Modern PhysicsHigh Yield (2 Qs in JEE)

Dual Nature of Radiation & Matter Formulas

Photoelectric effect, Einstein's equation, work function, cut-off frequency, and de Broglie matter waves.

7 Formulas•535+ Questions in Bank

Core Formulas & Mathematical Identities

Einstein's Photoelectric Equation

K_{\text{max}} = h\nu - \Phi_0 = h\nu - h\nu_0 = e V_0

Conservation of energy in photon-electron interaction.

Examiner Tip: Graph of stopping potential V₀ versus frequency ν has slope h/e (universal constant).

De Broglie Matter Wavelength

\lambda = \frac{h}{p} = \frac{h}{m v} = \frac{h}{\sqrt{2mK}}

Wave-particle duality wavelength associated with moving particles of momentum p.

Examiner Tip: Wavelength of electron accelerated through potential V: λ = 1.227 / √V nm = √(150/V) Å.

Photon Momentum & Energy

E = h\nu = \frac{hc}{\lambda} \approx \frac{12400}{\lambda \text{ (\AA)}} \text{ eV}, \quad p = \frac{E}{c} = \frac{h}{\lambda}

Energy and momentum of light quanta.

Examiner Tip: Useful constant: hc ≈ 1240 eV·nm ≈ 12400 eV·Å.

Radiation Pressure on Surface

P = \frac{I}{c} \; (\text{Complete Absorption}), \quad P = \frac{2I}{c} \; (\text{Complete Reflection})

Mechanical force per unit area exerted by electromagnetic waves of intensity I.

Examiner Tip: Force on perfectly reflecting surface of area A is F = 2IA / c. For oblique incidence at angle θ: P = (2I/c)cos²θ.

De Broglie Wavelength of Accelerated Charged Particles

\lambda = \frac{h}{\sqrt{2mqV}} \implies \lambda_e = \frac{12.27}{\sqrt{V}}\,\text{\AA}, \quad \lambda_p = \frac{0.286}{\sqrt{V}}\,\text{\AA}, \quad \lambda_d = \frac{0.202}{\sqrt{V}}\,\text{\AA}, \quad \lambda_\alpha = \frac{0.101}{\sqrt{V}}\,\text{\AA}

Matter wavelengths of fundamental particles accelerated from rest through potential difference V in volts.

Examiner Tip: For electron: λ = √(150/V) Å. Ratio of wavelengths for same V: λ_p : λ_d : λ_α = 1 : 1/√2 : 1/(2√2).

Thermal De Broglie Wavelength

\lambda = \frac{h}{\sqrt{3m k_B T}} \approx \frac{25.17}{\sqrt{T}}\,\text{\AA} \quad (\text{for thermal neutron})

Wavelength associated with gas molecules or neutrons in thermal equilibrium at temperature T (Kelvin).

Examiner Tip: Mean translational kinetic energy is K_avg = (3/2)k_B T.

Photon Flux & Saturation Photocurrent

n = \frac{P}{E} = \frac{P\lambda}{hc} \approx 5 \times 10^{24} P\lambda, \quad i_{\text{sat}} = \eta \cdot n \cdot e

Number of photons incident per second for a source of power P, and resulting saturation current with quantum efficiency η.

Examiner Tip: In JEE questions, quantum efficiency η is typically 0.1% to 1% (i.e. only 1 out of 100 or 1000 incident photons ejects a photoelectron).

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in Dual Nature of Radiation & Matter

•Photoelectric current depends on INTENSITY of light, but maximum kinetic energy depends ONLY on FREQUENCY.
•Stopping potential is independent of light intensity.

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