explain planks quantum theory
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Learning Objective
Calculate the energy element E=hv, using Planck’s Quantum Theory
Key Points
Until the late 19th century, Newtonian physics dominated the scientific worldview. However, by the early 20th century, physicists discovered that the laws of classical mechanics do not apply at the atomic scale.The photoelectric effect could not be rationalized based on existing theories of light, as an increase in the intensity of light did not lead to the same outcome as an increase in the energy of the light.Planck postulated that the energy of light is proportional to the frequency, and the constant that relates them is known as Planck’s constant (h). His work led to Albert Einstein determining that light exists in discrete quanta of energy, or photons.
Terms
photoelectric effectThe emission of electrons from the surface of a material following the absorption of electromagnetic radiation.electromagnetic radiationRadiation (quantized as photons) consisting of oscillating electric and magnetic fields oriented perpendicularly to each other, moving through space.
In the late 18th century, great progress in physics had been made. Classical Newtonian physics at the time was widely accepted in the scientific community for its ability to accurately explain and predict many phenomena. However, by the early 20th century, physicists discovered that the laws of classical mechanics are not applicable at the atomic scale, and experiments such as the photoelectric effect completely contradicted the laws of classical physics. As a result of these observations, physicists articulated a set of theories now known as quantum mechanics. In some ways, quantum mechanics completely changed the way physicists viewed the universe, and it also marked the end of the idea of a clockwork universe (the idea that universe was predictable).
Learning Objective
Calculate the energy element E=hv, using Planck’s Quantum Theory
Key Points
Until the late 19th century, Newtonian physics dominated the scientific worldview. However, by the early 20th century, physicists discovered that the laws of classical mechanics do not apply at the atomic scale.The photoelectric effect could not be rationalized based on existing theories of light, as an increase in the intensity of light did not lead to the same outcome as an increase in the energy of the light.Planck postulated that the energy of light is proportional to the frequency, and the constant that relates them is known as Planck’s constant (h). His work led to Albert Einstein determining that light exists in discrete quanta of energy, or photons.
Terms
photoelectric effectThe emission of electrons from the surface of a material following the absorption of electromagnetic radiation.electromagnetic radiationRadiation (quantized as photons) consisting of oscillating electric and magnetic fields oriented perpendicularly to each other, moving through space.
In the late 18th century, great progress in physics had been made. Classical Newtonian physics at the time was widely accepted in the scientific community for its ability to accurately explain and predict many phenomena. However, by the early 20th century, physicists discovered that the laws of classical mechanics are not applicable at the atomic scale, and experiments such as the photoelectric effect completely contradicted the laws of classical physics. As a result of these observations, physicists articulated a set of theories now known as quantum mechanics. In some ways, quantum mechanics completely changed the way physicists viewed the universe, and it also marked the end of the idea of a clockwork universe (the idea that universe was predictable).
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Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The law is named after Max Planck, who proposed it in 1900. It is a pioneering result of modern physics and quantum theory.
The spectral radiance of a body, Bν, describes the amount of energy it gives off as radiation of different frequencies. It is measured in terms of the power emitted per unit area of the body, per unit solid angle that the radiation is measured over, per unit frequency. Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by
{\displaystyle B_{\nu }(\nu ,T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{\frac {h\nu }{k_{\mathrm {B} }T}}-1}}}
where kB is the Boltzmann constant, h is the Planck constant, and c is the speed of light in the medium, whether material or vacuum.[1][2][3] The spectral radiance can also be expressed per unit wavelength λ instead of per unit frequency. In this case, it is given by
{\displaystyle B_{\lambda }(\lambda ,T)={\frac {2hc^{2}}{\lambda ^{5}}}{\frac {1}{e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}-1}}}.
The law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation. The SI units of Bν are W·sr−1·m−2·Hz−1, while those of Bλ are W·sr−1·m−3.
In the limit of low frequencies (i.e. long wavelengths), Planck's law tends to the Rayleigh–Jeans law, while in the limit of high frequencies (i.e. small wavelengths) it tends to the Wien approximation.
Max Planck developed the law in 1900 with only empirically determined constants, and later showed that, expressed as an energy distribution, it is the unique stable distribution for radiation in thermodynamic equilibrium.[4]As an energy distribution, it is one of a family of thermal equilibrium distributions which include the Bose–Einstein distribution, the Fermi–Dirac distribution and the Maxwell–Boltzmann distribution.
The spectral radiance of a body, Bν, describes the amount of energy it gives off as radiation of different frequencies. It is measured in terms of the power emitted per unit area of the body, per unit solid angle that the radiation is measured over, per unit frequency. Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by
{\displaystyle B_{\nu }(\nu ,T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{\frac {h\nu }{k_{\mathrm {B} }T}}-1}}}
where kB is the Boltzmann constant, h is the Planck constant, and c is the speed of light in the medium, whether material or vacuum.[1][2][3] The spectral radiance can also be expressed per unit wavelength λ instead of per unit frequency. In this case, it is given by
{\displaystyle B_{\lambda }(\lambda ,T)={\frac {2hc^{2}}{\lambda ^{5}}}{\frac {1}{e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}-1}}}.
The law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation. The SI units of Bν are W·sr−1·m−2·Hz−1, while those of Bλ are W·sr−1·m−3.
In the limit of low frequencies (i.e. long wavelengths), Planck's law tends to the Rayleigh–Jeans law, while in the limit of high frequencies (i.e. small wavelengths) it tends to the Wien approximation.
Max Planck developed the law in 1900 with only empirically determined constants, and later showed that, expressed as an energy distribution, it is the unique stable distribution for radiation in thermodynamic equilibrium.[4]As an energy distribution, it is one of a family of thermal equilibrium distributions which include the Bose–Einstein distribution, the Fermi–Dirac distribution and the Maxwell–Boltzmann distribution.
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