An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
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 .
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Prove that the degeneracy of the nth energy level in the Hydrogen atom is n2(disregarding electron spin). Use the fact that the Hydrogen states are labeled by three integer quantum numbers, m, l and n, where −l ≤ m ≤ l and 0 ≤ l < n.
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,
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.
Chapter A Solutions
An Introduction to Thermal Physics
Knowledge Booster
Similar questions
- Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 156. Express your answer in units of ℏ to three significant figures.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_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
- Consider a two-electron spin system in a singlet state. a. If a measurement of one of the electrons shows that it is in a state with sz = 1/2, what is the probability of obtaining another state with sz= +1/2? b. If a measurement of one of the electrons shows that it is in a state with sx = 1/2, what is the probability of obtaining another state with sy = +1/2?arrow_forwardAnswer the following. (a) Write out the electronic configuration of the ground state for nitrogen (Z = 7). 1s22s22p11s22s22p2 1s22s22p31s22s22p41s22s22p51s22s22p6 (b) Write out the values for the set of quantum numbers n, ℓ, m, and ms for each of the electrons in nitrogen. (In cases where there are more than one value, enter the positive value first. Enter positive values without a '+' sign in front of them. Include all possible values.) 1s states n = ℓ = m = ms = ms = 2s states n = ℓ = m = ms = ms = 2p states n = ℓ = m = ms = ms = m = ms = ms = m = ms = ms =arrow_forwardA 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_forward
- In a one-dimensional system, the density of states is given by N(E)= 2m, where L is the length of the sample L√2m in the and m is the mass of the electron, as seen in class. There are N quantum particles with spin |S| = sample (the quantum particles can be understood as 'special electrons with spin [S] ='), so that each state can be occupied by 2|S| + 1 particles. Determine the Fermi energy at 0 K.arrow_forwardConstruct the wave function for an excited state of the helium atom with configuration 1s13s1 .Use Zeff = 2 for the 1s e- and Zeff = 1 for the 3s e-. SHOW PROCEDURE CLEARLY AND EXPLICITLY. DO NOT SKIP ANY STEParrow_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_forward
- Enumerate all states of the hydrogen atom corresponding to the principal quantum number n = 2, giving the spectroscopic designation for each. Calculate the energies of these states.arrow_forwardEnumerate and identify the states corresponding to the energy level E34, or n = 3, 1 = 2.arrow_forwardHow many electrons can occupy the system with l=0, l=2 and l=4. What is number of possibleorientations of the orbital angular momentum with l=4? What is the smallest z-component of theorbital angular momentum?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning