effect. 7. The process which proves the wave nature of light are: Photoelectric effect, absorption and emission by atoms. 8. Diffraction and interference describes the particle nature of light. 9. m = 5×10-10 d = 0.07mm = 7×10-5 m v = 0.4 m/s The magnitude of its momentum is p = mv λ = h/p λ = h/mv λ = 6.626×10-34 ÷ (5×10-10 x 0.4) λ = 3.308×10-24 m So this wavelength is very small. That’s why we cannot observe this in real life. A more massive and high moving body has more momentum and even smaller de Broglie wavelength. The effect of such tiny wavelengths is so small that they are never noticed in our daily life. |
Asking the learners questions to assess the achievement of the set objectives. |
| CONCLUSION | The teacher concluded the lesson We have heard about the nature of light and the characters it displays. Interference, reflection, refraction and diffraction are some of the characteristics. Wave-Particle Duality helps us to understand the particle and wave nature of light. Based on the idea that light and all other electromagnetic radiation may be considered a particle or a wave nature |
The students write down the conclusion of the lesson and listen attentively. | Better understanding of Wave Particle Duality. |
| ASSIGNMENT | The teacher gives learners take home. 1. Calculate the wavelength of a baseball, which has a mass of 149 g and a speed of 100 min/h. (Answer: 9.95 x 10-35 m) 2. Calculate the wavelength of a neutron that is moving at 3.00 × 103 m/s (in Å or pm). (Answer: 1.32 Å, or 132 pm) 3. Calculate the wavelength (in meters) associated with a 42 g baseball with speed of 80 m/s. (Answer: 1.97 x 10-34 m) 4. Calculate the de Broglie wavelengths of the following: a) An 8g bullet with velocity 340 m/s. (Answer: 2.44 x 10-33 m) b) A 10-5 g particle with velocity 10-5 m/s. (Answer: 6.626 x 10-21 m) c) A 10-8 g particle with velocity 10-8 m/s. (Answer: 6.626 x 10-15 m) d) An electron moving with velocity 4.8 x 106 m/s. (Answer: 1.52 x 10-10) |
The learners copy the assignment | Better understanding of Wave Particle Duality. |