Lecture 34 – THE PARTICLE NATURE OF LIGHT

A century ago, physics faced a profound question regarding light: whether light
behaved as a wave or as particles, serving as a source of energy. Around 350 years ago,
Newton's study of light suggested it comprised particles, based on observations of
sunlight's colors. This view gained widespread acceptance due to Newton's theory.
However, subsequent experiments, notably the double-slit experiment (fig 34.1),
challenged this view.
Here, light passing through two narrow slits onto a screen, created an interference
pattern, indicating wave-like behavior. This phenomenon arises due to variations in the
time taken for light to reach the screen through different slits, resulting in wave
interference and modulation of amplitude. This finding posed a significant challenge to
the particle theory of light.

Figure 34. 1. The double-slit experiment showing light's wave-like behavior through interference
patterns.

In the 19th century, Michael Faraday and James Clark Maxwell confirmed that light
behaves as electromagnetic waves, as discussed in previous lectures. They
demonstrated that changes in electric fields produce magnetic fields, and vice versa,
forming electromagnetic waves.
Heinrich Hertz, a German scientist, further validated this theory in 1880 through
experiments with transmitters and receivers, confirming the existence of these waves.
Electromagnetic waves feature perpendicular electric and magnetic fields, with the
electric field along the x-axis, the magnetic field along the y-axis, and the wave
propagation along the z-axis. As the electric field increases, the magnetic field
decreases, allowing these fields to propagate through space.
 Figure 34. 2. Electromagnetic waves featuring
perpendicular electric and magnetic fields.

Energy of Electromagnetic Wave

Electromagnetic fields carry energy, which can be calculated based on the product of
the electric and magnetic fields as E × B. The power in an electromagnetic wave is
proportional to the square of the maximum intensity of either the electric field (E0) or
the magnetic field (B0). Increasing the wave's amplitude, represented by E0 or B0,
results in a squared increase in energy.
2
Emax Bmax Emax
Average power per unit area = =
2 o 2 o c
E
 =c
B
2
c Bmax
Average power per unit area =
2 o

Additionally, electromagnetic waves possess momentum, despite us typically only

sensing their warmth when exposed to sunlight. The linear momentum (p) is given by:
2U
p=
c
Measurement of momentum
To detect momentum, a highly sensitive tool is required. In this setup depicted in fig
34.3, a mirror and a black disc are positioned such that when light strikes the mirror, it
reflects, causing the apparatus to rotate. The rotation angle increases with higher light
intensity, reflecting the energy density and momentum.
 Figure 34. 3. Rotating mirror and black disc
setup for momentum measurement.

Photoelectric Effect
In 1887, Heinrich Hertz conducted a groundbreaking experiment. Light illuminated a
metal surface, causing electrons to be emitted and collected elsewhere, known as the
photoelectric effect and the electrons that come out of the light are called
photoelectrons. This phenomenon revolutionized physics, leading to further
exploration.
Experimental Setup
Light of specific frequency light strikes a metal plate within a vacuum chamber to
ensure no air molecules interfere. Electrons are ejected from the metal upon light
collision and move toward the positive terminal, connected to a battery. The resulting
electron flow creates a measurable current, detectable by an ammeter.

Figure 34. 4. Experimental setup for demonstrating photoelectric effect.

Conclusions
This experiment yielded significant results.
1. Firstly, the kinetic energy of electrons reaching the anode is independent of light
intensity, contradicting classical theories from Newton to Maxwell. Increasing light
intensity doesn't result in higher electron energy, puzzling classical theory.
2. Secondly, electrons are not emitted unless light frequency exceeds a certain
threshold, regardless of intensity. Classical theory fails to explain why increasing
electromagnetic field intensity doesn't cause electron emission until a specific
frequency is reached.
3. The third crucial observation is that when light strikes a surface, classical theory
predicts a time delay before atoms gain sufficient energy to eject electrons.
However, electrons are emitted instantaneously upon light exposure, contradicting
classical predictions. These discrepancies caused a major upheaval in physics,
challenging classical mechanics and electromagnetic theory.
Einstein’s solution to photoelectric puzzle
In 1905, Einstein proposed a groundbreaking theory, which resolved these issues but
also triggered a conceptual crisis. Einstein suggested that light consists of discrete
particles called quanta, each carrying a specific amount of energy. These energy quanta,
or photons, are characterized by the equation:
E = h
( or E =  where = h 2 and  = 2 )
h (Planck's constant) = 6.626  10-34 Joule-seconds.
This equation ensures that as the
frequency increases, so does the energy
of the photons. Thus, Einstein's theory
revolutionized our understanding of
light, introducing the concept of
quantized energy and laying the
foundation for modern quantum
mechanics.
Radio waves have lower frequency,
which means that each quantum of a
radio frequency wave carries less
energy compared to a quantum of a
gamma ray. To illustrate this concept, let's Figure 34. 5. Graph showing the direct
use the analogy of climbing stairs. proportionality between the energy and frequency
of electromagnetic waves, illustrating that higher
Imagine each step on the staircase frequency waves have higher energy.
represents a quantum of energy. When
you climb the stairs, you can only move up by one full step at a time. You can't take
half or partial steps. Similarly, energy is quantized, meaning it comes in discrete units
or "quanta." Electrons, for instance, are only emitted from a material when the
frequency of the incoming light exceeds a certain threshold frequency. Below this
threshold, no electrons are emitted. However, once the threshold frequency is surpassed,
the number of emitted electrons depends on the intensity of the light.
Black Body Radiation
Classical theory failed to explain the photoelectric effect and faced another challenge

