Class 12 Physics Electrons and Photons Notes

Class 12 Physics Electrons and Photons Notes
Modern Physics
Chapter 20: Electrons • Chapter 21: Photons
Class 12 Physics

Electrons and Photons

Current NEB/CDC syllabus-aligned combined study page

On mobile, swipe inside the PDF to read all pages and pinch to zoom.

Curriculum alignment: The original Nepal eNotes source combines Electrons and Photons in one PDF. In the current Grade 12 Physics curriculum, the content is organized under Modern Physics as Chapter 20: Electrons and Chapter 21: Photons. Chapter 20 covers Millikan’s oil-drop experiment and quantization of charge, motion of electrons in electric and magnetic fields, J.J. Thomson’s experiment and related numericals. Chapter 21 covers quantum nature and properties of photons, work function and photoelectric effect, Einstein’s photoelectric equation, stopping potential, Millikan’s verification of the equation and determination of Planck’s constant, plus related numericals.

1. Important Constants and Symbols

QuantitySymbolValue / unit
Electronic charge magnitudee1.602 × 10⁻¹⁹ C
Electron massme9.11 × 10⁻³¹ kg
Specific charge of electrone/m≈ 1.76 × 10¹¹ C kg⁻¹
Planck constanth6.626 × 10⁻³⁴ J s
Speed of lightc3.00 × 10⁸ m s⁻¹
Electron-volteV1 eV = 1.602 × 10⁻¹⁹ J

2. Electron: Basic Properties

Electron An electron is a fundamental negatively charged particle with charge −e and mass me.
  • Charge: −1.602 × 10⁻¹⁹ C.
  • Rest mass: 9.11 × 10⁻³¹ kg.
  • Charge-to-mass magnitude: e/m ≈ 1.76 × 10¹¹ C kg⁻¹.
  • Its motion is affected by electric and magnetic fields.
Sign convention In many derivations, e means the positive magnitude of the electron charge. The actual electron charge is −e. Hence force direction on an electron is opposite to the electric-field direction.

3. Millikan’s Oil-Drop Experiment

Purpose Millikan’s oil-drop experiment measured the elementary charge and demonstrated that electric charge is quantized.

3.1 Main Apparatus

  • Two parallel horizontal metal plates separated by a small distance.
  • Potential difference across plates to produce a nearly uniform electric field.
  • Atomizer producing tiny oil droplets.
  • Illumination and microscope for observing droplets.
  • Ionizing source used to alter droplet charge when required.
Millikan Oil-Drop Experiment upper plate lower plate charged oil drop electric force qE effective weight E Microscope observe motion Atomizer Compare droplet motion with and without electric field. Measured charges occur as integral multiples of the elementary charge e.

Diagram 1: Simplified Millikan oil-drop apparatus and force balance

3.2 Radius of the Oil Drop

First allow a drop of radius r and density ρ to fall through air of density σ. At terminal speed v1:

effective weight = viscous drag (4/3)πr³(ρ − σ)g = 6πηrv₁

Therefore,

r = √[9ηv₁ / {2(ρ − σ)g}]

3.3 Charge on a Rising Drop

If the electric field causes a negatively charged drop to rise with terminal speed v2, the electric force balances effective weight plus viscous drag:

qE = (4/3)πr³(ρ − σ)g + 6πηrv₂

Using the falling condition,

qE = 6πηr(v₁ + v₂) q = 6πηr(v₁ + v₂) / E

If plate separation is d and potential difference is V:

E = V/d
Exam Important The experiment found that measured charges were always q = ne, where n is an integer. This established the quantization of electric charge.

4. Quantization of Electric Charge

Quantization of charge The charge on an isolated body occurs in discrete integral multiples of the elementary charge.
q = ±ne

n = 0, 1, 2, 3, … and e = 1.602 × 10⁻¹⁹ C.

Quantization of Charge −2e −e 0 +e +2e Allowed isolated charge values occur in steps of e. Millikan’s measured droplet charges supported q = ne.

Diagram 2: Discrete charge values

5. Motion of an Electron in an Electric Field

5.1 Electric Force and Acceleration

For a charge q in uniform electric field E:

F = qE

For an electron, the force direction is opposite to E. The magnitude of acceleration is:

a = eE / m

5.2 Electron Entering Perpendicular to E

Suppose an electron enters with horizontal speed u and the electric field is vertical. Horizontal acceleration is zero while vertical acceleration is constant.

x = ut y = (1/2)(eE/m)t²

Eliminating t = x/u gives:

y = eE x² / (2mu²)

This is an equation of a parabola.

