Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 36, Problem 62P
(a)
To determine
The possible values for the total angular momentum of the hydrogen atom in the
F
(b)
To determine
The number of possible values for the component of
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Students have asked these similar questions
a) 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.)
You are working on determining the angle that separates two hybridized
orbitals. In the process of determining the coefficients in front of the various
atomic orbitals, you align the first one along the z-axis and the second in the
x/z-plane (so o = 0). The second hybridized orbital was determined to be:
W2 = R1s + R2p, sin 0 + R2p, cos 0
Determine the angle, 0, in degrees to one decimal place (XX.X) that separates
these two orbitals. Assume that the angle will be between 0 and 90 degrees.
an angular momentum vector has a maximum z component of +3ℏ, how many different z components can it have?
Chapter 36 Solutions
Essential University Physics
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 11ECh. 36 - Prob. 12ECh. 36 - Prob. 13ECh. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34ECh. 36 - Prob. 35ECh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Solar physicists measure the strong magnetic...Ch. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
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- Consider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. What is the potential energy of the system (the nucleus and the two electrons)?arrow_forwardA) If two operators commute, show that they have the same eigenfunction. B) Prove that [A^, (B^ + C^)] = [A^, B^] + [A^, C^] C) Write the differential expression of the angular momentum components Lx, L, and L,. D) Determine the value of the total angular momentum L for the H-atom in the orbit l=3 and plot a diagram to show its projections on the z-axis.arrow_forwardB) A spin state in an arbitrary direction is given by directions. Cas 2 -io sin 2 Find the form of the states in z, x and yarrow_forward
- The electron in a hydrogen atom is in the state |v) N[3]W100) + 4 |v211)] where ynlm represents the spatial eigen functions of hydrogen atom. (a) Find N such that the above state normalized. Assume N is real and positive. (b) Is y) an eigen state of the Hamiltonian of hydrogen atom? Justify your answer. (c) Determine expectation value of the Hamiltonian in terms of eigen energies Ei and E2. (d) Determine the expectation values of L, and L?.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_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, L₂ = m₂h, 1 = 0,1,2,..., n-1 m₁ = 0, +1, +2, ..., ±l 3 1 S² = s(s+1)h²=h², S₂ = m₂h = + = h +/-ħ 4 Consider an excited electron (n > 1) on an H-atom. What is the minimum angle 0min that the S can have with the z-axis? Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_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_forwardWhat are the possible values for the angle that the orbital angular moment vector L of d-electrons makes with the xy plane? Show your solution in detail.arrow_forwardConsider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. What is the total kinetic energy of the electrons?arrow_forward
- Construct nine possible angular momentum states for L1=1 and L2=1 and 8 possible states for L1=3/2 and L2=1/2arrow_forwardAn electron is in an angular momentum state with /= 3. (a) What is the length of the electron's angular momen- tum vector? (b) How many different possible z compo- nents can the angular momentum vector have? List the possible z components. (c) What are the values of the angle that the L vector makes with the z axis?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_forward
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