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Ch.6 - Electronic Structure of Atoms
All textbooksBrown 14th EditionCh.6 - Electronic Structure of AtomsProblem 106
Chapter 6, Problem 106

The stratospheric ozone (O3) layer helps to protect us from harmful ultraviolet radiation. It does so by absorbing ultraviolet light and falling apart into an O2 molecule and an oxygen atom, a process known as photodissociation. O3(g) → O2(g) + O(g). Use the data in Appendix C to calculate the enthalpy change for this reaction. What is the maximum wavelength a photon can have if it is to possess sufficient energy to cause this dissociation? In what portion of the spectrum does this wavelength occur?

Verified step by step guidance
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Step 1: Identify the reaction and the enthalpy change needed. The reaction is O_3(g) \rightarrow O_2(g) + O(g). We need to calculate the enthalpy change (\Delta H) for this reaction using standard enthalpies of formation from Appendix C.
Step 2: Use the formula for the enthalpy change of a reaction: \Delta H_{reaction} = \sum \Delta H_f^{\circ} (products) - \sum \Delta H_f^{\circ} (reactants). Look up the standard enthalpies of formation for O_3(g), O_2(g), and O(g) in Appendix C.
Step 3: Substitute the values from Appendix C into the enthalpy change formula. Calculate \Delta H_{reaction} by subtracting the enthalpy of formation of O_3(g) from the sum of the enthalpies of formation of O_2(g) and O(g).
Step 4: To find the maximum wavelength of a photon that can cause this dissociation, use the energy-wavelength relationship: E = \frac{hc}{\lambda}, where E is the energy required (equal to \Delta H_{reaction} per mole of O_3), h is Planck's constant, c is the speed of light, and \lambda is the wavelength.
Step 5: Solve for \lambda (wavelength) by rearranging the equation: \lambda = \frac{hc}{E}. Calculate \lambda using the energy value obtained from \Delta H_{reaction}. Determine the portion of the electromagnetic spectrum this wavelength falls into by comparing it to known ranges (e.g., ultraviolet, visible, etc.).
Related Practice
Textbook Question

In the experiment shown schematically below, a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams. (a) What is the significance of the observation that the single beam splits into two beams?

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Textbook Question

In the experiment shown schematically below, a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams. (c) What do you think would happen if the beam of hydrogen atoms were replaced with a beam of helium atoms? Why?

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Open Question
Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food. (a) Suppose that the microwave radiation has a wavelength of 10 cm. How many photons are required to heat 200 mL of water from 25 to 75 °C?
Textbook Question

The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58–71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and G. von Hevesy, working in Bohr's laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (a) How would you use electron configuration arguments to justify Bohr's prediction?

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Textbook Question

The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58–71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and G. von Hevesy, working in Bohr's laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (d) Using their electron configurations, account for the fact that Zr and Hf form chlorides MCl4 and oxides MO2.

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Textbook Question

The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58–71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and G. von Hevesy, working in Bohr’s laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (c) Solid zirconium dioxide, ZrO2, reacts with chlorine gas in the presence of carbon. Starting with a 55.4-g sample of ZrO2, calculate the mass of ZrCl4 formed, assuming that ZrO2 is the limiting reagent and assuming 100% yield.