Electron in a Transverse Electric Field + − E u Uniform transverse electric field produces a parabolic electron path.

Diagram 3: Parabolic path in a transverse electric field

6. Motion of an Electron in a Magnetic Field

6.1 Magnetic Force

Magnitude of magnetic force on a charge moving with velocity v at angle θ to B:

F = evB sinθ

6.2 Electron Moving Perpendicular to B

For θ = 90°, magnetic force provides centripetal force:

evB = mv²/r

Hence:

r = mv / (eB) v = eBr / m

6.3 Time Period and Frequency

T = 2πr/v

Using r = mv/(eB):

T = 2πm / (eB) f = eB / (2πm)

In the non-relativistic model, the period and frequency are independent of the electron speed.

Electron Perpendicular to Uniform Magnetic Field ×× ×× ×× ×× ×× ×× ×× ×× ×× v FB Magnetic force is always perpendicular to velocity, so it changes direction—not speed.

Diagram 4: Circular motion in a perpendicular magnetic field

7. Electron in Crossed Electric and Magnetic Fields

If electric and magnetic fields are mutually perpendicular and the electron beam is undeflected, the electric and magnetic forces have equal magnitudes:

eE = evB
v = E/B

This arrangement acts as a velocity selector: only particles with speed E/B pass undeflected.

Crossed-Field Velocity Selector electron beam, speed v electric force magnetic force × × × × B into page Undeflected condition: eE = evB → v = E/B

Diagram 5: Electric and magnetic forces cancel for selected speed

8. J.J. Thomson’s Experiment and Specific Charge of Electron

Specific charge Specific charge is the charge-to-mass ratio of a particle. For an electron, its magnitude is e/m.

J.J. Thomson studied the deflection of cathode-ray electrons in electric and magnetic fields and determined their specific charge.

8.1 Velocity from Crossed Fields

v = E/B

8.2 Magnetic Deflection

With magnetic field alone producing a circular path of radius r:

evB = mv²/r

Therefore:

e/m = v/(Br) e/m = E/(B²r)
Importance The high and constant value of e/m for cathode-ray particles, independent of cathode material and gas, supported the conclusion that electrons are universal constituents of matter.
J.J. Thomson: Determining e/m Electron source cathode rays Crossed E and B region eE evB Screen spot Step 1: crossed fields give v = E/B Step 2: magnetic radius r gives e/m = E/(B²r)

Diagram 6: Conceptual Thomson specific-charge method

9. Quantum Nature of Radiation and Photons

Classical wave theory successfully describes interference, diffraction and polarization, but the photoelectric effect requires energy exchange in discrete packets.

Photon A photon is a quantum of electromagnetic radiation carrying energy proportional to its frequency.
E = hf = hc/λ p = E/c = h/λ

9.1 Properties of Photons

  • Photon energy is E = hf.
  • Photon momentum is p = h/λ.
  • Photons have zero rest mass.
  • They carry no electric charge.
  • In vacuum they move at speed c.
  • They are not deflected by ordinary electric or magnetic fields.
  • Energy transfer in light–matter interactions can occur photon by photon.
Photon Energy wavelength λ E = hf = hc/λ Higher frequency → greater photon energy; longer wavelength → lower photon energy.

Diagram 7: Energy carried by a photon

10. Photoelectric Effect

Photoelectric effect The photoelectric effect is the emission of electrons from a material surface when electromagnetic radiation of sufficiently high frequency falls on it.

The emitted electrons are called photoelectrons.

10.1 Work Function

Work function, φ The minimum energy required to remove an electron from the surface of a given material.
φ = hf₀ = hc/λ₀

f0 is the threshold frequency and λ0 is the threshold wavelength.

10.2 Threshold Frequency

If f < f0, no photoelectron is emitted, regardless of how intense the light is in the ideal single-photon model.

Basic Photoelectric-Effect Arrangement Emitter photosensitive metal Collector anode light, hf photoelectrons A Photocurrent measures the rate at which emitted electrons reach the collector.

