# 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.

which one of the Lewis structure
Lewis structure just shows Valence electrons
Cassie
what is a solution
A liquid mixture in which the minor component (the solute) is uniformly distributed within the major component (the solvent).
Gabby
what is an acid and base
Joy
acids are substances that ionize (break off) in an aqueous solution to produce hydrogen (H+) ions. pH level less than 7  bases produce hydroxide (OH-) ions in solution. pH level greater than 7
Gabby
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 .
Lawal
acid is a substance that produce hydrogen ion as only positive ion when dissolve in water
Ayomide
what is flame
my new mix tape
Jake
What is Stoichiometry?
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.
Gabby
A radioactive subtance has a half life of 20hrs what fraction of the original radioactive nuclear will remain in 80hrs
1/16th
Ian
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.
Gabby
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am just tried of it😭🙏
Same here
Brianna
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
Professor
I find it very hard to understand and remember things I read please I need help. Is just as if chemistry is difficult to me
Precious
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pray it will favour me
get good or find something else. don't do it if you don't love it
Professor
what is dative bond?
A coordinate covalent bond, also known as a dative bond or coordinate bond is a kind of 2-center, 2-electron covalent bond in which the two electrons derive from the same atom.
dharshika
how can i write iupac nunber
Emmanuel
In chemical nomenclature, the IUPAC nomenclature of organic chemistry is a method of organic chemical compounds as recommended by the International Union of Pure and Applied Chemistry. It is published in the Nomenclature of Organic Chemistry
Nike
How can I know the logic for writing the configuration of an element?
Brianna
s and p diagram
Papa
I dont understand that
Brianna
what is elemental composition of earth
what if we try copper and the hydrogen what happened
law of definite proportion
Law of Definite Proportion states that all pure samples of the same chemical compound contains the same elements in proportion by mass
Eunice
what is chemistry
It is that branch of Science which deals with the study of composition, structure and properties of matter .... Ok
ShAmy
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
Young
what is the constitution of substance
ShAmy
chemistry is the study of matter and the changes it undergoes.
Bernard
picture of periodic table
what is matter
matter is any thing that has weight or mass and can occupy spaces
Bernard
What are the classes of colloid