Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 12, Problem 12.46E
Explain why assuming an “effective nuclear charge,” as used for our treatment of the helium atom in Example 12.11, is unnecessary for a treatment of the hydrogen atom.
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Students have asked these similar questions
a) For an ionized Het atom (that is, without one
of its electrons), calculate the binding energy with
respect to the nucleus of the electron in its
ground state. Express it in electron volts.
b) What is the potential difference that will be
required to ionize the He* electron?
What is the least possible initial kinetic energy Kmin the oxygen atom could have and still excite the cesium atom?
Express your answer in electron volts, to one decimal place.
Born-Oppenheimer approximation. The hypothesis is
a) The potential energy of the nuclei is zero
b) Nuclei occupy fixed positions with respect to electrons
c) Nuclei move faster than electrons
d) The different types of energy levels of molecules cannot be considered separately.
Chapter 12 Solutions
Physical Chemistry
Ch. 12 - In the Stern-Gerlach experiment, silver atoms were...Ch. 12 - Prob. 12.2ECh. 12 - Prob. 12.3ECh. 12 - Suppose s=12 for an electron. Into how many parts...Ch. 12 - Using and labels, write two possible...Ch. 12 - List all possible combinations of all four quantum...Ch. 12 - What are the degeneracies of the H atom...Ch. 12 - Prob. 12.8ECh. 12 - a Differentiate between the quantum numbers s and...Ch. 12 - Is the spin orbital 1s for the H atom still...
Ch. 12 - Draw a diagram analogous to Figure 11.15, but now...Ch. 12 - Are mathematical expressions for the following...Ch. 12 - Prob. 12.13ECh. 12 - Prob. 12.14ECh. 12 - a Assume that the electronic energy of Li was a...Ch. 12 - Spin orbitals are products of spatial and spin...Ch. 12 - If 1 and 2 are the individual wavefunctions for...Ch. 12 - Show that the correct behavior of a wavefunction...Ch. 12 - Prob. 12.19ECh. 12 - Why isnt the electron configuration of beryllium,...Ch. 12 - Prob. 12.21ECh. 12 - Write a Slater determinant for the lithide ion,...Ch. 12 - Why does the concept of antisymmetric...Ch. 12 - a Construct Slater determinant wavefunctions for...Ch. 12 - Prob. 12.25ECh. 12 - Prob. 12.26ECh. 12 - Prob. 12.27ECh. 12 - Suppose an electron had three possible values of...Ch. 12 - Using a periodic table or Table 12.1, find the...Ch. 12 - Write an acceptable electron configuration for...Ch. 12 - Prob. 12.31ECh. 12 - Prob. 12.32ECh. 12 - Prob. 12.33ECh. 12 - An anharmonic oscillator has the potential...Ch. 12 - Prob. 12.35ECh. 12 - In a particle-in-a-box having length a, the...Ch. 12 - Prob. 12.37ECh. 12 - Prob. 12.38ECh. 12 - Prob. 12.39ECh. 12 - The Stark effect is the change in energy of a...Ch. 12 - Prob. 12.41ECh. 12 - Prob. 12.42ECh. 12 - Prob. 12.43ECh. 12 - Show that a variation theory treatment of H using...Ch. 12 - Prob. 12.45ECh. 12 - Explain why assuming an effective nuclear charge,...Ch. 12 - Prob. 12.47ECh. 12 - Consider a real system. Assume that a real...Ch. 12 - Prob. 12.49ECh. 12 - Prob. 12.50ECh. 12 - Prob. 12.51ECh. 12 - Prob. 12.52ECh. 12 - State the Born-Oppenheimer approximation in words...Ch. 12 - Prob. 12.54ECh. 12 - Spectroscopy deals with differences in energy...Ch. 12 - Prob. 12.56ECh. 12 - What is the bond order for the lowest excited...Ch. 12 - The helium atom was defined as two electrons and a...Ch. 12 - Explain how we know that the first in equation...Ch. 12 - Prob. 12.60ECh. 12 - Prob. 12.61ECh. 12 - Use molecular orbital arguments to decide whether...Ch. 12 - Prob. 12.63ECh. 12 - Prob. 12.65ECh. 12 - Prob. 12.67ECh. 12 - Prob. 12.68E
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- Mars is roughly 60 million km from the earth. How long does it take for a radio signal originating from the earth to reach Mars?arrow_forwardThe wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (r)=( 1 a 0 3 )1/2exp(r a 0 )ao=0.5291010m (a) What is the probability of finding the electron inside a sphere of volume 1.0pm2 , centered at the nucleus (1pm=1012m) ? (b) What is the probability of finding the electron in a volume of 1.0pm2 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? (c) What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?arrow_forwardWhat is the difference between an atom’s ground state and an excited state?arrow_forward
- The following is an energy-level diagram for electronic transitions in the Bohr hydrogen atom. a. Explain why the energy levels get closer together as they increase. Provide mathematical support for this. b. Verify that the colors given in the diagram are correct. Provide mathematical support.arrow_forwardVerify the specific value of a, the Bohr radius, by using the values of the various constants and evaluating equation 11.68.arrow_forwardAre mathematical expressions for the following potential energies positive or negative? Explain why in each case. a The attraction between an electron and a helium nucleus b The repulsion between two protons in a nucleus c The attraction between a north and a south magnetic pole d The force of gravity between the Sun and Earth e A rock perched on the edge of a cliff with respect to the base of the cliffarrow_forward
- How is the Bohr theory of the hydrogen atom inconsistent with the uncertainty principle? In fact, it was this inconsistency, along with the theorys limited application to non-hydrogen-like systems, that limited Bohrs theory.arrow_forwardAn Mg atom is in the excited electron configuration [Ne]4s2. What are the possible term symbols for this atom?arrow_forwardThe photoelectric effect is used today to make light-sensitive detectors; when light hits a sample of metal in a sealed compartment, a current of electrons may flow if the light has the proper wavelength. Cesium is a desirable component for such detectors. Why?arrow_forward
- Why isnt the electron configuration of beryllium, given as 1s22s2, considered a violation of the Pauli principle? Hint: See example 12.6.arrow_forwarda 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_forwardof the velocity in (c) to the speed of light? 2. In 1913 Neils Bohr proposed a model for the hydrogen, now known as the Bohr atom, that explained the emission spectrum of the hydrogen atom as well as one-electron ions like Het. The model permits the electron to orbit the nucleus by a set of discrete orbits where each orbit is associated with an integer value n, known as the principal quantum number. Depending upon the orbital occupied by the electron, the energy of the hydrogen atom (or one-electron ions) can only assume the following discrete values 1terd 30 tF aconstant En n2 prineiple 2 S1 where RH 2.18x10-18 J is the Rydberg constant and Z is the number of protons in the nucleus.(a) List the energies of the hydrogen atom for the first three orbits (n-1, 2, and 3).*(b) Compute the energy absorbed by the hydrogen atom when the electron is excited from the lowest orbit (n 1) to the third lowest orbit (n 3). (c) Calculate the frequency v of the photon E = y absorbed by the hydrogen…arrow_forward
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