Diagram 8: Simplified photoelectric cell

11. Experimental Laws of the Photoelectric Effect

  1. Threshold frequency exists: below f0, photoemission does not occur.
  2. Photoelectric current depends on intensity: for frequency above threshold, increasing light intensity generally increases the number of emitted electrons per second and hence saturation current.
  3. Maximum kinetic energy depends on frequency: increasing frequency increases Kmax and stopping potential.
  4. Kinetic energy is not controlled by intensity: intensity mainly changes the number of photons/electrons, not the maximum energy per emitted electron.
  5. Emission is essentially immediate: there is no classical energy-accumulation delay at sufficiently high frequency.
Most-tested distinction Intensity controls photocurrent; frequency controls maximum kinetic energy/stopping potential.

12. Einstein’s Photoelectric Equation

Einstein applied Planck’s quantum concept: one photon transfers energy hf to one electron.

photon energy = work function + maximum electron kinetic energy
hf = φ + Kmax hf = φ + ½mvmax²

Since φ = hf0:

Kmax = h(f − f₀)

Using stopping potential Vs:

Kmax = eVs hf = φ + eVs
Einstein’s Photoelectric Energy Balance hf photon energy = φ escape energy + Kmax electron kinetic energy If hf < φ, photoemission cannot occur.

Diagram 9: Photon energy is divided between escape work and kinetic energy

13. Stopping Potential

Stopping potential The minimum reverse potential required to reduce the photoelectric current to zero by stopping even the most energetic emitted photoelectrons.
eVs = Kmax

Combining with Einstein’s equation:

Vs = (h/e)f − φ/e

Thus a graph of Vs versus f is a straight line with:

  • Slope = h/e
  • Frequency-axis intercept = f0

14. Millikan’s Photoelectric Experiment and Planck’s Constant

Millikan carefully measured stopping potential for different light frequencies and verified Einstein’s linear photoelectric equation.

eVs = hf − φ

Rearranging:

Vs = (h/e)f − φ/e

If the slope of the Vs-versus-f graph is S:

S = h/e h = eS
Verification The experimentally observed straight-line relation between stopping potential and frequency verified Einstein’s prediction and allowed Planck’s constant to be measured.
Millikan Verification: Vₛ vs Frequency f Vₛ f₀ Δf ΔVₛ slope = ΔVₛ/Δf = h/e Frequency below f₀ gives no photoemission.

Diagram 10: Stopping potential varies linearly with frequency

15. Important Photoelectric Graphs

15.1 Photocurrent vs Applied Potential: Effect of Intensity

At the same frequency above threshold, higher light intensity produces a larger saturation current because more photons arrive per second and more electrons are emitted.

Photocurrent vs Potential: Changing Intensity V I higher intensity lower intensity −Vₛ Same frequency → approximately same stopping potential; intensity changes saturation current.

Diagram 11: Intensity changes saturation photocurrent

15.2 Effect of Frequency

At comparable intensity, increasing frequency increases maximum electron kinetic energy, so a larger stopping potential magnitude is needed.

Photocurrent vs Potential: Changing Frequency V I higher f → larger |Vₛ| same illustrative saturation level Higher frequency → greater Kmax → greater stopping potential magnitude.

Diagram 12: Frequency changes stopping potential

16. Worked Numericals

Example 1: Electron in a Magnetic Field

An electron moves at 3.0 × 10⁶ m/s perpendicular to a magnetic field of 0.020 T. Find the radius.

r = mv/(eB) r = (9.11 × 10⁻³¹ × 3.0 × 10⁶)/(1.602 × 10⁻¹⁹ × 0.020) r ≈ 8.53 × 10⁻⁴ m
Example 2: Crossed Fields

E = 3.0 × 10⁴ V/m and B = 2.0 × 10⁻³ T. Find the speed of an undeflected electron.

v = E/B v = (3.0 × 10⁴)/(2.0 × 10⁻³) v = 1.5 × 10⁷ m/s
Example 3: Photon Energy

Find the energy of a 500 nm photon.

E = hc/λ E = (6.626 × 10⁻³⁴)(3.00 × 10⁸)/(500 × 10⁻⁹) E ≈ 3.98 × 10⁻¹⁹ J ≈ 2.48 eV
Example 4: Photoelectric Maximum Kinetic Energy

A metal has work function 2.0 eV and receives photons of energy 3.5 eV.

Kmax = 3.5 − 2.0 = 1.5 eV

Therefore:

Vₛ = 1.5 V
Example 5: Threshold Frequency

Work function φ = 3.0 eV.

