An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter A.4, Problem 21P
To determine
The quantum numbers ( n, l and m ) for all the independent states of a hydrogen atom with definite E ,
To check: The numbers of independent states for level n is equal to n2 .
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Chapter A Solutions
An Introduction to Thermal Physics
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- The radial wave function of a quantum state of Hydrogen is given by R(r)= (1/[4(2π)^{1/2}])a^{-3/2}( 2 - r/a ) exp(-r/2a), where a is the Bohr radius.(a) Determine the radial probability density P(r) associated with the quantum state in question. (b) Show that the function P(r) you determined in part (a) is properly normalized.arrow_forwardFor a hydrogen atom, determine the allowed states corresponding to the principal quantum number n = 2 and calculate the energies of these states.arrow_forwardThe wavefunction for an electron in the Hydrogen atom is provided in figure 1, where B is a constant, and a0 is the Bohr radius. By inspection and using the angular part of the wavefunction, identify the value of the quantum numbers l and ml, then operate on this wavefunction with Lˆz, and use your result to verify the value of ml identified.arrow_forward
- For a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is =cos1( n1n) .arrow_forwardCalculate the probability that the electron in the hydrogen atom, in its ground state, will be found between spherical shells whose radii are a and 2a, where a is the Bohr radius.arrow_forwardAt time t = 0 the wave function of the hydrogen atom is: where we ignore the spin.(a) Calculate the expected value of energy for this system.(b) What is the probability of finding the system at l = 1, m = +1 as a function of time?(c) What is the probability of finding the electron around 10−10 cm from the proton, at t = 0s (canapproximate).(d) Write the time-dependent wave function: ψ (r,t)arrow_forward
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- Considering <r> = a0/2 [3n2 - l (l +1)] The results of <r> for the states of the hydrogen atom with n = 2 and l = 1, and for n = 2 and l are: For n = 2 and l = 1 For n = 2 and l = 0 <r> = 5a0 <r> = 6a0 The question is: Do the results obtained surprise you? Explain your answer.arrow_forwardCalculate the energy changes corresponding to the transitions of the hydrogen atom: (a) from n=3 to n=4 ; (b) from n=2 to n=1 ; and (c) from n=3 to n= .arrow_forwardA researcher observes hydrogen emitting photons of energy 1.89 eV. What are the quantum numbers of the two states involved in the transition that emits these photons?arrow_forward
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