Dual Nature Of Radiation And Matter Class 12 Physics Chapter 11 Notes

Dual Nature of Radiation and Matter Class 12 Physics Chapter 11 Notes

Maxwell’s Equations and Hertz’s Experiments (1887):

Demonstrated the wave nature of light.
Maxell’s equations describe the behavior of electric and magnetic fields.
Hertz’s experiments confirmed the existence of electromagnetic waves.

Electric Discharge Through Gases at Low Pressure (Late 19th Century):

Investigated electrical conduction through low-pressure gases in discharge tubes.
Discharge occurred at around 0.001 mm of mercury column under an electric field.
A fluorescent glow was observed on the glass opposite the cathode.
The glow’s color depended on the glass type (e.g., yellowish-green for soda glass).
This fluorescence was attributed to radiation from the cathode.

Cathode Rays:

Discovered by William Crookes in 1870.
Consisted of fast-moving negatively charged particles.
J. J. Thomson confirmed this and determined the speed and specific charge (e/m) by applying electric and magnetic fields.
Cathode rays traveled at speeds around 0.1 to 0.2 times the speed of light (3 × 10^8 m/s).
Accepted value of e/m is 1.76 × 10^11 C/kg.
e/m was independent of cathode material and gas in the tube, suggesting universality.

Discovery of Electrons (Around 1887):

Certain metals emitted negatively charged particles when irradiated with ultraviolet light.
Heating some metals also resulted in the emission of negatively charged particles.
These particles had the same e/m as cathode ray particles.
J. J. Thomson named them electrons and proposed they were universal constituents of matter.
Thomson received the Nobel Prize in Physics in 1906 for his electron discovery.

Millikan’s Oil-Drop Experiment (1913):

Conducted by Robert A. Millikan.
Precisely measured the charge on an electron, finding it to be 1.602 × 10^(-19) C.
Established that electric charge is quantized.
Allowed for the determination of the electron’s mass from charge (e) and specific charge (e/m).

Electron Emission

Free Electrons in Metals:
- Metals contain free electrons responsible for their electrical conductivity.
- These electrons are normally bound within the metal due to attractive forces of ions.
- Attempted escape of an electron from the metal results in the metal’s surface acquiring a positive charge, pulling the electron back.
Work Function:
- The minimum energy required for an electron to escape the metal surface is called the work function (denoted as f0).
- Work function is measured in electron volts (eV), where 1 eV is the energy gained by an electron accelerated by a 1-volt potential difference (1 eV = 1.602 × 10^(-19) J).
- The work function varies with the metal’s properties and surface characteristics.
Methods of Supplying Minimum Energy for Electron Emission:
- Thermionic Emission:
  - Heating the metal provides thermal energy to free electrons, allowing them to escape the metal surface.
- Field Emission:
  - Applying a very strong electric field (of about 10^8 V/m) to a metal can overcome the binding forces and eject electrons (e.g., spark plugs).
- Photoelectric Emission:
  - When light of suitable frequency illuminates a metal surface, it causes the emission of electrons (photoelectrons).
  - The energy of the incident photons must exceed the work function for this process to occur.
Units of Energy:
- In atomic and nuclear physics, the energy unit commonly used is the electron volt (eV).
- 1 eV is equivalent to the energy gained by an electron when accelerated by a 1-volt potential difference (1 eV = 1.602 × 10^(-19) J).

Photoelectric Effect – Hertz’s Observations

Discovery by Heinrich Hertz (1887):
- Heinrich Hertz, a pioneer in electromagnetic wave experiments, discovered the photoelectric effect during his investigations.
- While conducting experiments on the production of electromagnetic waves using spark discharges, Hertz made an intriguing observation.
Hertz’s Observation:
- Hertz noted that when he illuminated the emitter plate (a metal surface) with ultraviolet light from an arc lamp, it had a significant effect on the experiment.
- High voltage sparks generated across the detector loop were enhanced when the emitter plate was illuminated.
- This suggested that the emission of charged particles from the emitter plate was facilitated by the incident light.
Mechanism of Photoelectric Effect:
- When light shines on a metal surface, it interacts with the surface’s electrons.
- Some of the electrons absorb sufficient energy from the incident radiation, which enables them to overcome the attractive forces of the positive ions present in the material.
- Having gained enough energy from the incident light, these electrons are able to escape from the surface of the metal into the surrounding space.
- These escaped electrons are what we now recognize as photoelectrons.

