# 6.2 The bohr model  (Page 2/9)

 Page 2 / 9

In 1913, Niels Bohr attempted to resolve the atomic paradox by ignoring classical electromagnetism’s prediction that the orbiting electron in hydrogen would continuously emit light. Instead, he incorporated into the classical mechanics description of the atom Planck’s ideas of quantization and Einstein’s finding that light consists of photons whose energy is proportional to their frequency. Bohr assumed that the electron orbiting the nucleus would not normally emit any radiation (the stationary state hypothesis), but it would emit or absorb a photon if it moved to a different orbit. The energy absorbed or emitted would reflect differences in the orbital energies according to this equation:

$\mid \text{Δ}E\mid =\mid {E}_{\text{f}}-{E}_{\text{i}}\mid =h\nu =\phantom{\rule{0.2em}{0ex}}\frac{hc}{\lambda }$

In this equation, h is Planck’s constant and E i and E f are the initial and final orbital energies, respectively. The absolute value of the energy difference is used, since frequencies and wavelengths are always positive. Instead of allowing for continuous values for the angular momentum, energy, and orbit radius, Bohr assumed that only discrete values for these could occur (actually, quantizing any one of these would imply that the other two are also quantized). Bohr’s expression for the quantized energies is:

${E}_{n}=\text{−}\frac{k}{{n}^{2}}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.2em}{0ex}}n=1,\phantom{\rule{0.2em}{0ex}}2,\phantom{\rule{0.2em}{0ex}}3,\phantom{\rule{0.2em}{0ex}}\dots$

In this expression, k is a constant comprising fundamental constants such as the electron mass and charge and Planck’s constant. Inserting the expression for the orbit energies into the equation for Δ E gives

$\text{Δ}E=k\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{1}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{2}^{2}}\phantom{\rule{0.2em}{0ex}}\right)=\phantom{\rule{0.2em}{0ex}}\frac{hc}{\lambda }$

or

$\phantom{\rule{0.2em}{0ex}}\frac{1}{\lambda }\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{k}{hc}\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{1}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{2}^{2}}\phantom{\rule{0.2em}{0ex}}\right)$

which is identical to the Rydberg equation for ${R}_{\infty }=\phantom{\rule{0.2em}{0ex}}\frac{k}{hc}.$ When Bohr calculated his theoretical value for the Rydberg constant, ${R}_{\infty },$ and compared it with the experimentally accepted value, he got excellent agreement. Since the Rydberg constant was one of the most precisely measured constants at that time, this level of agreement was astonishing and meant that Bohr’s model was taken seriously, despite the many assumptions that Bohr needed to derive it.

The lowest few energy levels are shown in [link] . One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. Thus, the electron in a hydrogen atom usually moves in the n = 1 orbit, the orbit in which it has the lowest energy. When the electron is in this lowest energy orbit, the atom is said to be in its ground electronic state (or simply ground state). If the atom receives energy from an outside source, it is possible for the electron to move to an orbit with a higher n value and the atom is now in an excited electronic state (or simply an excited state) with a higher energy. When an electron transitions from an excited state (higher energy orbit) to a less excited state, or ground state, the difference in energy is emitted as a photon. Similarly, if a photon is absorbed by an atom, the energy of the photon moves an electron from a lower energy orbit up to a more excited one. We can relate the energy of electrons in atoms to what we learned previously about energy. The law of conservation of energy says that we can neither create nor destroy energy. Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, that same amount of energy will be liberated when the electron returns to its initial state ( [link] ). In effect, an atom can “store” energy by using it to promote an electron to a state with a higher energy and release it when the electron returns to a lower state. The energy can be released as one quantum of energy, as the electron returns to its ground state (say, from n = 5 to n = 1), or it can be released as two or more smaller quanta as the electron falls to an intermediate state, then to the ground state (say, from n = 5 to n = 4, emitting one quantum, then to n = 1, emitting a second quantum).

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what is an acid and base
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An acid is a substances when dissolve in water to produce hydrogen ion as the only positive ion or proton. while base is a substances when dissolve in water to produce hydroxide ion .
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acid is a substance that produce hydrogen ion as only positive ion when dissolve in water
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my new mix tape
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sir I don't know
favour
the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically a ratio of whole integers.
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1/16th
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general properties of transition metal
form stable complexes Have high melting and boiling points Contain large charge/radius ratio Form compounds which are often paramagnetic Are hard and possess high densities Form compounds with profound catalytic activity Show variable oxidation states form coloured ions and compounds.
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am just tried of it😭🙏
Same here
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organic chem tutor, hell teach you everything.. take notes clearly in a notebook and read it before you go to sleep until you know every topic like the back of your hand
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get good or find something else. don't do it if you don't love it
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s and p diagram
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I dont understand that
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Law of Definite Proportion states that all pure samples of the same chemical compound contains the same elements in proportion by mass
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The branch of natural science that deals with the constitution of substances and the changes that they undergo as a consequence of alterations in the constitution of their molecules
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what is the constitution of substance
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chemistry is the study of matter and the changes it undergoes.
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picture of periodic table
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matter is any thing that has weight or mass and can occupy spaces
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