Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Question
Chapter 7, Problem 69E
(a)
To determine
The solution of time independent Schrödinger equation
(b)
To determine
To verify:
The angular solution
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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...
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- Write an expression for the total number of states with orbital angular momentum l.arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², 1 = 0,1,2,..., n-1 Lz = m₂ħ, m₁ = 0, ±1, ±2,..., ±l 3 S² = s(s+1)h² = h², 4 Consider an excited electron (n > 1) on an H-atom. Sz = msh 1 =+=ħ Show that the minimum angle that the I can have with the z-axis is given by n-1 n L.min = cos Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_forwardThe expectation value,arrow_forwardAn electron is in the 4f state of the hydrogen atom. (a) What are the values of n and I for this state? (b) Find the energy of this state. (c) Find the magnitude of the electron's total angular momentum L. (d) Find the possible values of the z-component of angular momentum L₂. (e) Using your answer from part (d), determine the minimum angle that the angular mo- mentum vector I can make with respect to the z-axis for this state.arrow_forwarda) How many distinct angles from the vertical axis can the orbital angular momentum vector L make for an electron with l = 7? b)Calculate the smallest possible angle the L can make with respect to the vertical axis. (Hint: The smallest angle occurs when ml takes the maximum allowed value. Sketch L in that case and compare the vertical component, which is related to ml, to the magnitude of L, which is related to l.)arrow_forwardIf we neglect interaction between electrons, the ground state energy of the helium atom is E =2 z2((- e2)/(2ao)) = -108.848eV (Z=2). The true (measured) value is – 79.006eV.Calculate the interaction energy e2/r12 supposing that both electrons are in the 1s state and r12 that the spin wave function is anti-symmetric. What E is the ground state energy?arrow_forwardConsider the seventh excited level of the hydrogen atom. (a) What is the energy of this level? (b) What is the largest magnitude of the orbital angular momentum? (c) What is the largest angle between the orbital angular momentum and the z-axis?arrow_forwardAn electron in a hydrogen atom makes atransition from a 5p state to a 4d state. (a) Does the energy of theelectron increase, decrease, or stay the same? Explain. (b) Doesthe magnitude of the electron’s angular momentum increase,decrease, or stay the same? Explain. (c) Calculate the change inthe electron’s energy in eV. (d) Calculate the change in the magnitude of the electron’s angular momentum.arrow_forward(1) What are the possible values of Jz for the62F7/2 state? (2) Determine the minimum angle between the total angular momentum vector and the z axis for this state.arrow_forward) What are the allowed values for total spin angular momentum of the hydrogen atom having 1 proton and 1 electron, a deuterium atom and a tritium atom? Note: Your analysis should be restricted to just the spin angular momentum. The problem is not asking about orbital angular momentum. Based on your results, which atom types (hydrogen, deuterium, tritium) will respond as a composite boson?arrow_forwardConsider the sp hybrid orbital of the H-atom: |spx-> =. 1 -(|2s > - |2p,>) (a) Find the expectation value of Lz in the |spx-> state in units of h. That is, find: /ħarrow_forwardHow many electrons can occupy the system with l=0, l=2 and l=4. What is number of possible orientations of the orbital angular momentum with l=4? What is the smallest z-component of the orbital angular momentum?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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