Chemistry: Structure and Properties (2nd Edition)
2nd Edition
ISBN: 9780134293936
Author: Nivaldo J. Tro
Publisher: PEARSON
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Chapter 2, Problem 26E
What is the Schrödinger equation? What is a wave function? How is a wave function related to an orbital?
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Chapter 2 Solutions
Chemistry: Structure and Properties (2nd Edition)
Ch. 2 - Why is the quantum-mechanical model of the atom...Ch. 2 - What is light? How fast does it travel in a...Ch. 2 - Define the wavelength and amplitude of a wave.Ch. 2 - Define the frequency of electromagnetic radiation....Ch. 2 - What determines the color of light? Describe the...Ch. 2 - What determines the color of a colored object?...Ch. 2 - Give an approximate range of wavelengths for each...Ch. 2 - Explain the wave behavior known as interference....Ch. 2 - Explain the wave behavior known as diffraction....Ch. 2 - Describe the photoelectric effect. How did...
Ch. 2 - How did the photoelectric effect lead Einstein to...Ch. 2 - What is a photon? How is the energy of a photon...Ch. 2 - What is an emission spectrum? How does an emission...Ch. 2 - Describe the Bohr model for the atom. How did the...Ch. 2 - Explain electron diffraction.Ch. 2 - What is the de Broglie wavelength of an electron?...Ch. 2 - What are complementary properties? How does...Ch. 2 - Explain Heisenberg’s uncertainty principle. What...Ch. 2 - What is a trajectory? What kind of information do...Ch. 2 - Why does the uncertainty principle make it...Ch. 2 - Newton’s laws of motion are deterministic. Explain...Ch. 2 - An electron behaves in ways that are at least...Ch. 2 - What is a probability distribution map?Ch. 2 - For each solution to the Schrödinger equation,...Ch. 2 - What is a quantum-mechanical orbital?Ch. 2 - What is the Schrödinger equation? What is a wave...Ch. 2 - What are the possible values of the principal...Ch. 2 - What are the possible values of the angular...Ch. 2 - What are the possible values of the magnetic...Ch. 2 - Explain the difference between a plot showing the...Ch. 2 - Sketch the general shapes of the s, p, and d...Ch. 2 - List the four different sublevels. Given that only...Ch. 2 - Why are atoms usually portrayed as spheres when...Ch. 2 - The distance from the sun to Earth is 1.496108 km....Ch. 2 - The nearest star to our sun is Proxima Centauri,...Ch. 2 - List these types of electromagnetic radiation in...Ch. 2 - List these types of electromagnetic radiation in...Ch. 2 - Calculate the frequency of each wavelength of...Ch. 2 - Calculate the wavelength of each frequency of...Ch. 2 - Calculate the energy of a photon of...Ch. 2 - Calculate the energy of a photon of...Ch. 2 - A laser pulse with wavelength 532 nm contains 3.85...Ch. 2 - A heat lamp produces 32.8 watts of power at a...Ch. 2 - Determine the energy of 1 mol of photons for each...Ch. 2 - How much energy is contained in 1 mol of each?...Ch. 2 - Sketch the interference pattern that results from...Ch. 2 - What happens to the interference pattern described...Ch. 2 - The resolution limit of a microscope is roughly...Ch. 2 - The smallest atoms can themselves exhibit...Ch. 2 - What is the de Broglie wavelength of an electron...Ch. 2 - A proton in a linear accelerator has a de Broglie...Ch. 2 - Prob. 53ECh. 2 - A 0.22-caliber handgun fires a 27-g bullet at a...Ch. 2 - An electron has an uncertainty in its position of...Ch. 2 - An electron traveling at [1.35 \times {10^5}\] m/s...Ch. 2 - Which electron is, on average, closer to the...Ch. 2 - Which electron is, on average, further from the...Ch. 2 - What are the possible values of I for each given...Ch. 2 - What are the possible values of m1 for each given...Ch. 2 - Which set of quantum numbers cannot occur together...Ch. 2 - Which combinations of n and I represent real...Ch. 2 - Prob. 63ECh. 2 - Sketch the 3d orbitals. How do the 4d orbitals...Ch. 2 - An electron in a hydrogen atom is excited with...Ch. 2 - Determine whether each transition in the hydrogen...Ch. 2 - According to the quantum-mechanical model for the...Ch. 2 - According to the quantum-mechanical model for the...Ch. 2 - Calculate the wavelength of the light emitted when...Ch. 2 - Calculate the frequency of the light emitted when...Ch. 2 - Prob. 71ECh. 2 - An electron in a hydrogen atom relaxes to the [n =...Ch. 2 - Ultraviolet radiation and radiation of shorter...Ch. 2 - The human eye contains a molecule called...Ch. 2 - An argon ion laser puts out 5.0 W of continuous...Ch. 2 - A green leaf has a surface area of 2.50 cm2. If...Ch. 2 - Prob. 77ECh. 2 - An X-ray photon of wavelength 0.989 nm strikes a...Ch. 2 - Prob. 79ECh. 2 - The energy required to ionize sodium is 496...Ch. 2 - Prob. 81ECh. 2 - Suppose that, in an alternate universe, the...Ch. 2 - Prob. 83ECh. 2 - Prob. 84ECh. 2 - The binding energy of electrons in a metal is 193...Ch. 2 - In order for a thermonuclear fusion reaction of...Ch. 2 - Prob. 87ECh. 2 - Prob. 88ECh. 2 - The iodine molecule can be photodissociated...Ch. 2 - A sample of naphthalene in hexane contains 5.00104...Ch. 2 - Prob. 91ECh. 2 - Prob. 92ECh. 2 - Prob. 93ECh. 2 - The energy of a vibrating molecule is quantized...Ch. 2 - The wave functions for the 1s and 2s orbitals are...Ch. 2 - Before quantum mechanics was developed, Johannes...Ch. 2 - Find the velocity of an electron emitted by a...Ch. 2 - Water is exposed to infrared radiation of...Ch. 2 - Prob. 99ECh. 2 - A metal with a threshold frequency of 6.711014s1...Ch. 2 - Find the longest wavelength of a wave that can...Ch. 2 - The amount of heat to melt ice is 0.333 kJ/g. Find...Ch. 2 - Explain the difference between the Bohr model for...Ch. 2 - The light emitted from one of the following...Ch. 2 - Determine whether an interference pattern is...Ch. 2 - Which transition in the hydrogen atom results in...Ch. 2 - Discuss the nature of light with your group....Ch. 2 - How are electrons like baseballs? How are they...Ch. 2 - What are all the possible values of m1 if l = 0...Ch. 2 - Have each group member choose a set of quantum...Ch. 2 - How many nodes are there in the 1s, 2p, and 3d...Ch. 2 - Sunscreen contains compounds that absorb...Ch. 2 - Which wavelength of light has the highest...Ch. 2 - Which kind of electromagnetic radiation contains...Ch. 2 - How much energy (in J ) is contained in 1.00 mole...Ch. 2 - Light from three different lasers (A, B, and C),...Ch. 2 - Calculate the wavelength of an electron traveling...Ch. 2 - Which set of three quantum numbers does not...Ch. 2 - Calculate the wavelength of light emitted when an...Ch. 2 - Which electron transition produces light of the...Ch. 2 - How much time (in seconds) does it take light to...Ch. 2 - Which figure represents a d orbital? None of the...
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- a For a pendulum having classical frequency of 1.00s1, what is the energy difference in J between quantized energy levels? b Calculate the wavelength of light that must be absorbed in order for the pendulum to go from one level to another. c Can you determine in what region of the electromagnetic spectrum such a wavelength belongs? d Comment on your results for parts a and b based on your knowledge of the state of science in early twentieth century. Why wasnt the quantum mechanical behavior of nature noticed?arrow_forwardCalculate the energies of an electron in the fourth, fifth, and sixth energy levels of the Bohr hydrogen atom.arrow_forward• use Planck’s equation to calculate the energy of a photon from its wavelength or frequency.arrow_forward
- Some scientists study Rydberg atoms, atoms whose electron has a large value of the n quantum number. Some Rydberg hydrogen atoms may have consequences in interstellar chemistry. Predict the radius of a Rydberg hydrogen atom that has n=100.arrow_forwardConsider a one-dimensional particle-in-a-box and a three-dimensional particle-in-a-box that have the same dimensions. a What is the ratio of the energies of a particle having the lowest possible quantum numbers in both boxes? b Does this ratio stay the same if the quantum numbers are not the lowest possible values?arrow_forwardIn 1885, Johann Balmer, a mathematician, derived the following relation for the wavelength of lines in the visible spectrum of hydrogen =364.5 n2( n2 4) where in nanometers and n is an integer that can be 3, 4, 5, . . . Show that this relation follows from the Bohr equation and the equation using the Rydberg constant. Note that in the Balmer series, the electron is returning to the n=2 level.arrow_forward
- now have evidence that electron energy levels in atoms are quantized. What if energy levels in atoms were not quantized? What are some differences we would notice?arrow_forwardWhy was Bohr's theory for the hydrogen atom initially accepted, and why was it ultimately discarded?arrow_forwardWhy was Schrodinger not able to describe exactly the pathway an electron takes as it moves through the space of an atom?arrow_forward
- Determine the speed of an electron being emitted by rubidium (=2.16eV) when light of the following wavelengths is shined on the metal in vacuum: a550nm, b450nm,c350nm.arrow_forwardDefend and criticize Bohrs model. Why was it reasonable that such a model was proposed, and what evidence was there that it "works"? Why do we no longer "believe" in it?arrow_forwardGive a brief wave description of light. What are two characteristics of light waves?arrow_forward
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