Hertz’s observations laid the foundation for understanding the photoelectric effect, a phenomenon where incident light causes the emission of electrons from a material’s surface when the energy of the light exceeds a certain threshold.

Photoelectric Effect – Hallwachs’ and Lenard’s observations

Investigation (1886-1902):
- Wilhelm Hallwachs and Philipp Lenard conducted detailed investigations into the phenomenon of photoelectric emission during the late 19th and early 20th centuries.
Lenard’s Observation:
- Lenard observed that when ultraviolet radiations illuminated the emitter plate of an evacuated glass tube containing two metal electrodes (collector plates), current flowed in the circuit.
- As soon as the ultraviolet radiations were stopped, the current flow ceased.
- This indicated that ultraviolet radiations caused the emission of electrons from the emitter plate, which were then attracted to the positive collector plate by the electric field. The electrons traveled through the evacuated tube, resulting in current flow.
- In essence, light falling on the emitter’s surface generated a photo current in the external circuit.
Study of Photo Current:
- Hallwachs and Lenard examined how the photo current varied with changes in the collector plate potential, the frequency, and the intensity of the incident light.
Hallwachs’ Observation:
- In 1888, Hallwachs connected a negatively charged zinc plate to an electroscope.
- He observed that the zinc plate lost its charge when illuminated by ultraviolet light.
- Additionally, an uncharged zinc plate became positively charged when irradiated by ultraviolet light.
- The positive charge on a positively charged zinc plate increased when it was illuminated by ultraviolet light.
- These observations led Hallwachs to conclude that negatively charged particles (now known as electrons) were emitted from the zinc plate due to ultraviolet light.
Threshold Frequency:
- Hallwachs and Lenard observed that when ultraviolet light fell on the emitter plate, no electrons were emitted if the frequency of the incident light was below a certain minimum value, called the threshold frequency.
- The threshold frequency depends on the material of the emitter plate.
Photosensitive Materials:
- Certain metals like zinc, cadmium, and magnesium emitted electrons only in response to ultraviolet light, which has a short wavelength.
- Alkali metals such as lithium, sodium, potassium, cesium, and rubidium were even sensitive to visible light.
- These substances emit electrons when illuminated by light.
- With the discovery of electrons, these emitted particles were termed photoelectrons, and the phenomenon became known as the photoelectric effect.

Hallwachs and Lenard’s experiments provided critical insights into the photoelectric effect, particularly the role of the threshold frequency and the materials’ photosensitivity to different wavelengths of light.

Experimental Study of the Photoelectric Effect

Apparatus:

An evacuated glass/quartz tube with a photosensitive plate C and a metal plate A.
Monochromatic Light Source (S): Provides light of short wavelength.
Window (W): Allows ultraviolet radiation to pass and irradiate the photosensitive plate C.
Transparent Quartz Window: Sealed onto the tube for ultraviolet transmission.
Battery: Creates an electric field between plates C and A with a variable potential difference.
Commutator: Reverses the polarity of plates C and A, allowing for positive or negative potential.
Voltmeter (V): Measures the potential difference between the emitter C and collector A.
Microammeter (mA): Measures the resulting photoelectric current in the circuit.

Operation:

When the collector plate A is positively charged with respect to the emitter plate C, the emitted electrons are attracted to A.
This attraction of electrons to the collector plate results in the flow of an electric current in the circuit.
The potential difference between plates C and A is measured using the voltmeter (V), while the photoelectric current is measured with the microammeter (mA).
The photoelectric current can be adjusted by changing the potential difference (V) between plates C and A.
The intensity and frequency of the incident light can be varied.
By using colored filters or glass, light of different frequencies can be employed.
The intensity of light is altered by changing the distance of the light source from the emitter.

Study of the Photoelectric Effect: The experimental setup can be used to investigate the following aspects of the photoelectric effect:

Variation of photocurrent with:
- Intensity of radiation.
- Frequency of incident radiation.
- The potential difference between plates A and C.
- The nature of the material of plate C.

This apparatus allows for a comprehensive examination of how the photoelectric current is influenced by different experimental parameters, contributing to a deeper understanding of the photoelectric effect.

