Engineering Physics - 104: Photoelectric Effect & Postulates of Quantum Mechanics

ENGINEERING PHYSICS – 104
Lecture # 05
Photoelectric effect & Postulates of Quantum
Mechanics
Text Book (Solid State Electronic Devices) Ch-2

SECTION :
2.2.1,2.4.2
Class : 92nd EC
Number of slides : 25
Instructor : Wg Cdr Hina
Learning Objectives
After this lecture student will be able to:
 Explain the classical and quantum explanation of
Photoelectric effect
Understand the basic postulates of quantum
mechanics
QUANTUM MECHANICS
Classical Mechanics vs. Quantum mechanics
Formulated to explain the Formulated to explain
behavior of macroscopic the behavior of
objects. microscopic systems.
Newton’s second law: F  ma  m d2x
dt 2
Integrate twice → x(t).

CLASSICAL MECHANICS
 The mathematical study of the motion of everyday
objects and the forces that affect them is called
classical mechanics. Classical mechanics is often
called Newtonian mechanics because. Nearly the
entire study builds on the work of Isaac Newton .
 All Newtonian laws and some other principles are
considered to be the core of classical mechanics.
Photoelectric Effect
 In the photoelectric effect, you hit target with EM radiation and
electrons fly out!
 The electrons ejected from the target are called
“photoelectrons”. This phenomenon is called photoelectric
effect
 An adjustable voltage is applied.

Voltage can be forward or reverse
biased ( reverse biased voltage slows
down the electrons and maximum
energy of electrons can be calculated )
 Photoelectrons return to cathode

through an ammeter which records the
current
 The current increases when you increase the intensity

(brighter light = more photoelectrons). But above a “cutoff
wavelength”( below cutoff frequency) no photoelectrons get

ejected no matter how great the intensity of the incident
radiation. For wavelengths below the cutoff, decreasing the
radiation to very low intensities does not completely
eliminate the production of photo electrons
Current vs. Bias voltage
High intensity (bright)
Stopping potential
Low intensity (dim)

eV(stopping)
Stopping voltage vs. Frequency (c/)
frequency
Interpretation
 Slope is same for all targets
 Intercept is different for different target materials.
 hf =  + KE =  + eV
eV=hf - metal
where  = hf0 is the “work function” of the metal…the minimum

amount of energy required to remove an electron.
h=6.63 x 10-34 Js is Planck’s Constant!

 Planck’s EM “quanta” turn out to be real after all!
 Light comes in energy packets equal to hf
 Each packet acts more like a particle than a wave
 These light “particles” are called photons
 Rather than continuously absorbing wave radiation the

target is being bombarded by photons like tiny billiard
balls!
• It explained the particle
nature of light.
• It is the basis of the

quantum theory.
• It is used in photocells
e.g. in solar calculators,
alarms, automatic garage
door openers, flash of a
camera
Example
• A metal has work function of 4.3eV. What is the minimum
photon energy in eV to extract an electron with 1.0eV
Kinetic energy from this metal through the photoelectric
effect? What are the photon frequency and photon
wavelength? What is the corresponding photon momentum.
• Solution
• Hints, Use formula hf =  + KE =  + eV
PRACTICE PROBLEM
• A light source of wavelength λ illuminates a metal and ejects
photoelectrons with a maximum kinetic energy of 1.0 eV. A
second source with half the wavelength of the first ejects
photoelectrons with a maximum K.E of 4.0 eV. Determine the
work function of the metal and the threshold wavelength
required for the metal.
END
22
Postulates of Quantum Mechanics
 There are several ways to develop the Schrödinger wave equation

by applying quantum concepts to various classical equations of
mechanics. One of the simplest approaches is to consider the
basic postulates of quantum mechanics.
Postulate 1: The state of a quantum mechanical system is

completely specified by a function ψ(x, y, z, t) that depends on the
coordinates of the particle(s) and on time. This function, called the
wave function or state function.
Postulate 2: To every classical quantity there corresponds a
quantum mechanical operator
It means for every measurable property of the system in classical
mechanics such as position, momentum, and energy, there exists
a corresponding operator in quantum mechanics
Observable Operator Symbol of Operator

Momentum -iћ∂/∂x p^ x
Kinetic Energy (- ћ2/2m)∂2/∂2x E^x
Position x X^
Potential Energy V (x) V^
Total Energy ( ћ2/2m)∂2/∂2x + V (x) H^
• Postulate 3: Probability of finding a particle with wave function

ᴪ in volume dx dy dz(dτ) is ψ*(r,t)ψ(r,t) dτ
• The product ψ*(r,t)ψ(r,t) is normalized according to equation
∫ψ*(r,t)ψ(r,t)dτ = 1
Postulate 4: The average value <A> of any variable A is
calculated from the wave function by using operator form as
A^ is given by
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ENGINEERING PHYSICS – 104

Text Book (Solid State Electronic Devices) Ch-2

After this lecture student will be able to:

 Explain the classical and quantum explanation of

Understand the basic postulates of quantum

Integrate twice → x(t).

 An adjustable voltage is applied.

 Photoelectrons return to cathode

 The current increases when you increase the intensity

wavelength”( below cutoff frequency) no photoelectrons get

Current vs. Bias voltage

High intensity (bright)

Low intensity (dim)

 Intercept is different for different target materials.

where  = hf0 is the “work function” of the metal…the minimum

h=6.63 x 10-34 Js is Planck’s Constant!

 Planck’s EM “quanta” turn out to be real after all!

 Light comes in energy packets equal to hf

 Each packet acts more like a particle than a wave

 These light “particles” are called photons

 Rather than continuously absorbing wave radiation the

• It is the basis of the

 There are several ways to develop the Schrödinger wave equation

Postulate 1: The state of a quantum mechanical system is

Observable Operator Symbol of Operator

• Postulate 3: Probability of finding a particle with wave function

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