Explanation The wave function, Ψ itself has no direct physical meaning. But, the probability of finding the electron in a certain region of space is proportional to the square of the wave function, Ψ 2 . The idea of relating Ψ 2 to probability stemmed from a wave theory correlation

3rd Edition

ISBN: 9781259923142

Author: Burdge

Publisher: MCG

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Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are im…

Question

Chapter 3, Problem 3.65QP

Interpretation Introduction

Interpretation:

The physical significance of the wave function should be explained.

Concept Introduction:

The Schrodinger equation includes both particle behavior in terms of mass and wave behavior in terms of a wave function. It gives the probability of finding an electron in a certain region of space.

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Chapter 3, Problem 3.64QP

Chapter 3, Problem 3.66QP

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Chapter 3 Solutions

Chemistry: Atoms First

Ch. 3.1 - Calculate the kinetic energy of a helium atom...Ch. 3.1 - Calculate the energy in joules of a 5.25-g object...Ch. 3.1 - Prob. 1PPB Ch. 3.1 - Prob. 1PPC Ch. 3.1 - Prob. 3.2WE Ch. 3.1 - How much greater is the electrostatic potential...Ch. 3.1 - What must the separation between charges of +2 and...Ch. 3.1 - Prob. 2PPC Ch. 3.1 - Calculate the kinetic energy of a 5.0-kg mass...Ch. 3.1 - Prob. 3.1.2SR

