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Physics · Class 12 Science

Ch 11Dual Nature of Radiation and Matter — Class 12 Physics, concept-first.

The story of how we came to understand that light and matter have a dual nature begins not with a single discovery, but with a crisis. By the late 19th century, Maxwell's equations had unified electricity, magnetism, and light into a single, elegant wave theory.

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Key concepts

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Photon Energy

Light does not carry its energy in a continuous stream. It comes in discrete packets — like individual drops instead of a steady hose.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

11.1

Introduction

The story of how we came to understand that light and matter have a dual nature begins not with a single discovery, but with a crisis.

11.2

Electron Emission

Metals conduct electricity because they contain a sea of free electrons — negatively charged particles that are not bound to any particular atom and can drift through the lattice.

11.3

Photoelectric Effect

The photoelectric effect is the emission of electrons from a metal surface when light of suitable frequency falls on it.

11.3.1

Hertz's Observations

The story of the photoelectric effect begins not with a deliberate search for electrons, but with an experiment on electromagnetic waves.

11.3.2

Hallwachs' and Lenard's Observations

The photoelectric effect was not fully understood from Hertz's initial discovery alone. Between 1886 and 1902, Wilhelm Hallwachs and Philipp Lenard conducted systematic experiments that revealed the k…

11.4

Experimental Study of Photoelectric Effect

The photoelectric effect is studied using an evacuated glass or quartz tube containing two metal plates: a photosensitive plate C (the emitter) and another metal plate A (the collector).

11.4.1

Effect of Intensity of Light on Photocurrent

The experimental setup for studying the photoelectric effect places the collector A at a positive potential relative to the emitter C.

11.4.2

Effect of Potential on Photoelectric Current

The setup is straightforward. You have an emitter plate C (the photocathode) and a collector plate A, both inside an evacuated tube.

11.4.3

Effect of Frequency of Incident Radiation on Stopping Potential

The previous experiments held the light's frequency constant and varied its intensity. Now we ask a different question: if we keep the intensity the same but change the frequency (the colour) of the l…

11.5

Photoelectric Effect and Wave Theory of Light

By the end of the nineteenth century, the wave nature of light was firmly established. Phenomena like interference, diffraction, and polarisation were explained beautifully by treating light as an ele…

11.6

Einstein's Photoelectric Equation: Energy Quantum of Radiation

Einstein took Planck's quantum hypothesis one bold step further. In 1905, he proposed that light energy itself is not absorbed continuously the way a wave picture demands, but arrives in discrete pack…

11.7

Particle Nature of Light: the Photon

The photoelectric effect forced physicists to accept a deeply strange idea: light, when it interacts with matter, does not behave like a continuous wave.

+Worked Examplesi2 questions
  1. Example 11.1Monochromatic light of frequency $6.0 \times 10^{14}\ \text{Hz}$ is produced by a laser. The power emitted is $2.0 \times 10^{-3}\ \text{W}$…Free
  2. Example 11.2The work function of caesium is $2.14\ \text{eV}$. Find (a) the threshold frequency for caesium, and (b) the wavelength of the incident ligh…Preview
11.8

Wave Nature of Matter

The dual nature of light — wave-like in interference and diffraction, particle-like in the photoelectric and Compton effects — raises a natural question.

+Worked Examplesi1 question
  1. Example 11.3What is the de Broglie wavelength associated with (a) an electron moving with a speed of $5.4 \times 10^{6}\ \text{m/s}$, and (b) a ball of…Preview

Summary

- Photoelectric effect: Einstein’s equation , where is the work function. Stopping potential satisfies . The effect proves light is quantised as photons of energy .

Points to Ponder

1. The phrase "free electrons" in a metal is an approximation. These electrons can move freely inside the metal because they experience a roughly constant electric potential there.

