# 6.2 The bohr model  (Page 5/9)

 Page 5 / 9

## 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.

#### Questions & Answers

wat is electrolysis?
list the side effect of chemical industries
how do you ionise an atom
many ways ,but one of them is when the atom becomes heated to a certain temperature the surface electron becomes too energetic and leaves the atom because the attraction between the nucleus and the electron becomes overpowered by the energetic eletron
sunday
also hitting of two atoms can cause transfer of surface electrons
sunday
and when this transfers occur the atom becomes ionised
sunday
who is doing Cape chemistry tomorrow?
What is hybridization
the mix between different breeds of species in one
Jared
it is the blending of orbitals.
stanley
the mixing of orbital
caramel
are covalent bonds influenced by factors such as temperature and pressure?
what is catalyst used for mirror test
when an atom looses electron, what does it become?
it's oxidized and called an ion
Anora
thanks
Abdullahi
Now, I get it
Abdullahi
cation
Anora
can you give an example please, if you don't mind
Abdullahi
a positive ion,become positively charged/a cation.
Janis
sodium plus one is simple cation is exmpl
ajmal
what is copper
just an element
Power
Cu
daniel
Why is water a single covalent bond?
nitrogen is a gas whereas phosphorus is solid .Explain.
can you explain what you are needing it now better than maybe I'm just not interpreting it what you're needing to know
Alex
cool nitrogen down to around negative 270 °F and it will be solid. now they are both solid
daniel
whats a base
A base is a substance which will neutralize an acid to yield salt and water only
Zainab
base is a substance that produces OH(aq) ions in aqueous solution. Strong soluable bases are in water and are completely dislocated. Therefore weak base ionize slightly...
Roy
a base is a substance that neutralise and acid to form salt and water
Daksalma
write electrolysis of bright solution using either carbon or platinum and write the reaction at the anode or at the cathode
what is the H3O of a solution with the pH of 2.5
pH<7, therefore there are only H3O+HX3OX+particles in the solution. [H3O+]=10−pH=10−6.99=1.02⋅10−7[HX3OX+]=10−pH=10−6.99=1.02⋅10−7 When the pH is smaller than 6 or greater than 8, one will not notice the difference, but here it is logarithmically speaking  and I'll give you another one if this is ki
Alex
if I'm answering and interpreting what you're asking correctly
Alex
When the pH is smaller than 6 or greater than 8, one will not notice the difference, but here it is logarithmically speaking
Alex
sorry I don't know why that sent again
Alex
We have [H3O+]=10−pH=10−6.99=1.02⋅10−7[HX3OX+]=10−pH=10−6.99=1.02⋅10−7 and [OH−]=10−pOH=10−7.01=9.77⋅10−8[OHX−]=10−pOH=10−7.01=9.77⋅10−8.  Because of H3O++OH−⟶2H2OHX3OX++OHX−⟶2HX2O we are left with [H3O+]=1.02⋅10−7−9.77⋅10−8=4.6⋅10−9
Alex
What is chemistry
chemistry is an experimental study of matter and substances which is concerned with the structure composition and the changes these substances undergo
Mohamed
Chemistry=seemyhistory Life of the Past, Present and Future of a noun (person place or things) A compound of 3 words to create one word.
Debra
Chemistry=see my history che=see mi=my stry=story
Debra