Ch. 3.1 - Arrange the following pairs of charged particles...Ch. 3.2 - One type of laser used in the treatment of...Ch. 3.2 - What is the wavelength (in meters) of an...Ch. 3.2 - What is the frequency (in reciprocal seconds) of...Ch. 3.2 - Which of the following sets of waves best...Ch. 3.2 - Calculate the wavelength (in nanometers) of light...Ch. 3.2 - Prob. 3.2.2SR Ch. 3.2 - Prob. 3.2.3SR Ch. 3.2 - When traveling through a translucent medium, such...Ch. 3.3 - Calculate the energy (in joules) of (a) a photon...Ch. 3.3 - Calculate the energy (in joules) of (a) a photon...Ch. 3.3 - (a) Calculate the wavelength (in nanometers) of...Ch. 3.3 - Calculate the energy per photon of light with...Ch. 3.3 - Calculate the wavelength (in centimeters) of light...Ch. 3.3 - Calculate the maximum kinetic energy of an...Ch. 3.3 - A clean metal surface is irradiated with light of...Ch. 3.3 - Prob. 3.3.5SR Ch. 3.4 - Calculate the wavelength (in nanometers) of the...Ch. 3.4 - What is the wavelength (in nanometers) of a photon...Ch. 3.4 - What is the value of ni for an electron that emits...Ch. 3.4 - For each pair of transitions, determine which one...Ch. 3.4 - Calculate the energy of an electron in the n = 3...Ch. 3.4 - Calculate E of an electron that goes from n = 1 to...Ch. 3.4 - What is the wavelength (in meters) of light...Ch. 3.4 - What wavelength (in nanometers) corresponds to the...Ch. 3.5 - Calculate the de Broglie wavelength of the...Ch. 3.5 - Calculate the de Broglie wavelength (in...Ch. 3.5 - Use Equation 3.11 to calculate the momentum, p...Ch. 3.5 - Consider the impact of early electron diffraction...Ch. 3.5 - Calculate the de Broglie wavelength associated...Ch. 3.5 - At what speed must a helium-4 atom be traveling to...Ch. 3.5 - Determine the minimum speed required for a...Ch. 3.6 - An electron in a hydrogen atom is known to have a...Ch. 3.6 - Prob. 7PPA Ch. 3.6 - (a) Calculate the minimum uncertainty in the...Ch. 3.6 - Using Equation 3.13, we can calculate the minimum...Ch. 3.6 - What is the minimum uncertainty in the position of...Ch. 3.6 - What is the minimum uncertainty in the position of...Ch. 3.7 - What are the possible values for the magnetic...Ch. 3.7 - Prob. 8PPA Ch. 3.7 - Prob. 8PPB Ch. 3.7 - Prob. 8PPC Ch. 3.7 - Prob. 3.7.1SR Ch. 3.7 - How many subshells are there in the shell...Ch. 3.7 - What is the total number of orbitals in the shell...Ch. 3.7 - What is the minimum value of the principal quantum...Ch. 3.8 - Prob. 3.9WE Ch. 3.8 - Prob. 9PPA Ch. 3.8 - Prob. 9PPB Ch. 3.8 - Prob. 9PPC Ch. 3.8 - Prob. 3.8.1SR Ch. 3.8 - Prob. 3.8.2SR Ch. 3.8 - In a hydrogen atom, which orbitals are higher in...Ch. 3.8 - Which of the following sets of quantum numbers, n,...Ch. 3.9 - Write the electron configuration and give the...Ch. 3.9 - Prob. 10PPA Ch. 3.9 - Write the electron configuration and give the...Ch. 3.9 - Prob. 10PPC Ch. 3.9 - Which of the following electron configurations...Ch. 3.9 - Prob. 3.9.2SR Ch. 3.9 - Which orbital diagram is collect for the...Ch. 3.10 - Without referring to Figure 3.26, write the...Ch. 3.10 - Prob. 11PPA Ch. 3.10 - Prob. 11PPB Ch. 3.10 - Consider again the alternate universe and its...Ch. 3.10 - Which of the following electron configurations...Ch. 3.10 - Prob. 3.10.2SR Ch. 3.10 - Prob. 3.10.3SR Ch. 3.10 - Prob. 3.10.4SR Ch. 3 - Prob. 3.1KSP Ch. 3 - Which of the following electron configurations...Ch. 3 - Prob. 3.3KSP Ch. 3 - Prob. 3.4KSP Ch. 3 - Define these terms: potential energy, kinetic...Ch. 3 - What are the units for energy commonly employed in...Ch. 3 - A truck initially traveling at 60 km/h is brought...Ch. 3 - Describe the interconversions of forms of energy...Ch. 3 - Determine the kinetic energy of (a) a 1.25-kg mass...Ch. 3 - Determine the kinetic energy of (a) a 29-kg mass...Ch. 3 - Prob. 3.7QP Ch. 3 - Determine (a) the velocity of an electron that has...Ch. 3 - Prob. 3.9QP Ch. 3 - (a) How much greater is the electrostatic energy...Ch. 3 - Prob. 3.11QP Ch. 3 - Prob. 3.12QP Ch. 3 - List the types of electromagnetic radiation,...Ch. 3 - Prob. 3.14QP Ch. 3 - Prob. 3.15QP Ch. 3 - Prob. 3.16QP Ch. 3 - The SI unit of time is the second, which is...Ch. 3 - Prob. 3.18QP Ch. 3 - Prob. 3.19QP Ch. 3 - Four waves represent light in four different...Ch. 3 - Prob. 3.21QP Ch. 3 - Prob. 3.22QP Ch. 3 - Prob. 3.23QP Ch. 3 - What is a photon? What role did Einsteins...Ch. 3 - A photon has a wavelength of 705 nm. Calculate the...Ch. 3 - The blue color of the sky results from the...Ch. 3 - A photon has a frequency of 6.5 109 Hz. (a)...Ch. 3 - Prob. 3.28QP Ch. 3 - Calculate the difference in energy (in joules)...Ch. 3 - How much more energy per photon is there in green...Ch. 3 - Prob. 3.31QP Ch. 3 - A particular form of electromagnetic radiation has...Ch. 3 - Photosynthesis makes use of visible light to bring...Ch. 3 - The retina of a human eye can detect light when...Ch. 3 - Prob. 3.35QP Ch. 3 - The binding energy of magnesium metal is 5.86 ...Ch. 3 - What is the kinetic energy of the ejected electron...Ch. 3 - A red light was shined onto a metal sample and the...Ch. 3 - A photoelectric experiment was performed by...Ch. 3 - Which of the following best explains why we see...Ch. 3 - One way to see the emission spectrum of hydrogen...Ch. 3 - How many lines would we see in the emission...Ch. 3 - For a hydrogen atom in which the electron has been...Ch. 3 - Prob. 3.40QP Ch. 3 - Prob. 3.41QP Ch. 3 - Briefly describe Bohrs theory of the hydrogen atom...Ch. 3 - Explain the meaning of the negative sign in...Ch. 3 - Consider the following energy levels of a...Ch. 3 - Prob. 3.45QP Ch. 3 - Calculate the wavelength (in nanometers) of a...Ch. 3 - Calculate the frequency (hertz) and wavelength...Ch. 3 - What wavelength of light is needed to excite the...Ch. 3 - An electron in the hydrogen atom makes a...Ch. 3 - Explain why elements produce their own...Ch. 3 - Some copper-containing substances emit green light...Ch. 3 - Prob. 3.52QP Ch. 3 - Prob. 3.53QP Ch. 3 - Prob. 3.54QP Ch. 3 - Why is Equation 3.11 meaningful only for...Ch. 3 - Prob. 3.56QP Ch. 3 - Thermal neutrons are neutrons that move at speeds...Ch. 3 - Protons can be accelerated to speeds near that of...Ch. 3 - Prob. 3.59QP Ch. 3 - What is the de Broglie wavelength (in nanometers)...Ch. 3 - Prob. 3.61QP Ch. 3 - Prob. 3.62QP Ch. 3 - What are the inadequacies of Bohrs theory?Ch. 3 - What is the Heisenberg uncertainty principle? What...Ch. 3 - Prob. 3.65QP Ch. 3 - Prob. 3.66QP Ch. 3 - Prob. 3.67QP Ch. 3 - The speed of a thermal neutron (see Problem 3.57)...Ch. 3 - Alveoli are tiny sacs of air in the lungs. Their...Ch. 3 - In the beginning of the twentieth century, some...Ch. 3 - Suppose that photons of blue light (430 nm) are...Ch. 3 - Prob. 3.72QP Ch. 3 - Prob. 3.73QP Ch. 3 - Which of the four quantum numbers (n, , m, ms)...Ch. 3 - Prob. 3.75QP Ch. 3 - Prob. 3.76QP Ch. 3 - Indicate which of the following sets of three...Ch. 3 - Prob. 3.78QP Ch. 3 - Describe the shapes of s, p, and d orbitals. How...Ch. 3 - Prob. 3.80QP Ch. 3 - Describe the characteristics of an s orbital, p...Ch. 3 - Why is a boundary surface diagram useful in...Ch. 3 - Prob. 3.83QP Ch. 3 - Give the values of the four quantum numbers of an...Ch. 3 - Describe how a 1s orbital and a 2s orbital are...Ch. 3 - Prob. 3.86QP Ch. 3 - Prob. 3.87QP Ch. 3 - Make a chart of all allowable orbitals in the...Ch. 3 - Prob. 3.89QP Ch. 3 - Prob. 3.90QP Ch. 3 - A 3s orbital is illustrated here. Using this as a...Ch. 3 - Prob. 3.92QP Ch. 3 - Prob. 3.93QP Ch. 3 - State the Aufbau principle, and explain the role...Ch. 3 - Indicate the total number of (a) p electrons in N...Ch. 3 - Calculate the total number of electrons that can...Ch. 3 - Determine the total number of electrons that can...Ch. 3 - Determine the maximum number of electrons that can...Ch. 3 - Prob. 3.99QP Ch. 3 - The electron configuration of an atom in the...Ch. 3 - List the following atoms in order of increasing...Ch. 3 - Determine the number of unpaired electrons in each...Ch. 3 - Determine the number of impaired electrons in each...Ch. 3 - Determine the number of unpaired electrons in each...Ch. 3 - Prob. 3.105QP Ch. 3 - Portions of orbital diagrams representing the...Ch. 3 - Prob. 3.107QP Ch. 3 - Prob. 3.108QP Ch. 3 - Prob. 3.109QP Ch. 3 - Define the following terms and give an example of...Ch. 3 - Explain why the ground-state electron...Ch. 3 - Write the election configuration of a xenon core.Ch. 3 - Comment on the correctness of the following...Ch. 3 - Prob. 3.114QP Ch. 3 - Prob. 3.115QP Ch. 3 - Write the ground-state electron configurations for...Ch. 3 - Write the ground-state electron configurations for...Ch. 3 - What is the symbol of the element with the...Ch. 3 - Prob. 3.119QP Ch. 3 - Prob. 3.120QP Ch. 3 - Discuss the current view of the correctness of the...Ch. 3 - Distinguish carefully between the following terms:...Ch. 3 - What is the maximum number of electrons in an atom...Ch. 3 - Prob. 3.124QP Ch. 3 - Prob. 3.125QP Ch. 3 - A baseball pitchers fastball has been clocked at...Ch. 3 - A ruby laser produces radiation of wavelength 633...Ch. 3 - Four atomic energy levels of an atom are shown...Ch. 3 - Prob. 3.129QP Ch. 3 - Spectral lines of the Lyman and Balmer series do...Ch. 3 - Only a fraction of the electric energy supplied to...Ch. 3 - The figure here illustrates a series of...Ch. 3 - When one of heliums electrons is removed, the...Ch. 3 - The retina of a human eye can detect light when...Ch. 3 - An electron in an excited state in a hydrogen atom...Ch. 3 - Prob. 3.136QP Ch. 3 - The election configurations described in this...Ch. 3 - Draw the shapes (boundary surfaces) of the...Ch. 3 - Prob. 3.139QP Ch. 3 - Consider the graph here. (a) Calculate the binding...Ch. 3 - Scientists have found interstellar hydrogen atoms...Ch. 3 - Ionization energy is the minimum energy required...Ch. 3 - Prob. 3.143QP Ch. 3 - Prob. 3.144QP Ch. 3 - The cone cells of the human eye are sensitive to...Ch. 3 - (a) An electron in the ground state of the...Ch. 3 - Prob. 3.147QP Ch. 3 - Prob. 3.148QP Ch. 3 - When an election makes a transition between energy...Ch. 3 - Blackbody radiation is the term used to describe...Ch. 3 - Suppose that photons of red light (675 nm) are...Ch. 3 - In an election microscope, electrons are...Ch. 3 - According to Einsteins special theory of...Ch. 3 - The mathematical equation for studying the...

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The physical significance of the wave function should be explained. Concept Introduction: The Schrodinger equation includes both particle behavior in terms of mass and wave behavior in terms of a wave function. It gives the probability of finding an electron in a certain region of space.

Solution Summary: The author explains that the Schrodinger equation includes particle behavior and wave behavior in terms of a wave function.

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Chapter 3 Solutions