Photoelectric Effect: Hertz, Lenard, and Hallwachs' observations, and the concept of threshold frequency

🌟 PHOTOELECTRIC EFFECT

Hertz • Hallwachs • Lenard • Threshold Frequency • Work Function • Photon Theory

📌 1. Topic Description

Photoelectric Effect

The photoelectric effect is the phenomenon in which electrons are emitted from the surface of a metal when electromagnetic radiation of sufficiently high frequency falls on it.

ν ≥ ν₀ → Photoelectric Emission

Here ν₀ is the threshold frequency of the metal.

ν < ν₀ → No emission
ν = ν₀ → Electrons are just emitted
ν > ν₀ → Photoelectrons are emitted with kinetic energy

🔬 2. Hertz, Hallwachs and Lenard

🔬 Heinrich Hertz

Hertz observed that ultraviolet radiation facilitated spark discharge during his electromagnetic-wave experiments.

1887

UV Radiation

🔬 Wilhelm Hallwachs

Hallwachs observed that ultraviolet radiation caused a negatively charged zinc plate to lose its charge.

Zinc Plate

UV Light

🔬 Philipp Lenard

Lenard performed detailed experiments on photoelectric emission and studied the effects of frequency and intensity.

Photoelectrons

Frequency

⚡ 3. Hertz's Observation

• Hertz produced and detected electromagnetic waves.
• He observed that ultraviolet radiation helped spark discharge.
• UV radiation made the spark jump across the gap more easily.
• This observation became an important experimental clue for the photoelectric effect.

Exam Point: Hertz observed the phenomenon but did not give its complete theoretical explanation.

⚡ 4. Hallwachs' Observation

Hallwachs used a clean zinc plate connected to an electroscope. When ultraviolet light was incident on a negatively charged zinc plate, the electroscope gradually discharged.

UV Light → Electron Emission → Negative Charge Decreases

The emitted particles were electrons.

🔬 5. Lenard's Observations

• Photoelectric emission occurs only above a certain frequency.
• This minimum frequency is called threshold frequency.
• Increasing intensity increases the number of photoelectrons.
• Maximum kinetic energy depends on frequency.
• Photoelectric emission is practically instantaneous.

🎬 6. Interactive Photoelectric Effect Practical

Frequency: 8

Intensity: 6

Threshold Frequency: 6

📊 7. Effect of Frequency

Condition	Result
ν < ν₀	No photoelectric emission
ν = ν₀	Kmax = 0
ν > ν₀	Photoelectrons are emitted

💡 8. Threshold Frequency

The threshold frequency is the minimum frequency of incident radiation required to eject electrons from a particular metal.

ν₀ = φ / h

• ν₀ = threshold frequency
• φ = work function
• h = Planck's constant

🔋 9. Work Function

The minimum energy required to remove an electron from a metal surface is called the work function.

φ = hν₀

☀️ 10. Photon Energy

E = hν

The energy of a photon is directly proportional to its frequency.

hν = φ + K_max

K_max = hν − φ

K_max = h(ν − ν₀)

📈 11. Effect of Intensity

For radiation having frequency greater than threshold frequency, increasing intensity increases the number of incident photons per second.

Intensity ↑ → Number of photoelectrons ↑ → Photoelectric current ↑

However, intensity does not increase the maximum kinetic energy of individual photoelectrons.

📈 12. Effect of Frequency

K_max = hν − φ

Frequency ↑ → Maximum kinetic energy ↑

⏱️ 13. Instantaneous Nature

When ν ≥ ν₀, photoelectric emission starts practically immediately. There is no measurable time delay between incidence of radiation and emission of photoelectrons.

🚫 14. Why Intensity Alone Cannot Produce Emission?

If the frequency is below threshold frequency, every photon has insufficient energy to overcome the work function. Increasing the number of such photons cannot compensate for the insufficient energy of each individual photon.

hν < φ → No Photoelectric Emission

🧠 15. Important Experimental Conclusions

1️⃣ Threshold Frequency

Every metal has a minimum frequency required for photoemission.

2️⃣ Intensity

Above threshold frequency, increasing intensity increases photoelectric current.

3️⃣ Frequency

Increasing frequency increases maximum kinetic energy.

4️⃣ Instantaneous Emission

Photoemission starts practically instantaneously.

