Is it correct to say: Using photon energy formula E = ½mv² for radiation?

Photons are massless. Use E = hν = hc/λ, and p = h/λ.

Is it correct to say: Assuming photoelectric emission depends on light intensity to eject electrons?

It depends on frequency being above ν₀. Intensity affects only NUMBER of photoelectrons, not their KE.

Is it correct to say: Forgetting to convert eV to joules (or λ from Å to m) in numericals?

Use consistent SI units, or use the shortcut E(eV) = 1240/λ(nm).

Is it correct to say: Mixing up threshold frequency ν₀ with work function φ₀?

φ₀ = hν₀. ν₀ has units of Hz; φ₀ has units of joules or eV.

Is it correct to say: Using de Broglie formula with velocity in km/h or non-SI momentum?

Use SI units: momentum in kg·m/s. Then λ = h/p in metres.

Is it correct to say: Believing photoelectrons take a measurable time to emerge above threshold?

Emission is instantaneous — this is one of the four laws Einstein explained.

Dual Nature of Radiation and Matter

Photoelectric effect, Einstein's equation, de Broglie hypothesis, wave-particle duality — Maharashtra HSC Physics Ch 14

📐 10 formulas✏️ 3 examples🎯 5 practice⚖️ 4 marks🏫 Maharashtra State Board📚 Class 12✓ 2025–26 syllabus

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Board Exam Tips

→Einstein's photoelectric equation (hν = φ₀ + K_max) and interpretation of its terms is a 3-mark HSC question every year.
→Learn Millikan's oil-drop / photoelectric verification and the graph of K_max vs frequency — the slope gives Planck's constant h.
→de Broglie wavelength derivation from photon momentum p = h/λ and application to matter is a favourite 2-marker.
→Distinguish clearly between threshold frequency ν₀ and work function φ₀ = hν₀. HSC MCQs commonly test this.
→State the four experimental laws of photoelectric effect — this alone can give 2 marks in Section B.

📐 Formulas(10)

Energy of a Photon★ Board fav

E = h ν = \frac{h c}{λ}

Symbol	Meaning
$h$	Planck's constant = 6.626×10⁻³⁴ J·s
$ν$	Frequency of radiation (Hz)
$λ$	Wavelength (m)

Momentum of a Photon

p = \frac{h}{λ} = \frac{h ν}{c}

Work Function

φ_{0} = h ν_{0}

Einstein's Photoelectric Equation★ Board fav

h ν = φ_{0} + K_{ma x} = φ_{0} + e V_{0}

Stopping Potential★ Board fav

V_{0} = \frac{h}{e} ν - \frac{φ _{0}}{e}

de Broglie Wavelength★ Board fav

λ = \frac{h}{p} = \frac{h}{m v}

de Broglie Wavelength of Accelerated Electron

λ = \frac{h}{2 m e V} \approx \frac{12.27}{V} A ˚

Threshold Frequency and Wavelength

ν_{0} = \frac{φ _{0}}{h}, λ_{0} = \frac{h c}{φ _{0}}

Number of Photons per Second

n = \frac{P}{h ν} = \frac{P λ}{h c}

Compton Wavelength (reference)

λ_{c} = \frac{h}{m _{e} c} = 2.43 \times 1 0^{- 12} m

✏️ Solved Examples

1Solved Exampleeasy3 steps

A metal has work function 2.5 eV. Find the threshold wavelength.

Convert work function to joules.

φ_{0} = 2.5 \times 1.6 \times 1 0^{- 19} = 4.0 \times 1 0^{- 19} J

2Solved Exampleboard4 steps

Light of wavelength 400 nm falls on a sodium surface of work function 2.3 eV. Find (i) maximum kinetic energy of emitted electrons, (ii) stopping potential.

Photon energy in eV.

E = \frac{1240}{400} = 3.10 eV

3Solved ExampleHOTS3 steps

An electron and a proton have the same kinetic energy of 100 eV. Find the ratio of their de Broglie wavelengths. (m_p/m_e = 1836)

λ = h/p and p = √(2mK). So for equal K:

λ \propto \frac{1}{m}

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Using photon energy formula E = ½mv² for radiation
✓Photons are massless. Use E = hν = hc/λ, and p = h/λ.
2
Assuming photoelectric emission depends on light intensity to eject electrons
✓It depends on frequency being above ν₀. Intensity affects only NUMBER of photoelectrons, not their KE.
3
Forgetting to convert eV to joules (or λ from Å to m) in numericals
✓Use consistent SI units, or use the shortcut E(eV) = 1240/λ(nm).
4
Mixing up threshold frequency ν₀ with work function φ₀
✓φ₀ = hν₀. ν₀ has units of Hz; φ₀ has units of joules or eV.
5
Using de Broglie formula with velocity in km/h or non-SI momentum
✓Use SI units: momentum in kg·m/s. Then λ = h/p in metres.
6
Believing photoelectrons take a measurable time to emerge above threshold
✓Emission is instantaneous — this is one of the four laws Einstein explained.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
Find the energy in eV of a 600 nm photon.
Q2
Work function of caesium is 2.14 eV. What is its threshold wavelength?
Q3
An electron accelerated through 100 V. Find its de Broglie wavelength.
Q4
A 60 W source emits light of λ = 620 nm. Find the number of photons emitted per second.
Q5
State the four experimental laws of photoelectric effect.

📝 Notes

Dual Nature of Radiation and Matter — Maharashtra HSC Overview

Chapter 14 of the Balbharati Class 12 Physics textbook covers the photoelectric effect, Einstein's photon theory, and de Broglie matter waves.

Maharashtra syllabus specifics

The Balbharati book gives a full historical narrative — Hertz, Hallwachs, Lenard, Millikan — for the discovery of the photoelectric effect. Familiarity with names is expected for a 1-mark MCQ.
Einstein's equation and its interpretation as a manifestation of Planck's quantum hypothesis is emphasised. HSC expects mention of "photon", "quantum" and "instantaneous emission".
Davisson–Germer experiment is included in the Maharashtra syllabus as the experimental verification of de Broglie's hypothesis — often asked for 2 marks (description) or as an MCQ.
The electron microscope and Compton wavelength appear briefly — occasionally asked as a 1-mark objective.

Formula bank shortcut

E(eV) = 1240 / λ(nm) — memorise this. Cuts calculation time in half.
λ(Å) for accelerated electron ≈ 12.27/√V — same shortcut.

Board exam pattern

4-marker: Einstein's photoelectric equation + graph of K_max vs ν or V₀ vs ν.
3-marker: derivation of de Broglie wavelength or numerical on threshold.
2-marker: statement of laws of photoelectric effect, or definition of work function.