Domanda del libro di testo
Use Coulomb's law to calculate the ionization energy in kJ/mol of an atom composed of a proton and an electron separated by 110.00 pm. What wavelength of light has sufficient energy to ionize the atom?
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Ch.9 - Periodic Properties of the Elements
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving118
- Ch.2 - Atoms & Elements106
- Ch.3 - Molecules and Compounds131
- Ch.4 - Chemical Reactions and Chemical Quantities56
- Ch.5 - Introduction to Solutions and Aqueous Solutions82
- Ch.6 - Gases114
- Ch.7 - Thermochemistry96
- Ch.8 - The Quantum-Mechanical Model of the Atom60
- Ch.9 - Periodic Properties of the Elements90
- Ch.10 - Chemical Bonding I: The Lewis Model89
- Ch.11 - Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory85
- Ch.12 - Liquids, Solids & Intermolecular Forces51
- Ch.13 - Solids & Modern Materials47
- Ch.14 - Solutions90
- Ch.15 - Chemical Kinetics115
- Ch.16 - Chemical Equilibrium68
- Ch.17 - Acids and Bases136
- Ch.18 - Aqueous Ionic Equilibrium153
- Ch.19 - Free Energy & Thermodynamics93
- Ch.20 - Electrochemistry106
- Ch.21 - Radioactivity & Nuclear Chemistry74
- Ch.22 - Organic Chemistry140
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Non è quello che usi tu?Cambia libro di testo
Capitolo 9, Problema 112
The first ionization energy of lithium is 520 kJ/mol. Use Coulomb's law to estimate the average distance between the lithium nucleus and the 2s electron. How does this distance compare to the atomic radius of lithium? Assume an effective nuclear charge of 1+ for the valence electron.
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Identify the given values: the first ionization energy (IE) of lithium is 520 kJ/mol, and the effective nuclear charge (Z_eff) is +1.
Convert the ionization energy from kJ/mol to joules per atom. Use the conversion factor: 1 kJ/mol = 1,000 J/mol and Avogadro's number (6.022 x 10^23 atoms/mol).
Apply Coulomb's law to relate the ionization energy to the distance (r) between the nucleus and the electron. Coulomb's law is given by: E = k * (Z_eff * e^2) / r, where E is the ionization energy, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), and e is the elementary charge (1.602 x 10^-19 C).
Rearrange the formula to solve for the distance r: r = k * (Z_eff * e^2) / E.
Compare the calculated distance r to the known atomic radius of lithium, which is approximately 152 pm (picometers).
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Concetti chiave
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Ionization Energy
Ionization energy is the energy required to remove an electron from an atom in its gaseous state. For lithium, the first ionization energy is 520 kJ/mol, indicating the energy needed to remove the outermost electron. This concept is crucial for understanding the strength of the attraction between the nucleus and the electrons, which influences the distance between them.
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01:19
Ionization Energy
Coulomb's Law
Coulomb's law describes the electrostatic interaction between charged particles. It states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law can be used to estimate the distance between the lithium nucleus and its valence electron by relating the ionization energy to the attractive force experienced by the electron.
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01:15Coulomb's Law Concept 2
Effective Nuclear Charge
Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom, accounting for shielding by other electrons. For lithium, an effective nuclear charge of 1+ means that the valence electron feels a reduced attraction due to the presence of the inner electron. This concept is essential for calculating the distance between the nucleus and the electron, as it influences the strength of the electrostatic force in Coulomb's law.
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01:51Effective Nuclear Charge
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You have cracked a secret code that uses elemental symbols to spell words. The code uses numbers to designate the elemental symbols. Each number is the sum of the atomic number and the highest principal quantum number of the highest occupied orbital of the element whose symbol is to be used. The message may be written forward or backward. Decode the following messages: a. 10, 12, 58, 11, 7, 44, 63, 66
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Domanda del libro di testo
Consider the elements: Na, Mg, Al, Si, P. b. Which element has the smallest atomic radius?
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Domanda del libro di testo
Consider the elements: Na, Mg, Al, Si, P. c. Which element is least metallic?
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Domanda del libro di testo
Consider the elements: B, C, N, O, F. d. Which element has three unpaired electrons?
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