Exercises

+Show 19 questions19 questions
  1. 11.1Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by $30\ \text{kV}$ electrons.Free
  2. 11.2The work function of caesium metal is $2.14\ \text{eV}$. When light of frequency $6 \times 10^{14}\ \text{Hz}$ is incident on the metal surf…Free
  3. 11.3The photoelectric cut-off voltage in a certain experiment is $1.5\ \text{V}$. What is the maximum kinetic energy of photoelectrons emitted?Free
  4. 11.4Monochromatic light of wavelength $632.8\ \text{nm}$ is produced by a helium-neon laser. The power emitted is $9.42\ \text{mW}$. (a) Find th…Preview
  5. 11.5The energy flux of sunlight reaching the surface of the earth is $1.388 \times 10^{3}\ \text{W/m}^2$. How many photons (nearly) per square m…Preview
  6. 11.6In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be $4.12 \times 10…Preview
  7. 11.7A $100\ \text{W}$ sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs…Preview
  8. 11.8The threshold frequency for a certain metal is $3.3 \times 10^{14}\ \text{Hz}$. If light of frequency $8.2 \times 10^{14}\ \text{Hz}$ is inc…Preview
  9. 11.9The work function for a certain metal is $4.2\ \text{eV}$. Will this metal give photoelectric emission for incident radiation of wavelength…Preview
  10. 11.10Light of frequency $7.21 \times 10^{14}\ \text{Hz}$ is incident on a metal surface. Electrons with a maximum speed of $6.0 \times 10^{5}\ \t…Preview
  11. 11.11Light of wavelength $488\ \text{nm}$ is produced by an argon laser which is used in the photoelectric effect. When light from this spectral…Preview
  12. 11.12Calculate the (a) momentum, and (b) de Broglie wavelength of the electrons accelerated through a potential difference of $56\ \text{V}$.Preview
  13. 11.13What is the (a) momentum, (b) speed, and (c) de Broglie wavelength of an electron with kinetic energy of $120\ \text{eV}$.Preview
  14. 11.14The wavelength of light from the spectral emission line of sodium is $589\ \text{nm}$. Find the kinetic energy at which (a) an electron, and…Preview
  15. 11.15What is the de Broglie wavelength of (a) a bullet of mass $0.040\ \text{kg}$ travelling at the speed of $1.0\ \text{km/s}$, (b) a ball of ma…Preview
  16. 11.16An electron and a photon each have a wavelength of $1.00\ \text{nm}$. Find (a) their momenta, (b) the energy of the photon, and (c) the kine…Preview
  17. 11.17(a) For what kinetic energy of a neutron will the associated de Broglie wavelength be $1.40 \times 10^{-10}\ \text{m}$? (b) Also find the de…Preview
  18. 11.18Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).Preview
  19. 11.19What is the de Broglie wavelength of a nitrogen molecule in air at $300\ \text{K}$? Assume that the molecule is moving with the root-mean-sq…Preview

Additional Exercises

+Show 18 questions18 questions
  1. 11.20(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a pote…Free
  2. 11.21(a) A monoenergetic electron beam with electron speed of $5.20 \times 10^{6}\ \text{m s}^{-1}$ is subject to a magnetic field of $1.30 \time…Free
  3. 11.22An electron gun with its collector at a potential of $100\ \text{V}$ fires out electrons in a spherical bulb containing hydrogen gas at low…Free
  4. 11.23(a) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at $0.45\ \text{Å}$. What is the maximum energy…Preview
  5. 11.24In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an ele…Preview
  6. 11.25Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much abo…Preview
  7. 11.26Ultraviolet light of wavelength $2271\ \text{Å}$ from a $100\ \text{W}$ mercury source irradiates a photo-cell made of molybdenum metal. If…Preview
  8. 11.27Monochromatic radiation of wavelength $640.2\ \text{nm}$ ($1\text{nm} = 10^{-9}\ \text{m}$) from a neon lamp irradiates photosensitive mater…Preview
  9. 11.28A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines…Preview
  10. 11.29The work function for the following metals is given: Na: $2.75\ \text{eV}$; K: $2.30\ \text{eV}$; Mo: $4.17\ \text{eV}$; Ni: $5.15\ \text{eV…Preview
  11. 11.30Light of intensity $10^{-5}\ \text{W m}^{-2}$ falls on a sodium photo-cell of surface area $2\ \text{cm}^2$. Assuming that the top 5 layers…Preview
  12. 11.31Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater…Preview
  13. 11.32(a) Obtain the de Broglie wavelength of a neutron of kinetic energy $150\ \text{eV}$. As you have seen in Exercise 11.31, an electron beam o…Preview
  14. 11.33An electron microscope uses electrons accelerated by a voltage of $50\ \text{kV}$. Determine the de Broglie wavelength associated with the e…Preview
  15. 11.34The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons a…Preview
  16. 11.35Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature ($27\ °\text{C}$) and $1\ \text{atm}$ pre…Preview
  17. 11.36Compute the typical de Broglie wavelength of an electron in a metal at $27\ °\text{C}$ and compare it with the mean separation between two e…Preview
  18. 11.37Answer the following questions: (a) Quarks inside protons and neutrons are thought to carry fractional charges $[(+2/3)e ; (-1/3)e]$. Why do…Preview