📝 16. MCQ Practice — 15 Questions

1. Who observed that ultraviolet radiation helps spark discharge?

A. Einstein

B. Hertz

C. Bohr

D. Millikan

✔ Answer: B. Hertz

2. Hallwachs used which radiation?

A. Infrared

B. Microwave

C. Ultraviolet

D. Radio waves

✔ Answer: C. Ultraviolet

3. Minimum frequency required for photoelectric emission is called:

A. Resonant frequency

B. Threshold frequency

C. Natural frequency

D. Critical frequency

✔ Answer: B. Threshold frequency

4. Threshold frequency depends mainly on:

A. Intensity

B. Nature of metal

C. Distance only

D. Area only

✔ Answer: B. Nature of metal

5. Photoelectric emission occurs when:

A. ν < ν₀

B. ν = 0

C. ν ≥ ν₀

D. Intensity = 0

✔ Answer: C. ν ≥ ν₀

6. Energy of a photon is:

A. h/ν

B. hν

C. ν/h

D. hcν

✔ Answer: B. hν

7. Work function is:

A. h/ν₀

B. hν₀

C. ν₀/h

D. hc/ν₀

✔ Answer: B. hν₀

8. Increasing intensity above threshold frequency increases:

A. Maximum KE

B. Photoelectric current

C. Work function

D. Threshold frequency

✔ Answer: B. Photoelectric current

9. Increasing frequency increases:

A. Maximum kinetic energy

B. Work function

C. Threshold frequency

D. None

✔ Answer: A. Maximum kinetic energy

10. Maximum kinetic energy is:

A. hν + φ

B. hν − φ

C. φ − hν

D. h/ν

✔ Answer: B. hν − φ

11. If ν < ν₀:

A. Electrons are emitted

B. No photoelectrons are emitted

C. Current becomes infinite

D. KE becomes infinite

✔ Answer: B

12. Photoelectric emission is practically:

A. Delayed

B. Instantaneous

C. Periodic

D. Impossible

✔ Answer: B. Instantaneous

13. Photoelectrons are:

A. Protons

B. Neutrons

C. Electrons

D. Alpha particles

✔ Answer: C. Electrons

14. Photon energy is directly proportional to:

A. Wavelength

B. Frequency

C. Time

D. Distance

✔ Answer: B. Frequency

15. Hallwachs' experiment demonstrated emission of:

A. Protons

B. Neutrons

C. Electrons

D. Ions only

✔ Answer: C. Electrons

🟣 17. Assertion–Reason — 5 Questions

Options:
A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true but R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.

Assertion: Photoelectric emission does not occur below threshold frequency.

Reason: Photon energy is insufficient to overcome the work function.

Answer: A

Assertion: Increasing intensity increases maximum kinetic energy.

Reason: Photon energy depends on frequency.

Answer: D

Assertion: Increasing frequency increases maximum kinetic energy.

Reason: Photon energy is directly proportional to frequency.

Answer: A

Assertion: Photoelectric emission is practically instantaneous.

Reason: A photon transfers its energy to an electron in a single interaction.

Answer: A

Assertion: Threshold frequency is the same for all metals.

Reason: Work function is a property of the metal.

Answer: D

🟢 18. 2 Marks — 6 Questions

Q1. Define photoelectric effect.

Q2. What is threshold frequency?

Q3. State Hallwachs' observation.

Q4. What did Hertz observe?

Q5. Define work function.

Q6. Why does emission not occur below threshold frequency?

🟡 19. 3 Marks — 6 Questions

Q1. Explain Hertz's observation.

Q2. Explain Hallwachs' experiment.

Q3. State Lenard's observations.

Q4. Explain threshold frequency.

Q5. Differentiate the effects of intensity and frequency.

Q6. Why is photoelectric emission instantaneous?

🟠 20. 4 Marks — 6 Questions

Q1. Explain Hertz's and Hallwachs' observations.

Q2. Describe Lenard's experimental observations.

Q3. Explain threshold frequency and work function.

Q4. Explain the effect of intensity.

Q5. Explain the effect of frequency.

Q6. Why can't intensity alone produce photoemission below threshold frequency?

🔴 21. 5 Marks — 6 Questions

Q1. Describe the observations of Hertz, Hallwachs and Lenard.

Q2. Explain threshold frequency and derive φ = hν₀.

Q3. Explain the effects of intensity and frequency.

Q4. Why does classical wave theory fail to explain photoelectric effect?

Q5. Explain photoelectric effect using photon theory.

Q6. Discuss experimental evidence for particle nature of light.

🔵 22. 6 Marks — 6 Questions

Q1. Explain in detail the observations of Hertz, Hallwachs and Lenard.

Q2. Define threshold frequency and work function and derive Einstein's photoelectric equation.

Q3. Explain the complete experimental characteristics of photoelectric emission.

Q4. Explain how photoelectric effect proves the quantum nature of light.

Q5. Compare the effects of intensity and frequency on photoelectric current and kinetic energy.

Q6. Explain photoelectric emission using hν = φ + K_max.

🧮 23. Numerical Practice — 6 Questions

Q1. A metal has a work function of 2 eV. Calculate its threshold frequency.

Q2. Light of frequency 8 × 10¹⁴ Hz falls on a metal whose threshold frequency is 5 × 10¹⁴ Hz. Will photoelectric emission occur?

Q3. The threshold frequency of a metal is 6 × 10¹⁴ Hz. Calculate its work function.

Q4. Radiation of frequency 1 × 10¹⁵ Hz falls on a metal having work function 2 eV. Calculate maximum kinetic energy.

Q5. A metal has threshold wavelength 500 nm. Calculate threshold frequency.

Q6. Light of frequency 7 × 10¹⁴ Hz falls on a metal whose threshold frequency is 4 × 10¹⁴ Hz. Explain what happens to maximum kinetic energy when frequency is increased.

📚 24. Formula Sheet

Photon Energy

E = hν

Work Function

φ = hν₀

Threshold Frequency

ν₀ = φ/h

Einstein Equation

hν = φ + K_max

Maximum Kinetic Energy

K_max = hν − φ

Threshold Wavelength

λ₀ = c/ν₀

🚀 25. Quick Revision

🔹 Hertz → UV radiation enhanced spark discharge
🔹 Hallwachs → UV caused negatively charged zinc plate to discharge
🔹 Lenard → Detailed photoelectric observations
🔹 ν₀ → Threshold frequency
🔹 ν < ν₀ → No emission
🔹 ν = ν₀ → K_max = 0
🔹 ν > ν₀ → Photoelectric emission
🔹 Intensity ↑ → Number of photoelectrons ↑
🔹 Frequency ↑ → K_max ↑
🔹 φ = hν₀
🔹 E = hν
🔹 hν = φ + K_max
🔹 Emission is practically instantaneous

📘 Class 12 Physics | Photoelectric Effect | Board + Competitive Exam Practice