400nm 500nm 600nm 700nm

Figure 34. 6. visible light spectrum

regarding black body radiation. When observing the frequencies emitted by a heated
black body, a continuous spectrum spanning from deep blue to deep red is observed.
However, heating individual atoms results in only specific colours of light being
emitted. This phenomenon puzzled scientists as classical mechanics and
electromagnetic theory couldn't account for it. Spectroscopic analysis of elements like
hydrogen, helium, neon, and carbon revealed distinct spectral lines, such as Hα, Hβ, and
Hγ for hydrogen. The origin of these lines remained a mystery, leaving scientists
perplexed about atomic behaviour.
Rutherford's Experiment
Rutherford's experiment challenged the Plum
Pudding Model of the Atom, which proposed
that electrons and protons were evenly
distributed throughout. Rutherford's
experiment involved bombarding atoms with
alpha particles. Surprisingly, while some alpha
particles passed straight through, others were
deflected, and some even rebounded. This
unexpected result led Rutherford to propose
that atoms contained a dense central core,
which he termed the nucleus. This nucleus, he
reasoned, must be positively charged to repel the Figure 34. 7. Simplified model of a
hydrogen atom with a single electron
positively charged alpha particles. Thus, electrons orbiting a proton, highlighting the
orbit the nucleus much like planets orbit the sun. balance between attractive and
centrifugal forces.
This revolutionary insight, confirmed around a
century ago.
In the case of the simplest atom, hydrogen, a single proton forms the nucleus around
which an electron orbit (see fig 34.7). This orbital motion is balanced by the attractive
force of the proton and the centrifugal force exerted by the electron's motion. However,
this model posed new questions, suggesting a problem that demands further
exploration.
As the electron orbits the nucleus, its velocity continuously changes due to rotation,
resulting in acceleration. According to electromagnetic theory, accelerating charges
emit light waves, releasing energy. This energy cannot come from the potential energy
between the proton and electron, as separating opposite charges requires work.
Therefore, the electron's energy loss implies it moves closer to the nucleus over time.
Calculations suggest that a hydrogen atom would collapse within 10-8 s due to this
radiation. This phenomenon applies not only to hydrogen but to all atoms, leading to
electron-nucleus collisions and destruction of atom.
Bohr’s Atomic Model
To prevent this destruction, Niels Bohr, a Danish scientist, proposed a hypothesis
suggesting that electrons could remain stable by orbiting the nucleus in specific circular
paths, where their angular momentum is quantized as n times ħ (ħ = h/2π), with n being
integers (1, 2, 3, etc.). If an electron's angular momentum follows this quantization, it
will not emit radiation or lose energy, allowing the atom to maintain stability. This
hypothesis was further investigated to determine its validity and implications for
understanding the atomic structure.
The Bohr Atom
This atom exhibits equilibrium when the electrical force (between the nucleus (+e) and
electron (-e)), balances the centrifugal force.
(e)(e) v2
F = ma = = m
rn 2 rn
e2 mv 2
= ....................(1)
rn2 rn

According to Niels Bohr's proposal, angular momentum is quantized as

h
L = rn  p = rn p sin 90o = rn p = mvrn = n n
2
n
v=
mrn

By putting the value of v in eq (1), we get the value of rn

e2 e 2 mrn2
rn = =
mv 2 n2 2
n2 2
rn =
me 2
From this, we deduce that the electron can orbit the nucleus without emitting radiation,
n2 2 n2 2
provided its distance equals . This allows for specific orbit radii. = 0.5 Å,
me 2 me 2
implying one possible value of rn is 0.5 Å, followed by subsequent values increasing
by squares (4, 9, 16, etc.). Thus, the electron can occupy specific orbits but not
intermediate ones.
If we add both potential and kinetic energy,

e2
PE = −eV = −
r
2
1 e2 1  n  e2 1 n2 2 e2
En = mv 2 − = m  − = −
2 rn 2  mrn  rn 2 mrn 2 rn
putting the value of rn
1 me 4 n 2 2 me 4 1 me 4 me 4
− = −
2 n4 4 n2 2 2 n2 2 n2 2
e4 m
En = − 2 2
2n
E1 = −13.6 eV

