Domanda del libro di testo
Consider the electronic structure of the element bismuth.
(d) Would you expect element 115 to have an ionization ene-rgy greater than, equal to, or less than that of bismuth? Explain.
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Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory
McMurry8th EditionChemistryISBN: 9781292336145
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TOC.tableOfContents
- Ch.1 - Chemical Tools: Experimentation & Measurement170
- Ch.2 - Atoms, Molecules & Ions160
- Ch.3 - Mass Relationships in Chemical Reactions169
- Ch.4 - Reactions in Aqueous Solution199
- Ch.5 - Periodicity & Electronic Structure of Atoms102
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory92
- Ch.7 - Covalent Bonding and Electron-Dot Structures61
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure59
- Ch.9 - Thermochemistry: Chemical Energy122
- Ch.10 - Gases: Their Properties & Behavior155
- Ch.11 - Liquids & Phase Changes54
- Ch.12 - Solids and Solid-State Materials73
- Ch.13 - Solutions & Their Properties120
- Ch.14 - Chemical Kinetics98
- Ch.15 - Chemical Equilibrium125
- Ch.16 - Aqueous Equilibria: Acids & Bases110
- Ch.17 - Applications of Aqueous Equilibria147
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium86
- Ch.19 - Electrochemistry154
- Ch.20 - Nuclear Chemistry96
- Ch.21 - Transition Elements and Coordination Chemistry156
- Ch.22 - The Main Group Elements187
- Ch.23 - Organic and Biological Chemistry51
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McMurry 8th EditionCh.6 - Ionic Compounds: Periodic Trends and Bonding TheoryProblema 103a
McMurry 8th EditionCh.6 - Ionic Compounds: Periodic Trends and Bonding TheoryProblema 103aCapitolo 6, Problema 103a
Consider the electronic structure of the element bismuth. (a) The first ionization energy of bismuth is Ei1 = +703 kJ/ mol. What is the longest possible wavelength of light that could ionize an atom of bismuth?
Guida verificata passo dopo passo1
Identify the relationship between energy and wavelength using the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy, \( h \) is Planck's constant (6.626 \(\times\) 10^{-34} \(\text{ J s}\)), \( c \) is the speed of light (3.00 \(\times\) 10^8 \(\text{ m/s}\)), and \( \lambda \) is the wavelength.
Convert the ionization energy from kJ/mol to J/atom. Since 1 mol contains Avogadro's number of atoms (6.022 \(\times\) 10^{23} \(\text{ atoms/mol}\)), use the conversion: \( 703 \text{ kJ/mol} \times \frac{1000 \text{ J}}{1 \text{ kJ}} \times \frac{1 \text{ mol}}{6.022 \times 10^{23} \text{ atoms}} \).
Substitute the converted energy value into the equation \( E = \frac{hc}{\lambda} \) to solve for \( \lambda \).
Rearrange the equation to solve for wavelength: \( \lambda = \frac{hc}{E} \).
Calculate the wavelength using the values for \( h \), \( c \), and the converted \( E \) to find the longest possible wavelength of light that could ionize an atom of bismuth.
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Ionization Energy
Ionization energy is the amount of energy required to remove an electron from an atom in its gaseous state. For bismuth, the first ionization energy is 703 kJ/mol, indicating the energy needed to remove the outermost electron. This concept is crucial for understanding how much energy is necessary to ionize an atom and relates directly to the wavelength of light that can provide this energy.
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Percorso guidato
01:19
Ionization Energy
Photon Energy and Wavelength Relationship
The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This relationship means that longer wavelengths correspond to lower energy photons. To find the longest wavelength capable of ionizing bismuth, one must calculate the wavelength that corresponds to the ionization energy.
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00:31Frequency-Wavelength Relationship
Planck's Constant
Planck's constant (h) is a fundamental constant in quantum mechanics, valued at approximately 6.626 x 10^-34 J·s. It relates the energy of a photon to its frequency and wavelength. Understanding this constant is essential for calculating the energy of photons and determining the wavelength of light needed to achieve specific energy transitions, such as ionization.
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Percorso guidato
00:50Photons and Planck's Constant
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Many early chemists noted a diagonal relationship among ele-ments in the periodic table, whereby a given element is some-times more similar to the element below and to the right than it is to the element directly below. Lithium is more similar to magnesium than to sodium, for example, and boron is more similar to silicon than to aluminum. Use your knowledge about the periodic trends of such properties as atomic radii and Zeff to explain the existence of diagonal relationships.
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