# 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).

what is an anode
what is electrochemical series
electrochemical series are tables that show the arrangement of standard electrode potentials of different systems in which the half cell reactions are written as reductions
Daniella
when making a chemical reaction how do u know the product of the reactant
As long as you know the reactants, you can definitely know the product
Francis
specifically I am talking about the bonding
Delma
depending on the nature of the rectants
Francis
The test tubes shown here contain equal amounts of the specified motor oils. Identical metal spheres were dropped at the same time into each of the tubes, and a brief moment later, the spheres had fallen to the heights indicated in the illustration. Rank the motor oils in order of increasing viscosity, and explain your reasoning:
Where are the test tubes
Zakaria
same question as zakariah
what exactly is e question based on
Snoe
guys I'm sorry I dont understand this application are you human beings or robots
Homo sapiens
Zakaria
hhhhh
Abdelkebir
what is atom
smallest particle of an element
Delma
an atom is a smallest particle an element that always takes the property of that element and can take part in chemical reaction
jason
atom is smallest particular which can not further divided
ZeShan
atom is the basic unit of matter that consist of dense Central nucleus sorronded by the clouds of negatively changed electrons.
Kibela
what is compressibility Factor?
Francis
z=pv/RT is unity for ideal gas
ZeShan
what are alkanes used for
it depends which alkane. Just Google 'list alkane and use' looking at fractional distillation may help too
superb
Alok
What is chemistry
chemistry is the understanding the concept of Matter
kingsley
there are thousands of concepts to explain what is. chemistry...
Alok
industrial chemistry and its features
what is physical properties
is the feutures that the thing have or what thing have in their physical shape
Fayruusa
it is thi features than an element or compound have and these features are used to differentiate these elements or compounds
what is saponification
Saponification- soaps are sodium or potassium salts of long chain fatty acids... It's basically turning fat/oil into soap. There was some other definition too, that i don't remember at the moment. Sorry! ;)
Bridgette
industrial use of hydrogen
hydrogen is used for industrial applications such as refining, treating metals, and food processing. Liquid hydrogen is the fuel that once propelled the space shuttle and other rockets. ...
Mark
what's flint
what is hydrocarbon
hydrocarbon consist of hydrogen and carbon
Hedosco
correct
magnus
what is alkenes
alkenes are molecules that have a carbon carbon double bond
the carbon contain hydrogen hydrogen double bond
Vishal
You can't get hydrogen hydrogen double bonds. Hydrogen bonds so it has a full outer shell. hydrogen has 1 electron and only needs one more go obtain outer shell stability.
oxygen exists as a double bond. How about carbon monoxide
Delma
in carbon monoxide 3 bond between c and o and lone pair of electron on each
ZeShan
sorry, I didn't quite understand
Delma
There is a triple covalent bond between C and O and both has a lone pair of electrons. Thus both has a full shell of valence electrons.
Attila