What does "minus" signify? It

represents the energy required to
remove an electron from the atom,
known as ionization potential,
which is 13.6 eV. Additionally,
various energy levels exist, with
values decreasing in multiples of 4
(13.6, 13.6/4, 13.6/9, 13.6/16, etc.).
Niels Bohr proposed that when
electrons transition between these
levels, light is emitted. The colour
or frequency of this light is
determined by the energy Figure 34. 8. Bohr's model: Electron transition
difference between the levels. between energy levels emitting light, with
frequency determined by the energy difference.
Consider an electron transitioning from
level 3 to level 2, with the extracted energy given by ħν = 13.6 [(1/2)2 - (1/3) 2]. Just as
the atom emits light, it becomes excited in the same manner. For instance, to transition
from n = 2 to n = 3, the photon's energy must satisfy ħν = E3 - E2. Deviations from this
energy level won't induce light emission.
In the hydrogen atom spectrum, depicted here, transitions from the fifth to the second
level emit blue light with a wavelength of 434 nm. Conversely, the transition from level
3 to level 2 results in red light, with the lowest energy photon having a wavelength of
656 nm. The strip below showcases four different colours, each representing distinct
frequencies generated by the atom. These differences arise from variations in spacing
between the energy levels.

Figure 34. 9. Hydrogen spectrum: transitions from higher to lower energy levels emit light at
specific wavelengths, creating distinct colors.

In the hydrogen atom spectrum, transitions like Hα, Hβ, and Hγ occur when the atom is
excited. These transitions emit specific wavelengths of light.
 Figure 34. 10. The hydrogen spectrum is well-documented, with series such as Lyman, Balmer,
Paschen, Brackett, etc., each depicting different transitions.

Fluorescence
When light strikes an object and is reflected, the frequency remains unchanged.
However, this isn't always the case. In fluorescence, incident light excites atoms,
causing them to temporarily transition to higher energy states before returning to lower
states. Here, an ultraviolet photon collides with an electron, elevating it to a higher state.
After a brief pause, the electron descends to a lower state, emitting a photon.
The emitted photon usually has a longer wavelength, hence a different color, compared
to the incident ultraviolet light as shown in fig. 34.11. This color difference, known as
the Stokes shift, is determined by the energy difference between the excited and ground
states, which is influenced by the atomic structure of the material. It highlights that
incoming and outgoing light can exhibit varying colors."
 Figure 34. 11. Fluorescence: Incident light excites atoms, resulting in emission of longer
wavelength photons, known as the Stokes shift.

Phosphorescence
Phosphorescence is like fluorescence but with a key difference in how long the light
lasts.
1. An ultraviolet photon hits an atom and excites an electron, making it move to a higher
energy level.
2. The electron then falls to a slightly lower energy level and stays there for a longer
period.
3. Finally, the electron drops back to its original level, emitting light in the process.
In fluorescence, this process happens almost instantly, so the emitted light fades quickly.
In phosphorescence, the electron stays in the intermediate level longer before returning
to its original state. This delay means the material can glow in the dark, as it continues
to emit light even after the original light source is removed. This glow can last for a
much longer time, making phosphorescent materials useful for things like glow-in-the-
dark items.
 Figure 34. 12. Phosphorescence: After exposure to light, atoms release energy
gradually, emitting light over an extended period.

