Chapter 9: Quantization of Light Max Planck started the revolution of quantum theory by challenging the classical physics and the classical wave theory of light. He proposed the concept of quantization of light to explain black body radiation. Later, Einstein extended the concept to explain the observation in photoelectric effect experiments.
Overview Physical Optics Planck s Quantum Theory Photoelectric Effect
9.1 Planck s Quantum Theory Distinguish between Planck s quantum theory and classical theory of energy. Use Einstein s formulae for a photon energy, E hf hc Learning Objectives
Classical Theory of Black Body Radiation The foundation of the Planck s quantum theory is a theory of black body radiation. Black body is defined as an ideal system that absorbs the entire radiation incident on it. The electromagnetic radiation emitted by the black body is called black body radiation. From the black body experiment, the distribution of energy in black body depends only on the temperature. If the temperature increases thus the energy of the black body increases and vice versa.
Classical Theory of Black Body Radiation The spectrum of electromagnetic radiation emitted by the black body (experimental result) is shown in figure Failed to explain the shape
Classical Theory of Black Body Radiation The Rayleigh-Jeans and Wien s theories failed to fit the experimental curve because this two theories based on classical ideas which are: i. Energy of the EM radiation does not depend on its frequency or wavelength. ii. Energy of the EM radiation is continuously.
Planck s Quantum Theory In 1900, Max Planck proposed his theory that is fit with the experimental curve in figure above at all wavelengths known as Planck s quantum theory. The assumptions made by Planck in his theory are: i. The EM. radiation emitted or absorb by the black body not in a continuous stream of waves but in discrete little bundles (separate) packets of energy or quanta, known as photon. This means the energy of e.m. radiation is quantized, not all values of energy are possible ii. The energy size of the radiation depends on its frequency.
Planck s Quantum Theory According to Planck s assumptions, the quantum E of the energy for radiation of frequency f is given by E hf Planck s quantum theory Since the speed of electromagnetic wave in a vacuum is c = fλ, then equation can also be written as E hc
Analogy
Photon In 1905, Albert Einstein proposed that light comes in bundle of energy (light is transmitted as tiny particles), called photons. Photon is defined as a particle with zero mass consisting of a quantum of electromagnetic radiation where its energy is concentrated. (Quantum means fixed amount ) In equation form, photon energy (energy of photon) is E = hf.
Photon Unit of photon energy is Joule (J) or electron-volt (ev). The electron-volt (ev) is a unit of energy that can be defined as the kinetic energy gained by an electron in being accelerated by a potential difference (voltage) of 1 volt. 1eV 1.6010 19 J Photons travel at the speed of light in a vacuum. They are required to explain the photoelectric effect and other phenomena that require light to have particle property.
Example 1 A photon of the green light has a wavelength of 740 nm. Calculate a. the photon s frequency b. the photon s energy in joule and electron-volt (Given the speed of light in the vacuum, c = 3.0010 8 m s 1 and Planck s constant, h = 6.6310 34 J s)
Example 1 Solution
Example 1 Solution
9.2 The Photoelectric Effect Explain the phenomenon of photoelectric effect. Describe and sketch diagram of the photoelectric effect experimental set up. Define and determine threshold frequency, work function and stopping potential. Learning Objectives
9.2 The Photoelectric Effect Explain by using graph and equations the observations of photoelectric effect experiment in terms of the dependence of: i. Kinetic energy of photoelectron in the frequency of light; 1 2 mvmax evs hf hf0 2 ii. Photoelectric current on intensity of incident light; iii. Work function and threshold frequency in the types of metal surface; W0 hf 0 Learning Objectives
9.2 The Photoelectric Effect Explain the failure of classical theory to justify the photoelectric effect. Use Einstein s photoelectric equation, K evs hf max W 0 Learning Objectives
The Photoelectric Effect The photoelectric effect is defined as the emission of electron from the surface of a metal when the EM radiation (light) of higher frequency strikes its surface. Figure below shows the emission of the electron from the surface of the metal after shining by the light.
The Photoelectric Effect Experiment
The Photoelectric Effect Experiment When a monochromatic light of known frequency (or wavelength) shines on the cathode, photoelectrons are emitted. These photoelectrons are attracted to the anode and give rise to a photoelectric current or photocurrent I which is detected by the galvanometer. When the positive voltage (potential difference) is increased, more photoelectrons reach the anode, hence the photoelectric current also increase.