NCERT Exemplar

Higher-order thinking problems from the NCERT Exemplar.

+Show 28 questions28 questions
  1. Q1A particle is dropped from a height $H$. The de Broglie wavelength of the particle as a function of height is proportional to (a) $H$ (b) $H…Free
  2. Q2The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with $1\ \text{MeV}$ energy is nearly (a)…Free
  3. Q3Consider a beam of electrons (each electron with energy $E_0$) incident on a metal surface kept in an evacuated chamber. Then (a) no electro…Free
  4. Q4A proton, a neutron, an electron and an $\alpha$-particle have same energy. Then their de Broglie wavelengths compare as (a) $\lambda_p = \l…Preview
  5. Q5An electron is moving with an initial velocity $\vec{v} = v_0\,\hat{i}$ and is in a magnetic field $\vec{B} = B_0\,\hat{j}$. Then its de Bro…Preview
  6. Q6An electron (mass $m$) with an initial velocity $\vec{v} = v_0\,\hat{i}$ ($v_0 > 0$) is in an electric field $\vec{E} = -E_0\,\hat{i}$ ($E_0…Preview
  7. Q7An electron (mass $m$) with an initial velocity $\vec{v} = v_0\,\hat{i}$ is in an electric field $\vec{E} = E_0\,\hat{j}$. If $\lambda_0 = h…Preview
  8. Q8A proton and an $\alpha$-particle are accelerated, using the same potential difference. How are the de Broglie wavelengths $\lambda_p$ and $…Preview
  9. Q9(i) In the explanation of photoelectric effect, we assume one photon of frequency $\nu$ collides with an electron and transfers its energy.…Preview
  10. Q10There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which a…Preview
  11. Q11Do all the electrons that absorb a photon come out as photoelectrons?Preview
  12. Q12There are two sources of light, each emitting with a power of $100\ \text{W}$. One emits X-rays of wavelength $1\ \text{nm}$ and the other v…Preview
  13. Q13In the photoelectric effect, light (photons) is incident on a metal surface travelling along one direction, and photoelectrons are ejected f…Preview
  14. Q14Consider a metal exposed to light of wavelength $600\ \text{nm}$. The maximum energy of the electron doubles when light of wavelength $400\…Preview
  15. Q15Assuming an electron is confined to a $1\ \text{nm}$ wide region, find the uncertainty in momentum using the Heisenberg Uncertainty principl…Preview
  16. Q16Two monochromatic beams A and B of equal intensity $I$, hit a screen. The number of photons hitting the screen by beam A is twice that by be…Preview
  17. Q17Two particles A and B of de Broglie wavelengths $\lambda_1$ and $\lambda_2$ combine to form a particle C. The process conserves momentum. Fi…Preview
  18. Q18A neutron beam of energy $E$ scatters from atoms on a surface with a spacing $d = 0.1\ \text{nm}$. The first maximum of intensity in the ref…Preview
  19. Q19Consider a thin target ($10^{-2}\ \text{m}$ square, $10^{-3}\ \text{m}$ thickness) of sodium, which produces a photocurrent of $100\ \mu\tex…Preview
  20. Q20Consider an electron in front of a metallic surface at a distance $d$ (treated as an infinite plane surface). Assume the force of attraction…Preview
  21. Q21In a photoelectric experiment carried out with two different metals A and B, the stopping potential $V_{stop}$ (in volts) is measured as a f…Preview
  22. Q22A particle A with a mass $m_A$ is moving with a velocity $v$ and hits a particle B (mass $m_B$) at rest (one dimensional motion). Find the c…Preview
  23. Q23Consider a $20\ \text{W}$ bulb emitting light of wavelength $5000\ \text{\AA}$ and shining on a metal surface kept at a distance $2\ \text{m…Preview
  24. Q24Relativistic corrections become necessary when the expression for the kinetic energy $\frac{1}{2}mv^2$ becomes comparable with $mc^2$, where…Preview
  25. Q25Two particles $A_1$ and $A_2$ of masses $m_1, m_2$ ($m_1 > m_2$) have the same de Broglie wavelength. Then (a) their momenta are the same. (…Preview
  26. Q26The de Broglie wavelength of a photon is twice the de Broglie wavelength of an electron. The speed of the electron is $v_e = \dfrac{c}{100}$…Preview
  27. Q27Photons absorbed in matter are converted to heat. A source emitting $n$ photon/sec of frequency $\nu$ is used to convert $1\ \text{kg}$ of i…Preview
  28. Q28A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the…Preview

