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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 stoichometry
ngwuebo Reply
what is atom
yinka Reply
An indivisible part of an element
ngwuebo
the smallest particle of an element which is indivisible is called an atom
Aloaye
An atom is the smallest indivisible particle of an element that can take part in chemical reaction
Alieu
is carbonates soluble
Ebuka Reply
what is the difference between light and electricity
Joshua Reply
What is atom? atom can be defined as the smallest particles
Adazion
what is the difference between Anode and nodes?
Adazion
What's the net equations for the three steps of dissociation of phosphoric acid?
Lisa Reply
what is chemistry
Prince Reply
the study of matter
Reginald
what did the first law of thermodynamics say
Starr Reply
energy can neither be created or distroyed it can only be transferred or converted from one form to another
Adedeji
Graham's law of Diffusion
Ayo Reply
what is melting vaporization
Anieke Reply
melting and boiling point explain in term of molecular motion and Brownian movement
Anieke
Scientific notation for 150.9433962
Steve Reply
what is aromaticity
Usman Reply
aromaticity is a conjugated pi system specific to organic rings like benzene, which have an odd number of electron pairs within the system that allows for exceptional molecular stability
Pookieman
what is caustic soda
Ogbonna Reply
sodium hydroxide (NaOH)
Kamaluddeen
what is distilled water
Rihanat
is simply means a condensed water vapour
Kamaluddeen
advantage and disadvantage of water to human and industry
Abdulrahman Reply
a hydrocarbon contains 7.7 percent by mass of hydrogen and 92.3 percent by mass of carbon
Timothy Reply
how many types of covalent r there
JArim Reply
how many covalent bond r there
JArim
they are three 3
Adazion
TYPES OF COVALENT BOND-POLAR BOND-NON POLAR BOND-DOUBLE BOND-TRIPPLE BOND. There are three types of covalent bond depending upon the number of shared electron pairs. A covalent bond formed by the mutual sharing of one electron pair between two atoms is called a "Single Covalent bond.
Usman
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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