φ = 3.0 × 1.602 × 10⁻¹⁹ = 4.806 × 10⁻¹⁹ J f₀ = φ/h ≈ 7.25 × 10¹⁴ Hz
Example 6: Planck Constant from Graph

The slope of a stopping-potential versus frequency graph is 4.14 × 10⁻¹⁵ V·s.

h = e × slope h = (1.602 × 10⁻¹⁹)(4.14 × 10⁻¹⁵) h ≈ 6.63 × 10⁻³⁴ J·s
Example 7: Quantization of Charge

A droplet carries charge 4.806 × 10⁻¹⁹ C.

n = q/e = 4.806/1.602 = 3

The drop carries 3 elementary charges.

17. Formula Sheet

TopicFormula
Charge quantizationq = ne
Electric forceF = qE
Electron acceleration in Ea = eE/m
Transverse electric pathy = eEx²/(2mu²)
Magnetic forceF = evB sinθ
Magnetic circular radiusr = mv/(eB)
Cyclotron periodT = 2πm/(eB)
Cyclotron frequencyf = eB/(2πm)
Velocity selectorv = E/B
Specific chargee/m = E/(B²r)
Photon energyE = hf = hc/λ
Photon momentump = h/λ
Work functionφ = hf₀ = hc/λ₀
Einstein equationhf = φ + Kmax
Stopping potentialKmax = eVₛ
Vₛ-frequency lineVₛ = (h/e)f − φ/e
Planck constant from slopeh = e(dVₛ/df)

18. Common Exam Mistakes

  • Using the electron charge as +e when discussing force direction. The electron charge is negative.
  • Forgetting buoyancy/effective weight in a careful Millikan oil-drop derivation.
  • Writing charge as any continuous value instead of q = ne.
  • Using v = E/B when electric and magnetic forces are not in the correct crossed-field configuration.
  • Writing magnetic force as evB for every angle; the full form is evB sinθ.
  • Claiming a magnetic field changes the electron’s speed in uniform circular motion. It mainly changes direction because magnetic force does no work.
  • Forgetting that r ∝ v/B for fixed particle.
  • Confusing e/m with m/e.
  • Writing photon energy as h/f. Correct: E = hf.
  • Writing photon momentum as hλ. Correct: p = h/λ.
  • Confusing intensity with frequency in the photoelectric effect.
  • Claiming high intensity can produce photoelectrons below threshold frequency.
  • Forgetting the work function in Einstein’s equation.
  • Using stopping potential as an accelerating potential. It is the reverse potential that just stops the most energetic photoelectrons.
  • Writing φ = h/ f₀ instead of φ = hf₀.
  • Forgetting that the slope of Vₛ versus f is h/e, not h alone.
  • Using wavelength in nm without converting to metres in SI calculations.
  • Using eV directly with h in J·s without converting units consistently.

19. Important Exam Questions

Chapter 20: Electrons — Short Questions

  1. State the charge and mass of an electron.
  2. What is quantization of charge?
  3. State the purpose of Millikan’s oil-drop experiment.
  4. Why is a non-volatile oil used in Millikan’s experiment?
  5. Write the force balance for a freely falling oil drop at terminal speed.
  6. Derive the expression for the radius of an oil drop.
  7. Show how Millikan’s experiment establishes q = ne.
  8. What is the force on an electron in an electric field?
  9. Show that an electron entering a transverse uniform electric field follows a parabolic path.
  10. Write the magnetic force on a moving electron.
  11. Derive r = mv/(eB).
  12. Show that the time period of circular motion in a uniform magnetic field is independent of speed.
  13. Derive the velocity-selector relation v = E/B.
  14. Define specific charge.
  15. Explain the principle of J.J. Thomson’s experiment.
  16. Derive e/m = E/(B²r).

Chapter 21: Photons — Short Questions

  1. What is a photon?
  2. State the quantum nature of electromagnetic radiation.
  3. Write any four properties of photons.
  4. Derive p = h/λ for a photon.
  5. Define work function.
  6. Define threshold frequency.
  7. Define photoelectric effect.
  8. State the laws of photoelectric emission.
  9. How does intensity affect photoelectric current?
  10. How does frequency affect maximum kinetic energy?
  11. State Einstein’s photoelectric equation.
  12. Define stopping potential.
  13. Show that Kmax = eVₛ.
  14. Derive Vₛ = (h/e)f − φ/e.
  15. How did Millikan verify Einstein’s photoelectric equation?
  16. How can Planck’s constant be determined from the Vₛ–f graph?