CBSE Sample Papers

Questions from official CBSE sample papers.

+Show 15 questions15 questions
  1. Q1The waves associated with a moving electron and a moving proton have the same wavelength $\lambda$. It implies that they have the same : (A)…Preview
  2. Q2Consider a neutron (mass $m$) of kinetic energy $E$ and a photon of the same energy. Let $\lambda_n$ and $\lambda_p$ be the de Broglie wavel…Preview
  3. Q3de Broglie wavelength $\lambda$ as a function of $\dfrac{1}{\sqrt{K}}$, for two particles of masses $m_1$ and $m_2$ are shown in the figure.…Preview
  4. Q4Choose the correct statement: (A) Photons of light show diffraction whereas electrons do not show diffraction. (B) Electrons have momentum w…Preview
  5. Q5The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio $\dfrac{\lambda_{\alpha}}{\lambda_{p}}$ of t…Preview
  6. Q6For questions 13 to 16, two statements are given – one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer f…Preview
  7. Q7Find the ratio $\left(\dfrac{\lambda_a}{\lambda_p}\right)$ of the de Broglie wavelengths $\lambda_a$ and $\lambda_p$ associated respectively…Preview
  8. Q8A proton and an alpha particle have equal momentum. The ratio of their kinetic energies $\left(\dfrac{E_p}{E_\alpha}\right)$ and the ratio o…Preview
  9. Q9A particle of mass $M$ at rest splits up into two particles of masses $m_1$ and $m_2$ having non-zero velocities. Calculate the ratio of the…Preview
  10. Q10Calculate the wavelength of de Broglie waves associated with a proton having $\dfrac{500}{1.673}\ \text{eV}$ energy. How will the wavelength…Preview
  11. Q11A proton and an alpha particle have the same kinetic energy. The ratio of de Broglie wavelengths associated with the proton to that with the…Preview
  12. Q12Find the ratio of the de Broglie wavelengths associated with an alpha particle and a proton, if both (a) have the same speeds, (b) have the…Preview
  13. Q13A photon and a proton have the same de-Broglie wavelength $\lambda$. Prove that the energy of the photon is $(2mc\lambda/h)$ times the kinet…Preview
  14. Q14Find the frequency of light which ejects electrons from a metal surface, fully stopped by a retarding potential of 3.3 V. If photo electric…Preview
  15. Q15State Einstein's photoelectric equation explaining the symbols used. Light of frequency $\nu$ incident is on a photosensitive surface. A gra…Preview