# 6.2 The bohr model  (Page 5/9)

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## Key equations

• ${E}_{n}=-\frac{k{Z}^{2}}{{n}^{2}}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.2em}{0ex}}n=1,\phantom{\rule{0.2em}{0ex}}2,\phantom{\rule{0.2em}{0ex}}3,\phantom{\rule{0.2em}{0ex}}\dots$
• $\text{Δ}E=k{Z}^{2}\left(\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{1}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{2}^{2}}\phantom{\rule{0.2em}{0ex}}\right)$
• $r=\phantom{\rule{0.2em}{0ex}}\frac{{n}^{2}}{Z}\phantom{\rule{0.2em}{0ex}}{a}_{0}$

## Chemistry end of chapter exercises

Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?

What does it mean to say that the energy of the electrons in an atom is quantized?

Quantized energy means that the electrons can possess only certain discrete energy values; values between those quantized values are not permitted.

Using the Bohr model, determine the energy, in joules, necessary to ionize a ground-state hydrogen atom. Show your calculations.

The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It is the amount of energy that an electron gains when subjected to a potential of 1 volt; 1 eV = 1.602 $×$ 10 –19 J. Using the Bohr model, determine the energy, in electron volts, of the photon produced when an electron in a hydrogen atom moves from the orbit with n = 5 to the orbit with n = 2. Show your calculations.

$\begin{array}{ll}E\hfill & =\phantom{\rule{0.2em}{0ex}}{E}_{2}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}{E}_{5}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}2.179\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-18}\left(\frac{1}{{n}_{2}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{n}_{5}^{2}}\right)\phantom{\rule{0.2em}{0ex}}\text{J}\hfill \\ \hfill & =\phantom{\rule{0.2em}{0ex}}2.179\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-18}\left(\frac{1}{{2}^{2}}\phantom{\rule{0.2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{1}{{5}^{2}}\right)\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}4.576\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-19}\phantom{\rule{0.2em}{0ex}}\text{J}\hfill \\ \hfill & =\phantom{\rule{0.2em}{0ex}}\frac{4.576\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-19}\phantom{\rule{0.2em}{0ex}}\overline{)\text{J}}}{1.602\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-19}\phantom{\rule{0.2em}{0ex}}\overline{)\text{J}}\phantom{\rule{0.2em}{0ex}}{\text{eV}}^{-1}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}2.856\phantom{\rule{0.2em}{0ex}}\text{eV}\hfill \end{array}$

Using the Bohr model, determine the lowest possible energy, in joules, for the electron in the Li 2+ ion.

Using the Bohr model, determine the lowest possible energy for the electron in the He + ion.

−8.716 $×$ 10 −18 J

Using the Bohr model, determine the energy of an electron with n = 6 in a hydrogen atom.

Using the Bohr model, determine the energy of an electron with n = 8 in a hydrogen atom.

−3.405 $×$ 10 −20 J

How far from the nucleus in angstroms (1 angstrom = 1 $\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}$ 10 –10 m) is the electron in a hydrogen atom if it has an energy of –8.72 $\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}$ 10 –20 J?

What is the radius, in angstroms, of the orbital of an electron with n = 8 in a hydrogen atom?

33.9 Å

Using the Bohr model, determine the energy in joules of the photon produced when an electron in a He + ion moves from the orbit with n = 5 to the orbit with n = 2.

Using the Bohr model, determine the energy in joules of the photon produced when an electron in a Li 2+ ion moves from the orbit with n = 2 to the orbit with n = 1.

1.471 $×$ 10 −17 J

Consider a large number of hydrogen atoms with electrons randomly distributed in the n = 1, 2, 3, and 4 orbits.

(a) How many different wavelengths of light are emitted by these atoms as the electrons fall into lower-energy orbitals?

(b) Calculate the lowest and highest energies of light produced by the transitions described in part (a).

(c) Calculate the frequencies and wavelengths of the light produced by the transitions described in part (b).

How are the Bohr model and the Rutherford model of the atom similar? How are they different?

Both involve a relatively heavy nucleus with electrons moving around it, although strictly speaking, the Bohr model works only for one-electron atoms or ions. According to classical mechanics, the Rutherford model predicts a miniature “solar system” with electrons moving about the nucleus in circular or elliptical orbits that are confined to planes. If the requirements of classical electromagnetic theory that electrons in such orbits would emit electromagnetic radiation are ignored, such atoms would be stable, having constant energy and angular momentum, but would not emit any visible light (contrary to observation). If classical electromagnetic theory is applied, then the Rutherford atom would emit electromagnetic radiation of continually increasing frequency (contrary to the observed discrete spectra), thereby losing energy until the atom collapsed in an absurdly short time (contrary to the observed long-term stability of atoms). The Bohr model retains the classical mechanics view of circular orbits confined to planes having constant energy and angular momentum, but restricts these to quantized values dependent on a single quantum number, n . The orbiting electron in Bohr’s model is assumed not to emit any electromagnetic radiation while moving about the nucleus in its stationary orbits, but the atom can emit or absorb electromagnetic radiation when the electron changes from one orbit to another. Because of the quantized orbits, such “quantum jumps” will produce discrete spectra, in agreement with observations.

The spectra of hydrogen and of calcium are shown in [link] . What causes the lines in these spectra? Why are the colors of the lines different? Suggest a reason for the observation that the spectrum of calcium is more complicated than the spectrum of hydrogen.

what exactly is e question based on
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
send me
Benjii
dont know
Alok
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
guys I'm sorry I dont understand this application are you human beings or robots
Delma
Homo sapiens
Zakaria
hhhhh
Abdelkebir
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
when making a chemical reaction how do u know the product of the reactant
Delma
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
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
What is the PDF of iron
What is catalyst
a catalyst increase the rate of chemical reactions without becoming apart of it...ex vitamins and minerals
Coach
catalyst is a substance added to the reaction that modifies the rate of the reaction ( make it happen faster or in some cases slower).
Attila
catalyst speeds up the rate of chemical reaction and has no effect in the product
Joesph
catalyst are substance that tends tew speed up the rate of reactions
Kedeh
1. Describe element that contain 4 protons in the outermost Shell (using 3 pages) 2. Explain why charges to mass ratio of all cathode drains are the same