Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 89CE
To determine
The solution for the Schrödinger equation is
The allowed angular momenta and energies for solutions of the form of Schrödinger equation.
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An electron, trapped in a one-dimensional infinite potential well 250 pm wide, is in its ground state. How much energy must it absorb if it is to jump up to the state with n= 4?
Show transcribed data (d) Find (r) and (r2) for an electron in a circular orbit of hydrogen with arbitrary prin- cipal quantum number n (corresponds to l = n - 1 and any allowed m). (e) Compute the RMS uncertainty ✓(r) – (r)2 in terms of r for the electron in part (d). Note that the fractional spread in r decreases with increasing n (in this sense the system "begins to look classical” for large n). How much more volume does a hydrogen atom in the n = 100 state occupy compared to the hydrogen atom in the ground state. (Hint - you might want to look at Griffiths 4.55, or 4.15 in the second edition)
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Chapter 7 Solutions
Modern Physics
Ch. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - What are the dimensions of the spherical harmonics...
Ch. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Prob. 16CQCh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Show that of hydrogen’s spectral seriesLyman,...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - A particle orbiting due to an attractive central...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - How many different 3d states are there? What...Ch. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - For states where l=n1 , the radial probability...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79CECh. 7 - Prob. 80CECh. 7 - Prob. 81CECh. 7 - Prob. 83CECh. 7 - Prob. 84CECh. 7 - Prob. 85CECh. 7 - Prob. 86CECh. 7 - Prob. 87CECh. 7 - Prob. 89CE
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- Sketch the potential energy function of an electron in a hydrogen atom, (a) What is the value of this function at r=0 ? in the limit that r=? (b) What is unreasonable or inconsistent with the former result?arrow_forwardProve that assuming n = 0 for a quantum particle in an infinitely deep potential well leads to a violation of the uncertainty principle Δpx Δx ≥ h/2.arrow_forwardCalculate the transmission coefficient for an electron of total energy 2eV incident upon a rectangular potential barrier of height 2 eV and width 10-9 marrow_forward
- An electron is trapped in a finite potential well that is deep enough to allow the electron to exist in a state with n= 4. How many points of (a) zero probability and (b) maximum probability does its matter wave have within the well?arrow_forwardA simple illustration of the variation method is provided by the hydrogen atom in the 1s state. Let us assume a form of the trial wave function ψ=e–br where b is a constant. For hydrogen atom, V=-e2/r, so the Hamiltonian operator is Ĥ=-h2/8π2m V2- e2/r.The energy depends on r for the 1s state of the hydrogen atom so the angular portion of the Laplacian can be omitted and replaced by the factor 4π after integration. Therefore, the radial portion of V2=1/r2 (∂/∂r) r2 ∂/∂r. Solve the energy minimum of the hydrogen atom, E = -2π2 me4/h2.arrow_forwardFind the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima.arrow_forward
- Whether the energy gap for a system decreases, is constant, or increases as the initial quantum number for the transition increases can be determined by calculating the second derivative of the energy level expression with respect to the quantum number. Calculate the second derivative with respect to the quantum number of the energy level expression for a linear rotor, EJ = hBJ(J+1) and also for the harmonic oscillator, Ev = hυ\upsilonυ(v+1/2).arrow_forwardWhat must be the width of a one-dimensional infinite potential well if an electron trapped in it in the n = 3 state is to have an energy of 4.7 eV?arrow_forwardConsider an electron in a 2D harmonic trap with force constants kxx = 232 N/m and kyy = 517 N/m. List the energies of the lowest 10 eigenfunctions.arrow_forward
- Two identical particles of spin ½ are moving under the influence of a onedimensional harmonic oscillator potential. Assuming that the two-particle system is in a triplet spin state, find the energy levels, the wave functions, and the degeneracies corresponding to the three lowest states.arrow_forwardWhat is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a one-dimensional infinite potential well that is 200 pm wide?arrow_forward
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