Скачать или смотреть DUAL NATURE OF RADIATION AND MATTER -1-PAGE FORMULA SHEET FOR CLASS 12TH PHYSICS

Dual nature of radiation and matter -1-page formula sheet for class 12 physics

Constants

Planck constant: h = 6.626 × 10⁻³⁴ J·s

Electron mass: mₑ = 9.11 × 10⁻³¹ kg

Light speed: c = 3 × 10⁸ m/s

Elementary charge: e = 1.6 × 10⁻¹⁹ C


Photon (Light as particle)

Energy: E = hν

Frequency–wavelength: c = νλ

Momentum: p = h/λ = E/c

Rest mass: m = 0, moves with speed c

No. of photons: N = Total Energy / (hν) = P·t / hν (P = power)


Photoelectric Effect (Einstein explanation)

Photoelectric equation: hν = ϕ + Kₘₐₓ

Max kinetic energy: Kₘₐₓ = ½ mₑ vₘₐₓ²

Work function: ϕ = hν₀ (ν₀ = threshold frequency)

Stopping potential: eVₛ = Kₘₐₓ

⇒ Kₘₐₓ = eVₛ = hν − ϕ

vₘₐₓ = √(2Kₘₐₓ/mₑ)


Key points: emission is instant, depends on frequency, not intensity.


Compton Effect (Compton discovery)

Wavelength shift:
Δλ = λ′ − λ = (h/mₑ c)(1 − cosθ)

Compton wavelength: λ꜀ = h/mₑ c = 2.43 × 10⁻¹² m

⇒ Δλ = λ꜀ (1 − cosθ)



de Broglie Hypothesis (Matter as wave)

Matter wavelength: λ = h/p = h/mv

Momentum: p = mv = √(2mK) (K = kinetic energy)

⇒ λ = h/√(2mK)


For electron using V (accelerating potential):
½ mₑ v² = eV ⇒ p = √(2 mₑ e V)

⇒ λ = h/√(2 mₑ e V)



Electron Diffraction Evidence

Wave nature of electrons verified by
Davisson–Germer experiment

Diffraction pattern ⇒ confirms matter waves.


Relation Summary

Quantity Formula

Photon Energy E = hν
Photon Momentum p = h/λ = E/c
Matter Wavelength λ = h/p = h/mv
Threshold relation ϕ = hν₀
Stopping potential Kₘₐₓ = eVₛ = hν − ϕ
Compton shift Δλ = (h/mₑc)(1 − cosθ)