Back
- In the television series Star Trek, the transporter beam is a device used to “beam down” people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a “Heisenberg compensator” into the transporter beam mechanism. Explain why such a compensator (which is entirely fictional) would be necessary to get around Heisenberg’s uncertainty principle.
Problem 96
- As discussed in the A Closer Look box on “Measurement and the Uncertainty Principle,” the essence of the uncertainty principle is that we can’t make a measurement without disturbing the system that we are measuring. (b) How is this concept related to the paradox discussed in the Closer Look box on “Thought Experiments and Schrödinger’s Cat”?
Problem 97
Problem 97a
As discussed in the A Closer Look box on 'Measurement and the Uncertainty Principle,' the essence of the uncertainty principle is that we can't make a measurement without disturbing the system that we are measuring. (a) Why can't we measure the position of a subatomic particle without disturbing it?
- Consider the discussion of radial probability functions in 'A Closer Look' in Section 6.6. (a) What is the difference between the probability density as a function of r and the radial probability function as a function of r ?
Problem 98
Problem 100a
The Chemistry and Life box in Section 6.7 described the techniques called NMR and MRI. (a) Instruments for obtaining MRI data are typically labeled with a frequency, such as 600 MHz. In what region of the electromagnetic spectrum does a photon with this frequency belong?
- Suppose that the spin quantum number, ms, could have three allowed values instead of two. How would this affect the number of elements in the first four rows of the periodic table?
Problem 101
Problem 102
Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) Cl (b) Al (c) Zr (d) As (e) Sb (f) W.
Problem 103
Scientists have speculated that element 126 might have a moderate stability, allowing it to be synthesized and characterized. Predict what the condensed electron configuration of this element might be.
Problem 104a
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?
- 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?
Problem 105
- 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?
Problem 106
Problem 107a
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?
Problem 107d
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.
Problem 107e
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.
- (c) Consider the metal oxides whose enthalpies of formation (in kJ mol⁻¹) are listed here: Oxide K₂O₍s₂₎, CaO₍s₂₎, TiO₂₍s₂₎, V₂O₅₍s₂₎, ΔHf° -363.2, -635.1, -938.7, -1550.6. Calculate the enthalpy changes in the following general reaction for each case: MnOm₍s₂₎ + H₂(g) → nM₍s₂₎ + mH₂O(g). (You will need to write the balanced equation for each case and then compute ΔH°.)
Problem 108
Problem 110b
The two most common isotopes of uranium are 235U and 238U. (b) Using the periodic table in the frontinside cover, write the electron configuration for a U atom.
Problem 110d
The two most common isotopes of uranium are 235U and 238U. (d) 238U undergoes radioactive decay to 234Th. How many protons, electrons, and neutrons are gained or lost by the 238U atom during this process? (e) Examine the electron configuration for Th in Figure 6.31. Are you surprised by what you find? Explain.