Planck's constant

Also called h

Planck's constant, h, is the proportionality constant between a photon's energy and its frequency. The AP Physics 2 table prints it as 6.63 times 10 to the minus 34 J s, and equivalently as 4.14 times 10 to the minus 15 eV s.

The table of information prints hh in two unit systems, and picking the right one removes most of the arithmetic.

  • h=6.63×10−34 J⋅sh = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s} for energies in joules.
  • h=4.14×10−15 eV⋅sh = 4.14 \times 10^{-15} \, \text{eV} \cdot \text{s} for energies in electron volts.

A third printed line does more work than either: hc=1.99×10−25 J⋅m=1240 eV⋅nmhc = 1.99 \times 10^{-25} \, \text{J} \cdot \text{m} = 1240 \, \text{eV} \cdot \text{nm}. Put a wavelength in nanometers into E=hc/λE = hc/\lambda using the second form and the photon energy falls out in electron volts with no powers of ten to carry.

Four of the ten Modern Physics equations on the sheet contain hh: E=hfE = hf, λ=h/p\lambda = h/p, Kmax⁡=hf−ϕK_{\max} = hf - \phi, and the Compton shift Δλ=hmec(1−cos⁡θ)\Delta \lambda = \frac{h}{m_e c}(1 - \cos\theta).

It also shows up as a gradient. Plot maximum kinetic energy against frequency for a photoelectric experiment and the slope is hh; plot stopping potential against frequency and the slope is h/eh/e. Sample instructional activity 2 in the CED has students recover hh in eV⋅s\text{eV} \cdot \text{s} from the voltage across colored LEDs.

Among the four AP physics equation sheets, hh is printed on the Physics 2 one alone.

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