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The proportionality can be replaced by an equality:

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## The proportionality can be replaced by an equality:

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**Quanta: The smallest quantity of energy that can be emitted**in the form of electromagnetic radiation. Quanta and quantum of radiant energy are used synonymously. The energy of the radiation is proportional to the frequency of the emitted radiation: E**The proportionality can be replaced by an equality:**E = h h is the proportionality constant, and is called Planck’s constant.**The proportionality can be replaced by an equality:**E = h h is the proportionality constant, and is called Planck’s constant. Planck’s constant has the value h = 6.62608 x 10-34 Js**According to Planck’s quantum theory, excited atoms**emit energy in multiples of h . For example, h , 2 h , 3 h , … but never values like 1.67 h , or 4.98 h .**According to Planck’s quantum theory, excited atoms**emit energy in multiples of h . For example, h , 2 h , 3 h , … but never values like 1.67 h , or 4.98 h . Photon: Single quantum of radiant energy h .**The idea that energies should be quantized in this manner**may seem strange, but the concept of quantization has ample analogy.**The idea that energies should be quantized in this manner**may seem strange, but the concept of quantization has ample analogy. For example, the electric charge is quantized.**The idea that energies should be quantized in this manner**may seem strange, but the concept of quantization has ample analogy. For example, the electric charge is quantized. Matter is quantized, since the number of electrons, protons, and neutrons in an atom must be integers.**Problem example: The maximum wavelength associated with the**light emitted from a certain electric heater is 625 nm. Calculate the frequency and energy associated with this wavelength.**Problem example: The maximum wavelength associated with the**light emitted from a certain electric heater is 625 nm. Calculate the frequency and energy associated with this wavelength.**Problem example: The maximum wavelength associated with the**light emitted from a certain electric heater is 625 nm. Calculate the frequency and energy associated with this wavelength.**Problem example: The maximum wavelength associated with the**light emitted from a certain electric heater is 625 nm. Calculate the frequency and energy associated with this wavelength. = 4.80 x 1014 s-1**Problem example: The maximum wavelength associated with the**light emitted from a certain electric heater is 625 nm. Calculate the frequency and energy associated with this wavelength. = 4.80 x 1014 s-1 = 4.80 x 1014 Hz**The energy is evaluated from**E = h = (6.626 x 10-34 Js)( 4.80 x 1014 s-1)**The energy is evaluated from**E = h = (6.626 x 10-34 Js)( 4.80 x 1014 s-1) = 3.18 x 10-19 J**Atomic Structure**Atomic Spectra: Energy Levels In Atoms**Atomic Structure**Atomic Spectra: Energy Levels In Atoms Electronic Structure: How electrons are distributed about the nucleus is called the atom’s electronic structure.**Atomic Structure**Atomic Spectra: Energy Levels In Atoms Electronic Structure: How electrons are distributed about the nucleus is called the atom’s electronic structure. Our understanding of electronic structure comes from the study of the light emitted when atoms of various elements are excited.**Spectrum: A plot of energy absorbed or emitted as a function**of the wavelength. A spectrum could be either a continuous plot, or a series of discrete lines.**Spectrum: A plot of energy absorbed or emitted as a function**of the wavelength. A spectrum could be either a continuous plot, or a series of discrete lines. Emission Spectra: A continuous or discrete series of lines representing the radiation emitted by an excited atom or molecule.**A feature displayed by the sun’s emission spectrum and**that of many heated solids is that they are both continuous, which means essentially all wavelengths of light are represented.**Very different appearance was noted in the study of the**emission spectra of atoms in the gas phase.**Very different appearance was noted in the study of the**emission spectra of atoms in the gas phase. These spectra did not show a continuous spread of wavelengths from red to violet; rather, they emitted light at only certain specific wavelengths, and not at others.**Very different appearance was noted in the study of the**emission spectra of atoms in the gas phase. These spectra did not show a continuous spread of wavelengths from red to violet; rather, they emitted light at only certain specific wavelengths, and not at others. Such spectra are called line spectra.**Line spectrum: A spectrum produced when electromagnetic**radiation is absorbed or emitted by a substance only at certain wavelengths.**The Bohr Model of the Hydrogen atom.**In the early 1900’s a principal unsolved problem was the need to provide a theory for the observed line spectra of excited atoms.**The Bohr Model of the Hydrogen atom.**In the early 1900’s a principal unsolved problem was the need to provide a theory for the observed line spectra of excited atoms. Even the line spectrum of the simplest atom – the hydrogen atom – could not be explained theoretically.**Bohr attacked this problem for the H atom by assuming**that in a stable atom the electron can circle the nucleus forever without losing energy and falling into the nucleus.**Bohr attacked this problem for the H atom by assuming**that in a stable atom the electron can circle the nucleus forever without losing energy and falling into the nucleus. An electron cannot circle the nucleus in just any orbit, rather, only certain specific orbits are allowed.**The emission of radiation by an atom such as hydrogen**could be “explained” in terms of the electron dropping from a higher orbit to a lower orbit, giving up a quantum of electromagnetic energy.**The emission of radiation by an atom such as hydrogen**could be “explained” in terms of the electron dropping from a higher orbit to a lower orbit, giving up a quantum of electromagnetic energy. Bohr’s result for the energy of each orbit, En, is given by:**where: m = the mass of the electron**e = charge on the electron**where: m = the mass of the electron**e = charge on the electron h = Planck’s constant**where: m = the mass of the electron**e = charge on the electron h = Planck’s constant n = a positive integer value ( n = 1, 2, 3, …)**where: m = the mass of the electron**e = charge on the electron h = Planck’s constant n = a positive integer value ( n = 1, 2, 3, …) = vacuum permittivity**where: m = the mass of the electron**e = charge on the electron h = Planck’s constant n = a positive integer value ( n = 1, 2, 3, …) = vacuum permittivity En= the energy of the different orbits**The Bohr formula for En will be simplified to read**k En = – n2**The Bohr formula for En will be simplified to read**k En = – n2 where k represents the collection of terms in the ( ….) in the previous formula. The constant k has the value**The Bohr formula for En will be simplified to read**k En = – n2 where k represents the collection of terms in the ( ….) in the previous formula. The constant k has the value k = 2.18 x 10-18 J**The negative sign is convention. When n = infinity, that**is, when the electron is completely separated from the nucleus,**The negative sign is convention. When n = infinity, that**is, when the electron is completely separated from the nucleus,