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2nd Edition

Ball + 3 others

Publisher: Wadsworth Cengage Learning,

ISBN: 9781133958437

Chapter 11, Problem 11.2E

Textbook Problem

A swinging pendulum has a frequency of

Physical Chemistry

Ch. 11 - Convert 3.558mdyn/A into units of N/m.Ch. 11 - A swinging pendulum has a frequency of 0.277Hz and...Ch. 11 - Calculate the frequency of a harmonic oscillator...Ch. 11 - A harmonic oscillator has a frequency of 7.04s1...Ch. 11 - An object having mass m at some height above the...Ch. 11 - What are the units on ? Do they make sense in...Ch. 11 - In equation 11.6, in order to properly subtract...Ch. 11 - Verify that the three substitutions mentioned in...Ch. 11 - Verify that the second derivative of given by...Ch. 11 - Derive equation 11.15 from the expression...

Ch. 11 - Derive equation 11.16 from the equation...Ch. 11 - Show that the energy separation between any two...Ch. 11 - a For a pendulum having classical frequency of...Ch. 11 - a A hydrogen atom bonded to a surface is acting as...Ch. 11 - The OH bond in water vibrates at a frequency of...Ch. 11 - Show that 2 and 3 for the harmonic oscillator are...Ch. 11 - Substitute 1 into the complete expression for the...Ch. 11 - Demonstrate that x=0 for any wavefunction of a...Ch. 11 - Calculate px for 0 and 1 for a harmonic...Ch. 11 - Use the expression for 1 in equations 11.17 and...Ch. 11 - Derive equation 11.19 from the information in...Ch. 11 - Simply using arguments based on odd or even...Ch. 11 - Consider Figure 11.4 and choose the correct...Ch. 11 - Based on the trend shown in Figure 11.5, draw the...Ch. 11 - What is x2 for 0 of a harmonic oscillator? Is it...Ch. 11 - Use your answer to exercise 11.25 to determine V...Ch. 11 - Determine the valuess of x for the classical...Ch. 11 - Determine a formula in terms of n for the number...Ch. 11 - What are the values of x for the nodes for 3 of a...Ch. 11 - Derive equation 11.23 from the expression...Ch. 11 - Compare the mass of the electron, me, with a the...Ch. 11 - Reduced mass is not reserved only for atomic...Ch. 11 - a Calculate the expected harmonic-oscillator...Ch. 11 - An OH bond has a frequency of 3650cm1. Using...Ch. 11 - The force constant in the HD molecule (D=2H) is...Ch. 11 - Why cant the quantized values of the 2-D angular...Ch. 11 - Show that 3 of 2-D rotational motion has the same...Ch. 11 - Show that 1 and 2 for 2-D rotational motion are...Ch. 11 - Show that the 2-D rotational motion wavefunctions...Ch. 11 - What are the energies and angular momenta of the...Ch. 11 - A proton rotates in a circle of radius 5.001011m....Ch. 11 - A 25-kg child is on a merry-go-round/calliope,...Ch. 11 - Using Eulers identity, rewrite the first four 2-D...Ch. 11 - a Using the expression for the energy of a 2-D...Ch. 11 - Derive equation 11.35 from 11.34.Ch. 11 - If a zero-point energy were defined for 2-D...Ch. 11 - A colleague proposed a simplification in the...Ch. 11 - The quantized angular momentum is choose one:...Ch. 11 - Use trigonometry to verify the relationships...Ch. 11 - Why cant the square root of equation 11.45 be...Ch. 11 - For both 2-D and 3-D rotations, the radius of the...Ch. 11 - Can you evaluate r for the spherical harmonic Y22?...Ch. 11 - Show that 1,0 and 1,1 for 3-D rotational motion...Ch. 11 - Using the complete form of 3,2 where l=3 and ml=2...Ch. 11 - A 3-D rotational wavefunction has the quantum...Ch. 11 - a Using the he expression for the energy of a 3-D...Ch. 11 - See example 11.17, regarding the sphericalC60...Ch. 11 - In exercise 11.57 regarding C60, what are the...Ch. 11 - Draw the graphical representations see Figure...Ch. 11 - Using the definition of the cosine function as...Ch. 11 - What is the physical explanation of the difference...Ch. 11 - List the charges on hydrogen-like atoms whose...Ch. 11 - Calculate the electrostatic potential energy V...Ch. 11 - Using the Newton law of gravity and the...Ch. 11 - Show that for constant r and V=0, equation 11.56...Ch. 11 - Calculate the difference between the Bohr radius...Ch. 11 - To four significant figures, the first four lines...Ch. 11 - What would the wavelengths of the Balmer series...Ch. 11 - Construct an energy level diagram showing all...Ch. 11 - In Chapter 9, the topic of Rydberg atoms was...Ch. 11 - What is the degeneracy of an h subshell? An n...Ch. 11 - What is the numerical value of the total angular...Ch. 11 - What are the values of E, L, and Lz for an F8+...Ch. 11 - Verify the normalization constant in Table 11.4 by...Ch. 11 - Why does the wavefunction 4,4,0 not exist?...Ch. 11 - Calculate the total electronic energy of a mole of...Ch. 11 - What is the probability of finding an electron in...Ch. 11 - What is the probability of finding an electron in...Ch. 11 - For what wavefunctions and which hydrogen-like...Ch. 11 - For hydrogen-like ions with Z1, does the...Ch. 11 - State how many radial, angular, and total nodes...Ch. 11 - a For what value of does 3d0 have an angular...Ch. 11 - Illustrate that the hydrogen wavefunctions are...Ch. 11 - Verify the specific value of a, the Bohr radius,...Ch. 11 - Show that rmax is given by equation 11.68 for 1s....Ch. 11 - Use the forms of the wavefunctions in Table 11.4...Ch. 11 - Evaluate Lz for 3px, Compare it to the answer in...Ch. 11 - Calculate V for 1s of the H atom and compare it to...Ch. 11 - Verify equation 11.66 for 1s by substituting the...Ch. 11 - Using equations 11.67 as an example, what would be...Ch. 11 - Evaluate r for 1s assume that the operator r is...Ch. 11 - Redraw Figure 11.19 and all plots in Figure 11.20...Ch. 11 - Graph the first five wavefunctions for the...Ch. 11 - Construct three-dimensional plots of the first...Ch. 11 - Set up and evaluate numerically the integral that...Ch. 11 - Plot the 90 surfaces of the hydrogen atom 2s and...

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