Effect of Intensity of Light on Photocurrent

In the experimental setup, the collector plate A is maintained at a positive potential relative to the emitter plate C. This setup ensures that electrons emitted from C are attracted toward A.
To investigate the effect of light intensity on the photoelectric current, the researchers keep the frequency of the incident radiation and the potential difference between the plates constant.
They then systematically vary the intensity of the incident light while measuring the resulting photoelectric current each time.
The experimental results show that the photocurrent increases linearly with the intensity of the incident light. This relationship is depicted graphically.
The key observation is that the photocurrent is directly proportional to the number of photoelectrons emitted per second.
This finding indicates that the number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation.

In other words, as the intensity of the incident light increases, more photoelectrons are emitted per second, resulting in a higher photocurrent. This illustrates the fundamental relationship between the intensity of light and the photoelectric effect.

Effect of Potential on Photoelectric Current

The experimental setup initially maintains the collector plate A at a positive potential with respect to the emitter plate C. Plate C is illuminated with light of a fixed frequency ν and a fixed intensity I₁.
Researchers then gradually vary the positive potential of plate A and measure the resulting photoelectric current each time.
Observations:
- The photoelectric current increases with an increase in the positive (accelerating) potential applied to plate A.
- At a certain positive potential of plate A, all the emitted electrons are collected, and the photoelectric current reaches a maximum, referred to as the saturation current. This corresponds to the case when all emitted photoelectrons reach plate A.
- Further increasing the accelerating potential of plate A beyond this point does not lead to an increase in the photocurrent.
Saturation Current: The maximum value of the photoelectric current is termed the saturation current. It occurs when all the emitted photoelectrons are collected by the collector plate A.
When a negative (retarding) potential is applied to plate A with respect to plate C, electrons are repelled, and only the most energetic electrons can reach the collector A. The photocurrent decreases rapidly until it drops to zero at a sharply defined, critical value of the negative potential, labeled V₀.
Cutoff or Stopping Potential: The minimum negative (retarding) potential V₀ for which the photocurrent becomes zero is known as the cutoff or stopping potential.
Interpretation:
- Not all photoelectrons emitted from the metal have the same energy. The photoelectric current is zero when the stopping potential is sufficient to repel even the most energetic photoelectrons, with the maximum kinetic energy (Kₘₐₓ).
- This relationship is expressed as: Kₘₐₓ = eV₀, where e is the charge of an electron.
If the experiment is repeated with incident radiation of the same frequency but different intensities (I₂ and I₃, where I₃ > I₂ > I₁), the saturation currents are found to be at higher values. This demonstrates that more electrons are emitted per second, proportional to the intensity of the incident radiation.
However, the stopping potential remains the same as that for the incident radiation of intensity I₁. This implies that for a given frequency of the incident radiation, the stopping potential is independent of its intensity. In other words, the maximum kinetic energy of photoelectrons depends on the light source and the emitter plate material but is independent of the intensity of the incident radiation.

Effect of Frequency of Incident Radiation on Stopping Potential

Researchers investigate the relationship between the frequency ν of incident radiation and the resulting stopping potential V₀.
Experiments involve adjusting the intensity of light radiation while keeping it at various frequencies and observing the variation of photocurrent with collector plate potential.
Observations:
- Different values of stopping potential are obtained, but the same value of the saturation current for incident radiation of different frequencies.
- The energy of the emitted electrons depends on the frequency of the incident radiation.
- The stopping potential is more negative for higher frequencies of incident radiation.
- The stopping potentials follow an order: V₀₃ > V₀₂ > V₀₁ if the frequencies are in the order ν₃ > ν₂ > ν₁.
Implications:
- Greater the frequency of incident light, greater is the maximum kinetic energy of the photoelectrons, and consequently, we need a greater retarding potential to stop them completely.
- A graph between the frequency of incident radiation and the corresponding stopping potential for different metals results in a straight line.
Summary of Experimental Observations:
- Photoelectric Current: For a given photosensitive material and frequency of incident radiation (above the threshold frequency), the photoelectric current is directly proportional to the intensity of the incident light.
- Saturation Current: For a given photosensitive material and frequency of incident radiation, the saturation current is found to be proportional to the intensity of incident radiation, while the stopping potential is independent of its intensity.
- Threshold Frequency: There exists a certain minimum cut-off frequency, known as the threshold frequency, below which no emission of photoelectrons occurs, regardless of the intensity of the incident light. Above the threshold frequency, the stopping potential or, equivalently, the maximum kinetic energy of the emitted photoelectrons, increases linearly with the frequency of the incident radiation but is independent of its intensity.
- Instantaneous Emission: Photoelectric emission is an instantaneous process without any apparent time lag, even when the incident radiation is made exceedingly dim, typically occurring within a time frame of 10^(-9) s or less.