LASER
Lasers, which are now common in many applications, work on a principle called "light
amplification by stimulated emission of radiation" (LASER).
1. Light Amplification: This means increasing the number of photons or increasing
the amplitude of EM wave. In other words, making the light brighter or stronger.
2. Stimulated Emission: Normally, when an atom's electron drops from a higher
energy level to a lower one, it emits a photon. In stimulated emission, an incoming
photon triggers the excited electron to drop to a lower energy level and emit a photon.
The emitted photon has the same energy, phase, and direction as the incoming photon,
creating a coherent light wave.
Working Mechanism:
• Excitation: Atoms in the laser material are excited to a higher energy level by an
external energy source, like an electrical current or another light source.
• Population Inversion: More atoms are in the excited state than in the lower energy
state.
• Stimulated Emission: When one of these excited atoms encounters a photon of the
right energy, it is stimulated to emit a photon that matches the incoming one. This
triggers a chain reaction where more and more photons are emitted in the same
phase and direction.
• Amplification: These photons bounce back and forth between mirrors at each end
of the laser medium, stimulating more emissions. One of the mirrors is partially
transparent, allowing some of the light to escape as the laser beam.
The success of the laser has confirmed that photons are fundamental to light. Without
the concept of photons, the development of lasers and many other technologies would
not have been possible.
Two key points illustrate the importance of photons:
1. The photoelectric effect cannot be explained by classical theory.
2. The spectra of different atoms cannot be understood without considering photons.
There is also a third compelling argument in support of photons, which is equally
significant i.e. Compton effect.
Compton Scattering
In Compton scattering, when light hits an electron, it scatters, and the outgoing light
does not necessarily have the same frequency as the incoming light. This might seem
like fluorescence and phosphorescence, where light excites an atom and then the
emitted light has a different frequency. However, there's a key difference: in
fluorescence and phosphorescence, the light transition occurs between specific atomic
energy levels.
In contrast, Compton scattering involves free electrons, which can move freely and
have any momentum. A bound electron in an atom can only occupy certain discrete
energy levels, whereas a free electron is not restricted in this way.
Classically, when a light wave interacts with an electron, the electric field of the wave
should cause the electron to oscillate and emit radiation at the same frequency as the
incoming light. However, in Compton scattering, the scattered light has a different
frequency, indicating that classical theory does not fully explain the phenomenon.
Quantum Mechanical Approach: In Compton scattering, a photon with energy hν
(where ν is the frequency of blue light) collides with an electron. This collision causes
the electron to gain momentum and move with increased kinetic energy. The scattered
photon, now with less energy, emerges with a lower frequency than the incoming
photon.
Two quantities remain conserved in this process: energy and momentum. Initially, the
energy consists of the photon’s energy plus the electron’s rest energy, which has no
kinetic component as the electron is initially at rest. Thus, the initial energy is the
photon's energy.
After scattering, the total energy includes the energy of the scattered photon and the
kinetic energy gained by the electron. For energy conservation to hold, the energy of
the scattered photon must be less than the energy of the incoming photon, as some
energy is transferred to the electron. Therefore, if a blue photon collides with an
electron and a red photon is emitted, it indicates a loss of energy from the photon to the
electron. This phenomenon supports the quantum theory of light and cannot be
explained by classical theory alone.
Do we see photons? Where are they? How many are there, and what is their energy?
• Sunny day (outdoors):1015 photons per second enter eye (2 mm pupil)
• Moonlit night (outdoors): 51010 photons/sec (6 mm pupil)
• Moonless night (clear, starry sky): 108 photons/sec (6 mm pupil)
 • Light from dimmest naked eye star (mag 6.5): 1000 photons/sec entering eye
So far, we have presented three arguments: the photoelectric effect, atomic spectra, and
the Compton effect. These arguments indicate that light consists of photons, which are
quanta of energy. A photon’s energy is given by ħω or hν, meaning it comes in discrete
packets. There is a fourth argument related to black body radiation, which will be
discussed later when we study heat.
Wave-Particle Duality
Presently, we have two different theories: the particle theory, which involves photons
and is associated with Einstein, and the wave theory of electromagnetic waves, related
to Maxwell and Faraday. In 1924, Einstein remarked that there are two theories of light,
both indispensable and without any logical connection. One suggests that light is
composed of particles, while the other suggests it is composed of waves. This raises a
dilemma: if one theory is correct, does it invalidate the other? This contradiction has
led to considerable complexity in understanding the nature of light.
To explore this problem further, let’s revisit the double-slit interference experiment. In
this experiment, a light source is split into two paths that interfere with each other. We
will examine this from two perspectives: light as particles and light as waves.
If we consider light as photons, individual atoms emit these photons. A photon can pass
through either one slit or the other and then hit a screen, leaving a mark. If we imagine
using bullets from a rifle instead of photons, the bullets will scatter randomly with no
distinct pattern, unlike waves. Waves can reinforce or cancel each other out, creating
an interference pattern. This suggests that if light exhibits interference, it must be waves,
contradicting the particle-based explanations of the photoelectric effect, atomic spectra,
and the Compton effect.
However, this is not the whole story. While particles like photons typically don’t
interfere in the way waves do, photons can indeed interfere under certain conditions.
The behavior of photons depends on the type of experiment performed. In some
experiments, photons exhibit particle properties, such as in the photoelectric effect. In
others, like the double-slit experiment, they exhibit wave properties. This dual nature
is known as wave-particle duality.
Initially, Einstein found this concept challenging, but it is now a cornerstone of modern
physics and the foundation of quantum mechanics. We will explore this further in
another lecture.