College Physics (10th Edition)
10th Edition
ISBN: 9780321902788
Author: Hugh D. Young, Philip W. Adams, Raymond Joseph Chastain
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 29, Problem 37GP
(a)
To determine
Find the lowest possible energy.
(b)
To determine
Find the smallest and largest value of orbital angular momentum in
(c)
To determine
Find the smallest and largest value of spin angular momentum.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
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.)
Angular 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/V
An electron is in the hydrogen atom with n = 5.
(a) Find the possible values of L and Lz for this electron, in units of h.
(b) For each value of L, find all the possible angles between L → and the z-axis. (c) What are the maximum and minimum values of the magnitude of the angle between L →and the z-axis?
Chapter 29 Solutions
College Physics (10th Edition)
Ch. 29 - Prob. 1CQCh. 29 - Prob. 2CQCh. 29 - Prob. 3CQCh. 29 - Prob. 4CQCh. 29 - Prob. 5CQCh. 29 - Prob. 6CQCh. 29 - Prob. 7CQCh. 29 - Prob. 8CQCh. 29 - Prob. 9CQCh. 29 - Prob. 10CQ
Ch. 29 - Prob. 1MCPCh. 29 - Prob. 2MCPCh. 29 - Prob. 3MCPCh. 29 - Prob. 4MCPCh. 29 - Prob. 5MCPCh. 29 - Prob. 6MCPCh. 29 - Prob. 7MCPCh. 29 - Prob. 8MCPCh. 29 - Prob. 9MCPCh. 29 - Prob. 10MCPCh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5PCh. 29 - What is the ratio of the number of different 3d...Ch. 29 - Prob. 7PCh. 29 - Prob. 8PCh. 29 - Prob. 9PCh. 29 - Prob. 10PCh. 29 - For bromine (Z = 35), make a list of the number of...Ch. 29 - (a) Write out the electron configuration (1s2 2s2,...Ch. 29 - Prob. 13PCh. 29 - Prob. 14PCh. 29 - Prob. 15PCh. 29 - Prob. 16PCh. 29 - Prob. 17PCh. 29 - Prob. 18PCh. 29 - Prob. 19PCh. 29 - Prob. 20PCh. 29 - Prob. 21PCh. 29 - Prob. 22PCh. 29 - Prob. 23PCh. 29 - Prob. 24PCh. 29 - Prob. 25PCh. 29 - Prob. 26PCh. 29 - Prob. 27GPCh. 29 - Prob. 28GPCh. 29 - An electron has spin angular momentum and orbital...Ch. 29 - Prob. 30GPCh. 29 - Prob. 31GPCh. 29 - Prob. 32GPCh. 29 - Prob. 33GPCh. 29 - Prob. 34GPCh. 29 - Prob. 35GPCh. 29 - Prob. 36GPCh. 29 - Prob. 37GPCh. 29 - Prob. 38GPCh. 29 - Prob. 39PPCh. 29 - Prob. 40PPCh. 29 - Prob. 41PPCh. 29 - Prob. 42PP
Knowledge Booster
Similar questions
- Chapter 39, Problem 043 In the ground state of the hydrogen atom, the electron has a total energy of -13.6 ev. What are (a) its kinetic energy and (b) its potential energy if the electron is a distance 4.0a from the central nucleus? Here a is the Bohr radius. (a) Number Units eV (b) Number Units eVarrow_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_forwardIn a hydrogen atom, the electron is at a distance of 4.768 Å from the nucleus. The angular momentum of the electron is......arrow_forward
- A hydrogen atom is in the stationary state (n, I, m) = (5, 3, 1) What is the angle between the angular momentum vector L and Lz? Give you answer to 3 significant figures and in units of degrees, but do not include the units in your answer.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, Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.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
- How 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_forward1. (a) Use the equation for energy Eigen values that result from the solution to the infinite square well to estimate the ground state energy (n = 1) in a hydrogen atom by assuming that an electron is confined in an infinite square well with L = 10-10 m. this is the average radius of an electron orbit in a hydrogen atom. Give your answer in units of J and eV. (b) Compare your answer in part (a) to the ground state energy value resulting from the use of the Bohr Model. Give your answer in units of J and eV. En moq4 2(4π, hn)² h where, ħ== m₁ = 9.11 x 10-³1 kg, q = 1.65 x 10-19 C, &o = 8.85 x 10-14. 2πT' Farad cm h = 6.63 x 10-34 Js.arrow_forwardYou 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.arrow_forward
- Why is the following situation impossible? An experiment is performed on an atom. Measurements of the atom when it is in a particular excited state show five possible values of the z component of orbital angular momentum, ranging between 3.16 x 10-34 kg ⋅ m2/s and -3.16 x 10-34 kg ⋅ m2/s.arrow_forwardAn electron occupying the n = 6 shell of an atom carries z-component orbital angular momentum = (–2) × h/2π. Given that the electron’s total orbital angular momentum is x × h/2π, what is the maximum possible value of numberx (remember to use the scientific notation)?arrow_forwardA magnetic field is applied to a freely floating uniform iron sphere with radius R = 2.00 mm. The sphere initially had no net magnetic moment, but the field aligns 12% of the magnetic moments of the atoms (that is, 12% of the magnetic moments of the loosely bound electrons in the sphere, with one such electron per atom). The magnetic moment of those aligned electrons is the sphere’s intrinsic magnetic moment .What is the sphere’s resulting angular speed v?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax