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Key equations

  • E n = k Z 2 n 2 , n = 1 , 2 , 3 ,
  • Δ E = k Z 2 ( 1 n 1 2 1 n 2 2 )
  • r = n 2 Z 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?

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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.

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

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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.

 
E = E 2 E 5 = 2.179 × 10 −18 ( 1 n 2 2 1 n 5 2 ) J = 2.179 × 10 −18 ( 1 2 2 1 5 2 ) = 4.576 × 10 −19 J = 4.576 × 10 −19 J 1.602 × 10 −19 J eV −1 = 2.856 eV

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

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

−8.716 × 10 −18 J

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

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

−3.405 × 10 −20 J

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How far from the nucleus in angstroms (1 angstrom = 1 × 10 –10 m) is the electron in a hydrogen atom if it has an energy of –8.72 × 10 –20 J?

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

33.9 Å

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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.

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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

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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).

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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.

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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.

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Questions & Answers

what is the 3d-orbital of Ti³+
Timi Reply
What is Lewis acids
Yabsra Reply
Lewis acid is any substance, such as the H+ ion, that can accept a pair of nonbonding electrons. In other words, a Lewis acid is an electron-pair acceptor. 
betuel
Thanks
Yabsra
🤜🤛
betuel
🤜🤛
betuel
describe the way of seperation of water and kerosene
Tang Reply
Kerosene is a hydrocarbon and non-polar. Water is a polar molecule. So a mixture of both liquids is immicible and by adding them to a separation funnel, you can open the tap flowing the less dense liquid in a container. You can read on bond polarity and separation techniques on Google.
Abdelkarim
kerosene will never with water cos its a immiscible liquid
SUNDAY
what is Chemistry
Papie Reply
Chemistry is a branch of natural light science
Yabsra
10 sentences discussing factors affecting solubility
Sara Reply
why is chemistry a science subject
Ukwumonu Reply
10 sentences discussing factors affecting solubility
Sara
How to name carbonique Atom
lix Reply
how many period do we have in the period table
Joseph Reply
187
Ukwumonu
how do i do ionic equations
Amantle Reply
what is the formula for alkanes
Amantle
CnH2n+2 is the alkane formula.
Walter
whenever you get off your fat arse
then you can start to do some real work
hmm
gabson
How much sodium hydroxide must be dissolved in 100mL of water to prepare a 3.95molL^_1
Cindy
what is vast array
benedict Reply
what is Nanoscience
benedict
from health care to manufacturing. Australian academy of science
what is the compound
Yaasmiin
what is Chemistry
Papie
What is array
Yabsra
what will be the total moles of all the molecule present when the different quantities of following gases are mixed together at step 4g of CH4, 22.4 dm3 of oxygen, 11.2dm3 of carbon dioxide and 3.02×10^23 molecules of ammonia.
Soni Reply
0.5 moles of methane and 0.5 mole of sulfur dioxide are mixed together what will be the mass of mixture. a.20g b.40g c.50g d.55g e.60g
Soni Reply
answer;b
Ravina
thnx
Soni
"the halogens are all oxidizing agents" what is the reason for this observation
Kelvin Reply
they are halogens....that is why numbnut 😁
This is not the place to talk down or be rude. Anonymous User keep your comments to yourself if you can't be more respectful.
Dionne
please what is a lightening thunder?
Onimisi Reply
wat are hydrocarbon s
Opio Reply
I think they are molecules that comprise only of hydrogen and carbon atoms ( they are organic if I'm not mistaken)
Mmathabo
am new here can I join
Yeko
yes u can
Benita
❤️
Ukwumonu
hydrocarbons are compunds of carbon and hydrogen but sometimes the hydrogen are replaced by some other elements like oxgen, ammonia and the hydroxyl groups.........thats what leads to the classification and names of hydrocarbons
SUNDAY
Practice Key Terms 4

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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