PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
2nd Edition
ISBN: 9781285074788
Author: Ball
Publisher: CENGAGE L
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Chapter 10, Problem 10.37E
Interpretation Introduction
Interpretation:
An explanation corresponding to the statement that the kinetic energy operator part of the Schrödinger equation is a derivative whereas the potential energy operator part of the Schrödinger equation is simply “multiplication times a function
Concept introduction:
In
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Chapter 10 Solutions
PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
Ch. 10 - State the postulates of quantum mechanics...Ch. 10 - Prob. 10.2ECh. 10 - State whether the following functions are...Ch. 10 - State whether the following functions are...Ch. 10 - Prob. 10.5ECh. 10 - Prob. 10.6ECh. 10 - Evaluate the operations in parts a, b, and f in...Ch. 10 - The following operators and functions are defined:...Ch. 10 - Prob. 10.9ECh. 10 - Indicate which of these expressions yield...
Ch. 10 - Indicate which of these expressions yield an...Ch. 10 - Why is multiplying a function by a constant...Ch. 10 - Prob. 10.13ECh. 10 - Using the original definition of the momentum...Ch. 10 - Under what conditions would the operator described...Ch. 10 - A particle on a ring has a wavefunction =12eim...Ch. 10 - Calculate the uncertainty in position, x, of a...Ch. 10 - For an atom of mercury, an electron in the 1s...Ch. 10 - Classically, a hydrogen atom behaves as if it were...Ch. 10 - The largest known atom, francium, has an atomic...Ch. 10 - How is the Bohr theory of the hydrogen atom...Ch. 10 - Though not strictly equivalent, there is a similar...Ch. 10 - The uncertainty principle is related to the order...Ch. 10 - Prob. 10.24ECh. 10 - Prob. 10.25ECh. 10 - For a particle in a state having the wavefunction...Ch. 10 - Prob. 10.27ECh. 10 - A particle on a ring has a wavefunction =eim,...Ch. 10 - Prob. 10.29ECh. 10 - Prob. 10.30ECh. 10 - Prob. 10.31ECh. 10 - Normalize the following wavefunctions over the...Ch. 10 - Prob. 10.33ECh. 10 - Prob. 10.34ECh. 10 - For an unbound or free particle having mass m in...Ch. 10 - Prob. 10.36ECh. 10 - Prob. 10.37ECh. 10 - Prob. 10.38ECh. 10 - Evaluate the expression for the total energies for...Ch. 10 - Prob. 10.40ECh. 10 - Verify that the following wavefunctions are indeed...Ch. 10 - In exercise 10.41a, the wavefunction is not...Ch. 10 - Prob. 10.43ECh. 10 - Prob. 10.44ECh. 10 - Explain why n=0 is not allowed for a...Ch. 10 - Prob. 10.46ECh. 10 - Prob. 10.47ECh. 10 - Prob. 10.48ECh. 10 - Carotenes are molecules with alternating CC and...Ch. 10 - The electronic spectrum of the molecule butadiene,...Ch. 10 - Prob. 10.51ECh. 10 - Prob. 10.52ECh. 10 - Show that the normalization constants for the...Ch. 10 - Prob. 10.54ECh. 10 - Prob. 10.55ECh. 10 - An official baseball has a mass of 145g. a...Ch. 10 - Is the uncertainty principle consistent with our...Ch. 10 - Prob. 10.58ECh. 10 - Prob. 10.59ECh. 10 - Instead of x=0 to a, assume that the limits on the...Ch. 10 - In a plot of ||2, the maximum maxima in the plot...Ch. 10 - Prob. 10.62ECh. 10 - Prob. 10.63ECh. 10 - The average value of radius in a circular system,...Ch. 10 - Prob. 10.65ECh. 10 - Prob. 10.66ECh. 10 - Prob. 10.67ECh. 10 - Prob. 10.68ECh. 10 - Prob. 10.69ECh. 10 - Assume that for a particle on a ring the operator...Ch. 10 - Mathematically, the uncertainty A in some...Ch. 10 - Prob. 10.72ECh. 10 - Prob. 10.73ECh. 10 - Verify that the wavefunctions in equation 10.20...Ch. 10 - An electron is confined to a box of dimensions...Ch. 10 - a What is the ratio of energy levels having the...Ch. 10 - Consider a one-dimensional particle-in-a-box and a...Ch. 10 - Prob. 10.78ECh. 10 - Prob. 10.79ECh. 10 - Prob. 10.80ECh. 10 - Prob. 10.81ECh. 10 - What are x,y, and z for 111 of a 3-D...Ch. 10 - Prob. 10.83ECh. 10 - Prob. 10.84ECh. 10 - Prob. 10.85ECh. 10 - Prob. 10.86ECh. 10 - Prob. 10.87ECh. 10 - Prob. 10.88ECh. 10 - Substitute (x,t)=eiEt/(x) into the time-dependent...Ch. 10 - Write (x,t)=eiEt/(x) in terms of sine and cosine,...Ch. 10 - Prob. 10.91ECh. 10 - Prob. 10.92ECh. 10 - Prob. 10.93ECh. 10 - Prob. 10.95E
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- Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.arrow_forwardA particle on a ring has a wavefunction =12eim where equals 0 to 2 and m is a constant. Evaluate the angular momentum p of the particle if p=i How does the angular momentum depend on the constant m?arrow_forwardThe normalized wave function for a particle in a one-dimensional box in which the potential energy is zero is (x)=2/Lsin(nx/L) , where L is the length of the box (with the left wall at x=0 ). What is the probability that the particle will lie between x=0 and x=L/4 if the particle is in its n=2 state?arrow_forward
- A particle on a ring has a wavefunction =eim, where =0to2 and m is a constant. a Normalize the wavefunction, where d is d. How does the normalization constant depend on the constant m? b What is the probability that the particle is in the ring indicated by the angular range =0to2/3? Does this answer make sense? How does the probability depend on constant m?arrow_forwardThe following operators and functions are defined: A=x()B=sin()C=1()D=10()p=4x32x2q=0.5r=45xy2s=2x3 Evaluate: a Ap b Cq c Bs d Dq e A(Cr) f A(Dq)arrow_forwardUsing the original definition of the momentum operator and the classical form of kinetic energy, derive the one-dimensional kinetic energy operator K=22m2x2arrow_forward
- Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?arrow_forwardThe de Broglie equation for a particle can be applied to an electron orbiting a nucleus if one assumes that the electron must have an exact integral number of wavelengths as it covers the circumference of the orbit having radius r:n=2r. From this, derive Bohrs quantized angular momentum postulate.arrow_forwardWhy is multiplying a function by a constant considered an eigenvalue equation?arrow_forward
- What is the degeneracy of an h subshell? An n subshell?arrow_forwardFor an unbound or free particle having mass m in the complete absence of any potential energy that is, V=0, the acceptable one-dimensional wavefunctions are =Aei(2mE)1/2x/h+Bei(2mE)1/2x/h, where A and B are constants and E is the energy of the particle. Is this wavefunction normalizable over the interval x+? Explain the significance of your answer.arrow_forwardAn official baseball has a mass of 145g. a Assuming that a baseball in New Orleans Superdome width =310m is acting as a particle-in-a-box, what is its energy in the n=1 state? b Assuming that the energy in part a is all kinetic energy (=12mv2), what is the velocity of the baseball in the n=1 state? c A hit baseball can travel as fast as 44.7m/s. Calculate the classical kinetic energy of the hit baseball and, assuming that this energy is quantized, determine the quantum number of the hit baseball.arrow_forward
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