Examples of Planck constant in the following topics:
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- Waves were poorly understood until the 1900s, when Max Planck and Albert Einstein developed modern corrections to classical theory.
- In his work he developed what is now known as "Planck's constant," which is approximately equal to 6.626×10-34 J·s.
- The energy (E) of a photon can be related to its frequency (f) by Planck's constant (h):
- Note that energy cannot take any value: it can only exist in increments of frequency times Planck's constant (or Planck's constant times c divided by wavelength).
- Substituting E with hc/λ cancels the c terms, making momentum also equal to the simple ratio of Planck's constant to wavelength.
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- Bohr explained hydrogen's spectrum successfully by adopting a quantization condition and by introducing the Planck constant in his model.
- Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency $\nu$ determined by the energy difference of the levels according to the Planck relation: $\Delta{E} = E_2-E_1=h\nu$ , where $h$ is the Planck constant.
- We have seen that Planck adopted a new condition of energy quantization to explain the black body radiation, where he introduced the Planck constant $h$ for the first time.
- Soon after, Einstein resorted to this new concept of energy quantization and used the Planck constant again to explain the photoelectric effects, in which he assumed that electromagnetic radiation interact with matter as particles (later named "photons").
- Here, Bohr explained the atomic hydrogen spectrum successfully for the first time by adopting a quantization condition and by introducing the Planck constant in his atomic model.
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- A black body in thermal equilibrium (i.e. at a constant temperature) emits electromagnetic radiation called black body radiation.
- The puzzle was solved in 1901 by Max Planck in the formalism now known as Planck's law of black-body radiation.
- Although Planck's derivation is beyond the scope of this section (it will be covered in Quantum Mechanics), Planck's law may be written:
- where $B$ is the spectral radiance of the surface of the black body, $T$ is its absolute temperature, $\lambda$ is wavelength of the radiation, $k_B$ is the Boltzmann constant, $h$ is the Planck constant, and $c$ is the speed of light.
- It is not a surprise that he introduced Planck constant $h = 6.626 \times 10^{-34} J \cdot s$ for the first time in his derivation of the Planck's law.
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- Building on Max Planck's theory of black body radiation, Einstein theorized that the energy in each quantum of light was equal to the frequency multiplied by a constant $h$, later called Planck's constant.
- According to Einstein, the maximum kinetic energy of an ejected electron is given by $K_{max} = h f - \phi$, where $h$ is the Planck constant and $f$ is the frequency of the incident photon.
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- In 2005, the International Committee for Weights and Measures (CIPM) recommended that the kilogram be redefined in terms of a fundamental constant of nature, due to evidence that the International Prototype Kilogram will vary in mass over time .
- At its 2011 meeting, the General Conference on Weights and Measures (CGPM) agreed that the kilogram should be redefined in terms of the Planck constant.
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- Max Planck explained black body radiation using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light, do so in amounts of energy that are quantized.
- Energy of photon: From the studies of photoelectric effects, energy of a photon is directly proportional to its frequency with the Planck constant being the proportionality factor.
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- Here h is Planck's constant and p the relativistic momentum of the electron.
- From the work by Planck (black body radiation) and Einstein (photoelectric effect), physicists understood that electromagnetic waves sometimes behaved like particles.
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- Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency $\nu$ determined by the energy difference of the levels according to the Planck relation:
- where $h$ is Planck's constant and $\nu$ is the frequency of the radiation.
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- Dividing electron volts by a constant with units of velocity results in a momentum.
- where h is the Planck constant and c is the speed of light.
- To convert to Kelvins, simply divide the value of 1 eV (in Joules) by the Boltzmann constant (1.3806505(24)×10-23 J/K).
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- First postulated by Planck, these "particles" conceptualized "quantized" elements of light as containing a specific amount of energy depending only on the frequency of the light.
- where λ\lambda is the initial wavelength, λ′\lambda' is the wavelength after scattering, $h$ is the Planck constant, mem_e is the Electron rest mass, $c$ is the speed of light, and θ\theta is the scattering angle.