☰ Contents · Physics

Origins of quantum physics, photoeffect

Lessons 34–35 · 2 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 11, 1st edition. Niso Poligraf Publishing House, Tashkent, 2018
34

The origin of quantum physics

Textbook: pp. 135–136
GoalKnow the laws of thermal radiation (Wien's displacement law), Planck's hypothesis and E = hν; calculate photon energy.
New words
thermal radiation · issiqlik nurlanishiquantum · kvantPlanck constant · Plank doimiysiWien's displacement law · Vin siljish qonuni
Explanation

Every hot body radiates; its spectrum is continuous and its maximum depends on temperature. Wien's displacement law: λ_m·T = b, b = 2.898·10⁻³ m·K; the hotter the body, the more the maximum shifts to short wavelengths (a glowing metal goes from red to white). At the end of the 19th century classical physics could not explain the shape of this spectrum: the Rayleigh–Jeans formula agreed with experiment at long wavelengths but predicted infinite radiation at short ones (the «ultraviolet catastrophe»). In 1900 Planck proposed that radiation and absorption exchange energy not continuously but in portions, quanta; the energy of one quantum is proportional to the frequency: E = hν, with h = 6.63·10⁻³⁴ J·s the Planck constant. Since ν = c/λ, E = hc/λ; in practice hc ≈ 1240 eV·nm is handy (1 eV = 1.6·10⁻¹⁹ J). Planck's hypothesis gave a spectrum that matches experiment and was the beginning of quantum physics.

Worked examples
A photon has wavelength 310 nm: E = hc/λ = 1240/310 = 4 eV = 4·1.6·10⁻¹⁹ = 6.4·10⁻¹⁹ J. Its frequency is ν = c/λ = 3·10⁸/(3.1·10⁻⁷) ≈ 9.7·10¹⁴ Hz.
A glowing filament at T = 2898 K: λ_m = b/T = 2.898·10⁻³/2898 = 10⁻⁶ m = 1 μm, in the infrared; that is why most of a lamp's radiation is invisible to the eye.
Class activity

In your notebook use 1240 eV·nm to calculate the photon energies of red (700 nm), green (550 nm) and violet (400 nm) light in eV and put them in order. Do not heat metal at home to observe it; do the calculation instead.

Practice
1
Write the formula for the energy of a quantum in Planck's hypothesis.
2
A photon has wavelength 248 nm. What is its energy in eV? (hc = 1240 eV·nm)
3
A body is at T = 5796 K. What is λ_m in nm? (b = 2.898·10⁶ nm·K)
4
Why does heated iron look red first and later yellowish-white?