Long Questions / Derivations

  1. Describe Millikan’s oil-drop experiment and explain quantization of charge.
  2. Derive the expression for charge on a rising oil drop.
  3. Derive the equation of the path of an electron in a transverse electric field.
  4. Derive radius, period and frequency of an electron moving perpendicular to a uniform magnetic field.
  5. Describe J.J. Thomson’s experiment and derive the electron’s specific charge.
  6. Explain the quantum nature of radiation and properties of photons.
  7. Explain the photoelectric effect and its experimental laws.
  8. Derive Einstein’s photoelectric equation.
  9. Explain stopping potential and threshold frequency.
  10. Describe Millikan’s photoelectric experiment and determination of Planck’s constant.

Numerical Practice

  1. Find charge on an oil drop and express it as a multiple of e.
  2. Calculate electron radius in a magnetic field.
  3. Calculate electron cyclotron frequency.
  4. Find undeflected velocity in crossed fields.
  5. Calculate e/m from E, B and r.
  6. Calculate photon energy from wavelength or frequency.
  7. Convert photon energy between joules and electron-volts.
  8. Calculate threshold frequency or threshold wavelength from work function.
  9. Calculate Kmax and stopping potential.
  10. Find Planck’s constant from the slope of a stopping-potential graph.
Exam Strategy For Electrons, prioritize Millikan oil-drop, transverse E-field motion, magnetic circular motion and Thomson e/m. For Photons, master the four equations E = hf, φ = hf₀, hf = φ + Kmax, and eVₛ = Kmax, then practice the Vₛ–f graph.

20. One-Minute Revision

  • Electron charge = −1.602 × 10⁻¹⁹ C.
  • Electron mass = 9.11 × 10⁻³¹ kg.
  • Charge is quantized: q = ne.
  • Millikan’s oil-drop experiment measured elementary charge.
  • For falling oil drop: effective weight = Stokes drag.
  • Uniform electric field gives electron acceleration magnitude eE/m.
  • Electron entering transverse E follows a parabola.
  • Magnetic force magnitude = evB sinθ.
  • For v ⟂ B, electron moves in a circle of radius mv/(eB).
  • Magnetic period T = 2πm/(eB).
  • Crossed-field undeflected speed v = E/B.
  • J.J. Thomson measured electron specific charge e/m.
  • Photon energy = hf = hc/λ.
  • Photon momentum = h/λ.
  • Photon rest mass = 0 and charge = 0.
  • Photoelectric effect emits electrons when f ≥ f₀.
  • Work function φ = hf₀.
  • Intensity mainly changes photocurrent.
  • Frequency changes Kmax and stopping potential.
  • Einstein equation: hf = φ + Kmax.
  • Kmax = ½mvmax² = eVₛ.
  • Stopping potential is the reverse potential that reduces photocurrent to zero.
  • Vₛ = (h/e)f − φ/e.
  • Slope of Vₛ vs f = h/e.
  • Planck constant can be obtained from h = e × slope.

21. Diagram Practice

Students should practice these labelled diagrams for the NEB examination:

  1. Millikan oil-drop apparatus and forces.
  2. Quantization-of-charge diagram.
  3. Electron path in transverse electric field.
  4. Electron circular motion in magnetic field.
  5. Crossed E and B velocity selector.
  6. J.J. Thomson specific-charge apparatus concept.
  7. Photon energy/wavelength diagram.
  8. Photoelectric cell arrangement.
  9. Einstein photoelectric energy balance.
  10. Stopping potential vs frequency graph.
  11. Photocurrent vs potential for different intensities.
  12. Photocurrent vs potential for different frequencies.
Source handling: The original Nepal eNotes PDF remains embedded above. The source page uses the older combined title “Electrons and Photons,” while the current NEB/CDC Grade 12 Physics curriculum organizes the same core material as Modern Physics Chapter 20 (Electrons) and Chapter 21 (Photons). The typed section follows the verified current syllabus and is designed as a searchable, responsive study companion. Where the PDF viewer does not expose page text, the typed section is a syllabus-aligned reconstruction and is not claimed to be a word-for-word transcription.
KEEP LEARNING View All Posts

Discussion

Share a helpful question, idea, or explanation with other students.

Leave a Comment

Write a clear question, answer, or helpful explanation.
Your email will not be published.

Download Our Offline App

Study class-wise notes even when internet is not available. Get the app from Play Store.

Nepal eNotes offline app preview
Get it on Google Play