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Chapter 8: Q12CQ (page 338)

Question: Solving (or attempting to solve!) a 4-electron problem is not twice as hard as solving a 2-electrons problem. Would you guess it to be more or less than twice as hard? Why?

Short Answer

Expert verified

Answer

Because there is an exact analytic solution for the two-electron problem, but not for the four-electron problem.

Step by step solution

01

Explanation.

A four-electron problem that involves only electrons and no nucleus would be more than twice as hard to solve as a two-electron problem" because there is an exact analytic solution for me two-electron problem, but not for the four-electron problem.

02

Reason.

However, what the question is probably asking about is finding the wave functions and energies for an atom with two electrons and an atom with four electrons. The two-electron problem is a three-body problem (with the nucleus as the third body).

The four-electron problem would be less man two times as difficult as the two-electron problem. This is because neither problem can be solved in analytic form like the hydrogen atom, but many of the approximations used in the approximate solution of the two-electron problem, such as regarding each electron to move in an average field of the other charges, would apply also in some form to the four-electron problem.

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Most popular questions from this chapter

The radius of cesium is roughly0.26nm.

(a) From this estimate the effective charge its valence electron orbits

(b) Given the nature of the electron's orbit. is this effective nuclearcharge reasonable?

(c) Compare this effective Zwith that obtained for sodium in Example 8.3. Are the values at odds with the evidence given in Figure8.16that it takes less energy to remove an electron from cesium than from sodium? Explain.

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(a) What is the probability of finding the particle spin up in the second apparatus? Of finding it spin down? Argue that these probabilities make sense individually for representative values of蠒and their sum is also sensible.

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Question: As indicated to remove one of the helium鈥檚 electrons requires24.6eV of energy when orbiting -24.6eV? Why or why not?

(a) To determine the repulsive energy between the two electrons in helium.

(b) To determine the distance of electrons that would have to be separated.

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The general rule for adding angular momenta is given in Exercise 66, when adding angular momenta withj1=2 and j2=32

(a) What are the possible values of the quantum numberjT and the total angular momentum jT.

(b) How many different states are possible and,

(c) What are the (jT,mjT)values for each of these states?
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