Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 8, Problem 29P
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Calculate the uncertainty in distance about the average value and compare it with the average value.
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1.5
The time-averaged potential of a neutral hydrogen atom is given by
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Chapter 8 Solutions
Modern Physics
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8 - Prob. 1QCh. 8 - Prob. 2QCh. 8 - Prob. 3QCh. 8 - Prob. 4QCh. 8 - Prob. 5QCh. 8 - Prob. 6Q
Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10PCh. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 34P
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- Consider a composite state of an electron with total angular momentum j1 = 1/2 and a proton with angular momentum j2 = 3/2. Find all the eigenstates of |j1,j2;j,m⟩ as the linear combination of product states of angular momentum of electron and proton |j1,j2;m1,m2⟩. Give the values of Clebsch-Gordon coefficients you get from here. If the system is found in state |j1 = 1/2,j2 = 3/2;j = 1,m = −1⟩, what is the probability that j1z = −1/2 and what is the probability that j1z = 1/2arrow_forwardConsider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?arrow_forwardThe three lowest energy levels of a hydrogen atom are -13.6 eV, -3.4 eV, and -1.5 eV. Place this atom in thermal contact with a reservoir and assume that there is only one way to occupy any one of these levels. Calculate the relative probability that this hydrogen atom at T = 316 K is in its first excited state (at -3.4 eV) relative to its ground state (at -13.6 eV). Write your answer in exponential form. An "eV" (electron volt) is the energy acquired by an electron accelerated across a 1 volt potential difference. This unit is used to describe electronic energy levels in atoms or solids (semiconductors, etc.). 1 eV = 1.602 x 10-19 J and Boltzmann's constant can be written as 8.617 x 10-5 eV K-1. If your calculator is unable to do this calculation try the web site https://www.wolframalpha.com In this site ex is entered as e^x, though exp(x) can also be used. If you haven't used this website before, a convenient tutorial can be found on youtube (for example,…arrow_forward
- A conduction electron is confined to a metal wire of length (1.46x10^1) cm. By treating the conduction electron as a particle confined to a one-dimensional box of the same length, find the energy spacing between the ground state and the first excited state. Give your answer in eV. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answerarrow_forwardCalculate the speed of the electron in a hydrogen atom in the state n = 5, in m/s. Express your answer as vx 10° m/s and type in just the value of v. Use three decimals in your answer.arrow_forwardThis question concerns the addition of 3 angular momenta (as covered in the tutorial). Consider again the hydrogen atom including the nuclear spin (1= 1/2). For an electron in a 3d level, what are all the possible values for the total angular momentum quantum number (including electron spin, nuclear spin and orbital motion)? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a b с d e 1,2,3 0,1,2,3 3/2,5/2 1,3/2,2,5/2,3 1,3arrow_forward
- A Construct the wavefunction V(r, 0, ¢) for an H atoms' electron in the state 2pz. Please note that in order to have a real-valued wavefunction of pr orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction. Px 1/2 Yg = ()"" (5 cos 0 -3 cos 0) cos e %3D (4x 21 12 64л/ 1/2 sin e (5 cos? e- 1)eti 87 -y Y = (3 cos²0 – 1) 105 1/2 32 sin e cos de2ie (167 15 12 sin e cos betie 35 12 (647 sin de i B Now consider an excited state of He atom with electron configuration 1s 2s'. In general, the wavefunction is a state: V(r, 0, 0, 02) = V(r,0, ø)V.. where V(r, 0, 6) and V,, represent the spatial and the spin part. The spatial part is constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, ø) and o (r, 0,…arrow_forwardCalculate the value of <r> for the states of the hydrogen atom with n = 2 and l = 1, and for n = 2 and l = 0. Are the results surprising you? Explain your answer?arrow_forwardConsider an object containing 6 one-dimensional oscillators (this object could represent a model of 2 atoms in an Einstein solid). There are 4 quanta of vibrational energy in the object. (a) How many microstates are there, all with the same energy? (b) If you examined a collection of 38000 objects of this kind, each containing 4 quanta of energy, about how many of these objects would you expect to find in the microstate 000004?arrow_forward
- QUESTION 1: Hydrogen atom in a general state (ignoring spin): The orthonormal energy eigenstates of the hydrogen atom n,,m are labelled by the principal quantum number n and the orbital angular momentum quantum numbers I and m. In the following you may write the energy eigenvalues as En E. The state of a hydrogen atom at time t = 0 is given by a linear combination of energy eigenstates V (√561,0,0 — √342,1,1 + i√3,2,-2) · (a) Write down the wave function for later times t> 0 assuming the atom is undisturbed. (b) Show that this state is correctly normalised. (c) Find the expectation values of the energy and Îz if the system is in the state V. 2² Hint: No integrations needed, just use the known eigenvalues of Un,1,m with respect to and write the energy eigenvalues as En = ₁. n². = and Îz,arrow_forward(1) Calculate (r) and (r²) for the ground state of the hydrogen atom, expressing your answer in term of the Bohr radius. Calculate (x) and (x²) for the ground state of the hydrogen atom. Note that you really do not have to do any more work than you already did in problem #1 if symmetry properties are invoked.arrow_forwardcalculate the expectation value for the potential energy of the H atom with the electron in the 1s orbital. Compare your result with the total energy. What is the kinetic energy of H atom in this state? Verify the virial theorem for the Coulomb potential.arrow_forward
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