Photoelectric Effect and Wave Theory of Light

The wave nature of light was well-established by the end of the 19th century. Phenomena like interference, diffraction, and polarization were explained satisfactorily by the wave theory of light, which depicted light as an electromagnetic wave with continuous energy distribution over space.
Wave Theory Expectations:
- According to the wave theory, when light falls on the surface of a metal, the free electrons should continuously absorb radiant energy.
- Greater radiation intensity implies larger amplitudes of electric and magnetic fields, and consequently, electrons should absorb more energy.
- In this context, the maximum kinetic energy of the photoelectrons on the metal surface should increase with increasing intensity.
- Additionally, the wave theory suggests that regardless of the frequency of radiation, a sufficiently intense beam of radiation over a sufficient duration should provide enough energy to electrons for them to escape from the metal surface. Therefore, there should be no threshold frequency.
Contradictions with Observations:
- These expectations from the wave theory of light directly contradict the observations described earlier, which include the existence of a threshold frequency and the fact that photoelectric emission is an instantaneous process even with dim radiation.
Energy Absorption and Emission Rates:
- In the wave theory, the absorption of energy by electrons is expected to occur continuously over the entire wavefront of the radiation.
- As a result, because many electrons absorb energy, the energy absorbed by each electron per unit time is relatively small.
- Calculations reveal that, in this scenario, it can take hours or more for a single electron to accumulate sufficient energy to overcome the work function and be emitted.
Striking Contrasts:
- These conclusions from the wave theory stand in striking contrast to the actual observations of the photoelectric effect, where photoelectron emission is nearly instantaneous.
Inadequacy of the Wave Theory:
- In summary, the wave theory of light is unable to explain the fundamental features of photoelectric emission, such as the existence of a threshold frequency and the instantaneous nature of the emission even with low-intensity radiation.

The shortcomings of the wave theory led to the development of quantum theory, particularly the concept of photons, to explain the photoelectric effect. This marked a significant departure from classical wave-based explanations and played a crucial role in the development of modern quantum mechanics.

Einstein’s Photoelectric Equation: Energy Quantum of Radiation

In 1905, Albert Einstein introduced a new concept to explain the photoelectric effect, departing from the wave theory. He proposed that electromagnetic radiation is composed of discrete energy units known as “quanta of energy.” Each quantum of radiant energy has an energy hn, where h is Planck’s constant, and n is the frequency of light.
Einstein’s Hypothesis:
- Photoelectric emission occurs not through continuous energy absorption but by the absorption of these energy quanta or photons.
- If the energy quantum absorbed by an electron (hn) exceeds the minimum energy needed for the electron to escape from the metal surface (work function f₀), the electron is emitted with a maximum kinetic energy:
  - Kmax = hn – f₀ (Einstein’s photoelectric equation).
Impact of Intensity:
- The intensity of light is determined by the number of photons incident per second.
- Increasing intensity increases the number of emitted electrons per second.
- However, the maximum kinetic energy of the photoelectrons is determined by the energy of each photon.
Implications of Einstein’s Photoelectric Equation:
- Kmax depends linearly on n and is independent of the intensity of radiation, in agreement with observations.
- Photoelectric effect arises from the absorption of a single quantum of radiation by a single electron, and the intensity of radiation is irrelevant to this basic process.
- Photoelectric emission is possible only if hn > f₀, leading to the existence of a threshold frequency n₀ = f₀/h below which no emission occurs, regardless of the intensity.
- Intensity is proportional to the number of energy quanta per unit area per unit time. Higher intensity leads to more electrons participating in the elementary process of absorption of a light quantum, resulting in a greater photoelectric current.
- The absorption of a light quantum by an electron is an instantaneous process, so intensity does not affect the time of emission; it only affects the number of electrons participating in the process.
The Equation and Planck’s Constant:
- Using Eq. (11.1), Einstein’s photoelectric equation can be expressed as eV₀ = hn – f₀, or V₀ = h/e * (n – n₀) for n ≥ n₀.
- This equation predicts that the V₀ vs. n curve is a straight line with a slope of h/e, independent of the material.
Verification by Millikan:
- In a series of experiments from 1906 to 1916, Robert A. Millikan aimed to disprove Einstein’s photoelectric equation.
- Instead, he confirmed its validity by measuring the slope of the straight line obtained for sodium. He determined the value of Planck’s constant h, which closely matched the value obtained from different experiments in an entirely different context.
Acceptance of Einstein’s Hypothesis:
- The successful explanation of the photoelectric effect using the concept of light quanta and the experimental determination of the values of h and f₀ led to the acceptance of Einstein’s model for the photoelectric effect.
- Millikan’s precise experiments further verified the validity of Einstein’s photoelectric equation for various metals and frequencies.

Einstein’s revolutionary hypothesis introduced the concept of quantization of light and laid the foundation for quantum mechanics.

Particle Nature of Light: The Photon

The photoelectric effect provided strong evidence that light, in its interaction with matter, behaves as if it consists of discrete energy quanta, each with an energy of hn. This observation raised the question of whether these light quanta should be associated with particles.
Albert Einstein made a crucial contribution by demonstrating that light quanta (photons) can also be associated with momentum, specifically (hn/c), where h is Planck’s constant, n is the frequency of light, and c is the speed of light. The association of both energy and momentum with light quanta strongly indicated their particle-like behavior.
Einstein’s result led to the naming of these light quanta as photons. Photons are the fundamental particles of electromagnetic radiation.
The photon picture of electromagnetic radiation can be summarized as follows:
1. Radiation behaves as if it is made up of particles called photons.
2. Each photon has energy (E) equal to hn and momentum (p) equal to hn/c. All photons of light of a specific frequency (n) or wavelength (λ) have the same energy and momentum, regardless of the intensity of the radiation.
3. Photon energy is independent of the intensity of radiation. Increasing the intensity only increases the number of photons per second without affecting the energy of each photon.
4. Photons are electrically neutral and are not deflected by electric and magnetic fields.
5. In a photon-particle collision, total energy and total momentum are conserved. However, the number of photons may not be conserved in the collision. Photons can be absorbed, or new photons may be created during the interaction.
The acceptance of the photon model for electromagnetic radiation was further confirmed by experiments like A.H. Compton’s study of X-ray scattering from electrons in 1924.
In recognition of his groundbreaking work on the photoelectric effect and the photon, Albert Einstein was awarded the Nobel Prize in Physics in 1921. Robert A. Millikan was also awarded the Nobel Prize in Physics in 1923 for his contributions to the understanding of the elementary charge of electricity and the photoelectric effect.

Wave Nature of Matter: de Broglie Hypothesis

We have seen that light exhibits both wave-like and particle-like properties. The wave nature of light is evident in phenomena like interference, diffraction, and polarization, while its particle-like behavior is observed in the photoelectric effect and Compton effect.
However, if radiation, which has a dual (wave-particle) nature, can exhibit these two aspects, then a natural question arises: Can particles of matter, such as electrons and protons, also exhibit wave-like properties under certain conditions?
In 1924, the French physicist Louis Victor de Broglie (1892-1987) proposed a bold hypothesis that moving particles of matter should display wave-like properties under specific circumstances. He reasoned that since nature is symmetric, matter and energy must have symmetrical characteristics. In other words, if radiation can exhibit both wave and particle properties, matter should also exhibit such dual characteristics.
de Broglie’s hypothesis suggests that the wavelength (λ) associated with a particle’s wave-like nature is given by the de Broglie relation: λ = h / (mv), where:
- λ is the de Broglie wavelength of the particle.
- h is Planck’s constant.
- m is the mass of the particle.
- v is the speed of the particle.
The de Broglie wavelength is the attribute of a wave, while momentum p (mass times velocity) is a typical attribute of a particle. Planck’s constant h relates these two attributes.
Remarkably, this de Broglie relation also holds for photons, the particles of light. For a photon with momentum p and frequency ν, we have p = hn/c. Substituting this into the de Broglie relation, we get the wavelength of a photon, which is indeed the same as its electromagnetic wavelength: λ = c / ν.
The de Broglie wavelength is inversely proportional to the momentum of a particle. Heavier particles or particles with higher energy have shorter de Broglie wavelengths. For macroscopic objects like a ball, this wavelength is so small that it’s beyond measurement. Therefore, we don’t observe wave-like properties for macroscopic objects in our daily life.
In the subatomic domain, where particles have much smaller masses and higher energies, their wave-like properties become significant and measurable.