The Photoelectric Effect Experiment As positive voltage becomes sufficiently large, the photoelectric current reaches a maximum constant value I m, called saturation current (the maximum constant value of photocurrent when all the photoelectrons have reached the anode). If the positive voltage is gradually decreased, the photoelectric current I also decrease slowly. Even at zero voltage there are still some photoelectrons with sufficient energy reach the anode and the photoelectric current flows is I 0.
The Photoelectric Effect Experiment Reversing power supply terminal
The Photoelectric Effect Experiment When the voltage is made negative by reversing the power supply terminal as shown in figure below, the photoelectric current decreases even further to very low values since most photoelectrons are repelled by anode which is now negative. As the potential of the anode becomes more negative, less photoelectrons reach the anode thus the photoelectric current drops until its value equals zero (no photoelectrons have sufficient kinetic energy to reach the collector). The electric potential at this moment is called stopping potential (voltage) V s (the minimum value of reverse potential (voltage) when there are no photoelectrons reaching the anode).
The Photoelectric Effect Experiment By using conservation of energy : (loss of KE of photoelectron = gain in PE) K max U 1 2 At stopping voltage mvmax ev S 2 The variation of photoelectric current I as a function of the voltage V can be shown through the graph in figure below.
Einstein s Theory of Photoelectric Effect According to Einstein s theory, an electron is ejected/ emitted from the target metal by a collision with a single photon. In this process, all the photon energy (E = hf ) is transferred to the electron on the surface of metal target. Since electrons are held in the metal by attractive forces, some minimum energy, W o (work function, which is on the order of a few electron volts for most metal) is required just enough to get an electron out through the surface.
Einstein s Theory of Photoelectric Effect hf W o Electron is emitted hf W 0 1 mv 2 2 max hf W o Electron is ejected. hf W o No electron is ejected.
Einstein s Theory of Photoelectric Effect This is summed up by Einstein s photoelectric equation: E Einstein s K max W o photoelectric equation hf 1 2 mv max W o or hf ev s W o where E is photon energy f is frequency of EM radiation /incoming light V s is the stopping voltage v max is the maximum speed of the photoelectron
Einstein s Theory of Photoelectric Effect Work function W 0 of a metal Is defined as the minimum energy of e.m. radiation required to emit an electron from the surface of the metal. It depends on the metal used. Equation : W E o min hf o
Einstein s Theory of Photoelectric Effect f o is known as threshold frequency Is defined as the minimum frequency of EM radiation required to emit an electron from the surface of the metal. If the frequency of the incident radiation is less than the threshold frequency (f < f 0 ) then electrons would not be removed from the metal surface. Since c = fλ, then f o c o
Einstein s Theory of Photoelectric Effect o is known as threshold wavelength Is defined as the maximum wavelength of EM radiation required to emit an electron from the surface of the metal. If the wavelength of the incident radiation is greater than the threshold wavelength ( > o ) then electrons would not be removed from the metal surface.
Example 2 The work function for a silver surface is W o = 4.74 ev. Calculate the a. minimum frequency that light must have to eject electrons from the surface b. maximum wavelength that light must have to eject electrons from the surface (Given c = 3.00 10 8 m s -1, h = 6.63 10-34 J s, 1 ev = 1.60 10-19 J, m e = 9.11 10-31 kg, e = 1.60 10-19 C)
Example 2 Solution
Example 3 What is the maximum kinetic energy of electrons ejected from calcium by 420 nm violet light, given the work function for calcium metal is 2.71 ev? (Given c = 3.00 10 8 m s -1, h = 6.63 10-34 J s, 1 ev = 1.60 10-19 J, m e = 9.11 10-31 kg, e = 1.60 10-19 C)
Example 3 Solution
Example 4 Sodium has a work function of 2.30 ev. Calculate a. its threshold frequency, b. the maximum speed of the photoelectrons produced when the sodium is illuminated by light of wavelength 500 nm, c. the stopping potential with light of this wavelength (Given c = 3.00 10 8 m s -1, h = 6.63 10-34 J s, 1 ev = 1.60 10-19 J, m e = 9.11 10-31 kg, e = 1.60 10-19 C)
Example 4 Solution
Example 4 Solution
