An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter 6.1, Problem 7P
To determine
The relative probability for a hydrogen atom of being in a first excited state.
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6.3 Consider an electron in a state in which the spin component along the z-axis
is +1/2. Calculate the probability that the component of the spin along direction
z' making an angle 0 with the z-axis is +1/2. What is the average value of the
component of spin along z'?
The ground state of the realistic Helium atom is nondegenerate. Let us now consider a
hypothetical Helium atom where the two electrons are replaced by identical particles of spin 1
and negative charge. What is the degeneracy of the ground state? Explain your reasoning
(ignore forces that depend on spin).
solve it completely.
What are the additional assumption made in the shell model ?
Discuss the possible cause for (a) the difference in the energy of j+1/2 and j-1/2 states
(b) the pairing energy.
Chapter 6 Solutions
An Introduction to Thermal Physics
Ch. 6.1 - Prob. 2PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.1 - Prob. 6PCh. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Prob. 9PCh. 6.1 - Prob. 10PCh. 6.1 - Prob. 11PCh. 6.1 - Prob. 12P
Ch. 6.1 - Prob. 13PCh. 6.1 - Prob. 14PCh. 6.2 - Prob. 15PCh. 6.2 - Prob. 16PCh. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - Prob. 19PCh. 6.2 - Prob. 20PCh. 6.2 - For an O2 molecule the constant is approximately...Ch. 6.2 - The analysis of this section applies also to...Ch. 6.3 - Prob. 31PCh. 6.4 - Calculate the most probable speed, average speed,...Ch. 6.4 - Prob. 35PCh. 6.4 - Prob. 36PCh. 6.4 - Prob. 37PCh. 6.4 - Prob. 39PCh. 6.4 - Prob. 40PCh. 6.5 - Prob. 42PCh. 6.5 - Some advanced textbooks define entropy by the...Ch. 6.6 - Prob. 44PCh. 6.7 - Prob. 45PCh. 6.7 - Equations 6.92 and 6.93 for the entropy and...Ch. 6.7 - Prob. 47PCh. 6.7 - For a diatomic gas near room temperature, the...Ch. 6.7 - Prob. 49PCh. 6.7 - Prob. 50PCh. 6.7 - Prob. 51PCh. 6.7 - Prob. 52PCh. 6.7 - Prob. 53P
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- Write 4 spin orbitals for the excited state He atom with the configuration 1S*2s4. Factor each spin orbital into a product of space and spin eigenfunctions. (b) What property does each of these spin orbitals have ? (c) Do the spin orbitals have the same of different energies ? Explain. 5.arrow_forwardConsider two spin 1 particles, that can be combined to form j = 0, 1, 2 states. Use a method of your choosing to express the nine global eigenkets |j, m) in terms of the local eigenkets |j1, j1; m1, m2).arrow_forwardWhat is the degeneracy of J=1 for a linear, symmetric, and spherical rotor? For each rotor, give the complete set of quantum numbers for each state. (Recall that there should be a unique set of quantum numbers for each state and that the total number of states should match the degeneracy.)arrow_forward
- What will happen if we put a spin-1 particle inside the 3D potentialwell? Find out the density of states for the system.arrow_forward(a) Draw the hydrogen energy-level diagram for all states through n = 2 as in the righthand part of Figure 8-11, but with the splitting according to l also shown. (b) With arrows connecting pairs of levels, show all the transitions that are allowed by the selectionarrow_forward(Hint: use the Schmidt form). 2. Suppose |) and Jo) are pure states in a qubit space, with | (vlo) | = cos 6. Show that the Bloch vectors for these states form an angle of 26.arrow_forward
- Calculate the radius of the sphere that encloses a 50% probability of finding a hydrogen 1s electron. Repeat the calculation for a 90% probability.arrow_forwardA system of 9 identical non-interacting spin-3/2 particles confined to a one-dimensional harmonic oscillator potential is in its minimum energy configuration for which E 5.75 eV. What is the minimum energy of the same system with 10 such particles? Recall that the energy levels of a single particle in a one-dimensional harmonic oscillator potential are given by En = (n+1) hwo with n = 0, 1, 2, .... =arrow_forward(A) Consider a particle in a cubic box. What is the degeneracy of the level it hasenergy three times greater than that of the lowest level? (Explain the combinations of n that led you to the answer given). (B) The addition of sodium to ammonia generates a solvated electron that is trapped in a cavity of 0.3 nm in diameter, formed by ammonia molecules. The solvated electron can be modeled as a particle that moves freely inside the cubic box with ammonia molecules in the cube surface. If the length of the box is 0.3 nm, what energy is needed for the electron undergo a transition from a lower energy state to the subsequent state?arrow_forward
- Consider a system of N spin 2 particles with allowed spin values −2,−1,0,1,2 for each particle. Compute the degeneracy factor for the case of zero total spin. Specialize to the case of N=10 for which compute the degeneracies for all possible total spin configurations. For each such configuration, draw a maximum of 10 representative examples.arrow_forwardprovided a system of 2 electrons in a one-dimensional box, write the approximate wavefunctions including the spin (but without considering interelectronic repulsion) for the states with an electron with n=1 and an electron with n=2. State which of the resulting states has the lowest energy. Symbolically build the linear combinations of the wavefunctions products (including spin). SHOW FULL AND COMPLETE PROCEDURE IN A CLEAR AND ORDERED WAYarrow_forward: Derive a state space model for the system shown in Figure below when the input is fa and the output is z.arrow_forward
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