Example 5 In a photoelectric effect experiment it is observed that no current flows unless the wavelength is less than 570 nm. Calculate a. the work function of this material in electron-volts b. the stopping voltage required if light of wavelength 400 nm is used (Given c = 3.00 10 8 m s -1, h = 6.63 10-34 J s, 1 ev = 1.60 10-19 J, m e = 9.11 10-31 kg, e = 1.60 10-19 C)
Example 5 Solution
Learning Objectives Explain by using graph and equations the observations of photoelectric effect experiment in terms of the dependence of: i. Kinetic energy of photoelectron on the frequency of light; 1 2 mvmax evs hf hf0 2 ii. Photoelectric current on intensity of incident light; iii. Work function and threshold frequency on the types of metal surface; W0 hf 0 Learning Objectives
Dependence of kinetic energy of photoelectron on the frequency of light
Graph of Photoelectric Experiment Generally, Einstein s photoelectric equation: E K max W o K max E W o K max K max h f W o y mx c Gradient = h f W 0 f 0 f, K max
Graph of Photoelectric Experiment Since K max = ev s, V s y h f e mx W e c o f, V s
Dependence of photoelectric current on intensity of incident light
Graph of Photoelectric Experiment Variation of photoelectric current I with voltage V for the radiation of different intensities but its frequency and metal are fixed When intensity is increased, the maximum current attained is higher showing that more electrons are emitted. Light intensity number of photons V s remains the same shows that the K max of photoelectron independent of intensity of light
Extra Knowledge Classical physics Light intensity Energy Time Area Quantum physics Light intensity Number of photon Time Area Since light intensity α number of photon Light intensity, number of photons, number of electrons, current. If light intensity, photoelectric current
Graph of Photoelectric Experiment Variation of photoelectric current I with voltage V for the radiation of different frequencies but its intensity and metal are fixed. V s h e f W e o, V s f V V s2 s1 f2 f 1
Graph of Photoelectric Experiment Variation of photoelectric current I with voltage V for the different metals but the intensity and frequency of the radiation are fixed. V s h e f W e o, V s Wo V V s2 s1 W02 W 01
Dependence of work function and threshold frequency on the types of metal surface Metal A Metal B
Graph of Photoelectric Experiment Variation of stopping voltage V s with frequency f of the radiation for different metals but the intensity is fixed V s W 01 W 02 W 03 Since W, o hf o W o f o W 03 W02 W01 f 01 f 02 f 03 f f 03 f02 f01 Different threshold frequency for different metal
Example 6 Use the graph above to find the value of a. work function and b. the threshold wavelength
Example 6 Solution
Example 7 Based on the graph, for the light frequency of 6.00 10 14 Hz, calculate a. the threshold frequency b. the maximum kinetic energy of the photoelectron c. the maximum velocity of the photoelectron (Given c = 3.00 10 8 m s -1, h = 6.63 10-34 J s, 1 ev = 1.60 10-19 J, m e = 9.11 10-31 kg, e = 1.60 10-19 C)
Example 7 Solution
Example 7 Solution
Example 8 V s Ceasium Zinc 4.8 f Explain why a. the graphs are parallel b. the visible light cause photoemission from cesium but not from zinc
Example 8 Solution
Failure of Classical Theory OBSERVATIONS of the photoelectric effects experiment 1. Electrons are emitted immediately 2. Stopping potential does not depend on the intensity of light. 3. Threshold frequency of light is different for different target metal. 4. Number of electrons emitted of the photoelectron current depends on the intensity of light.
Failure of Classical Theory SUMMARY: Comparison between classical physics and quantum physics about photoelectric effect experiment Feature Classical physics Quantum physics Threshold frequency An incident light of any frequency can eject electrons (independent of frequency), as long as the beam has sufficient intensity. To eject an electron, the incident light must have a frequency greater than a certain minimum value, (threshold frequency), no matter how intense the light. Maximum kinetic energy of photoelectrons Emission of photoelectrons Depends on the light intensity. There should be some delays to emit electrons from a metal surface. Depends only on the light frequency. Electrons are emitted spontaneously. Energy of light Depends on the light intensity. Depends only on the light frequency.
Failure of Classical Theory Experimental observations deviate from classical predictions based on Maxwell s EM theory. Hence the classical physics cannot explain the phenomenon of photoelectric effect. The modern theory based on Einstein s photon theory of light can explain the phenomenon of photoelectric effect. It is because Einstein postulated that light is quantized and light is emitted, transmitted and reabsorbed as photons.