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List the most important ideas of the quantum mechanical model of the atom. Include in your discussion the terms or names wave function, orbital, Heisenberg uncertainty principle, de Broglie, Schrodinger, and probability distribution.

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Coleen Amado
Coleen AmadoLv10
10 Dec 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A Particle in a box
In order to answer the following questions you will need toconsideran infinite potential
well of length L, in which a particle has been confined.



1. For principal quantum number n=7, write code to calculatethenormalization constant.
Then, plot the probability density function for this state (usingL= 10).
2. Using the properly normalized wave equation from Question1,write code to determine
the expectation values <x> and <x2> . Is <x>oneof the most probable positions? Explain
why.
3. Using the properly normalized wave equation from Question1,write code to determine
the expectation values <p> and <p2> . Show the valueyouobtain for <p2> is equal to
2mE7 (where E7 is the energy of the n = 7 level). Remember that pisa differential
operator so you will have to use the diff command.
4. The uncertainty of a quantum measurement is defined on page222,Equation 6.41 (3rd
edition SMM). Using this equation calculate the uncertainties oftheposition and
momentum of a particle in the n = 5 state. Compute the productofthese uncertainties and
compare this with the prediction of the Heisenberguncertaintyprinciple.
Quantum oscillator
5. Repeat calculations in the previous question for the groundstatewave function of the
quantum oscillator. Comment on the obtained result.

One facet of the central field approximation for many-electronatoms is that inner-shell electrons screen the nuclear charge. Tounderstand how this works quantitatively, first note that theprobability distributions for electrons in different shellsgenerally do not overlap much. For instance, the electrons in the Mshell (n=3) are almost always farther from the nucleus than theelectrons of the K (n=1) and L (n=2) shells. Thus, it is a goodapproximation to assume that the inner shells completely screen thenucleus from the outer shells. For example, if there are tenelectrons altogether in the K and L shells of an atom, then theelectrons in the M shell experience force from a charge of roughlyZ-10, where Z is the charge on the nucleus as an integer multipleof e, the magnitude of the charge on an electron. This is calledthe effective nuclear charge Z_eff.

a. In a beryllium atom (Z=4), how many electrons are in the Kshell?
Express your answer as an integer.

b. n xenon (Z=54), what is the effective charge Z_eff experiencedby an electron in the M (n=3) shell?
Express your answer as an integer.

c. How many electrons are there altogether in the K, L, and Mshells of xenon? Recall that for n=3, the orbital quantum number lmust be zero, one, or two and that m_l can take any value betweenpostive and negative l.
Express your answer as an integer.

d.

The idea of simply subtracting the number of inner-shell electronsworks well only for atoms with low values of Z. For atoms withlarger nuclear charge, the different shapes of the probabilitydistributions for different subshells becomes an important factor.For instance, in the N shell, electrons in the s subshell have amuch higher probability than those in the p or d subshells of beingfound closer to the nucleus than some of the K, L, or M electrons.It is said that the s electrons penetrate the inner shells morereadily than do the p or d electrons. Therefore, it is to beexpected that our simple subtraction model may not work well forouter-shell s electrons in large atoms. Keeping this in mind, wesee that the effective nuclear charge Z_eff for the outermostelectron in an atom may be found experimentally by measuring theionization energy of an atom and then calculating the effectivecharge using the equation

E_n=- \frac{Z_{\rm eff}^2}{n^2}(13.6\;\rm eV).

The energy for the 5p valence electron in indium (Z=49) is -5.79electron volts. What is the effective nuclear charge Z_effexperienced by this electron?
Express your answer to three significant figures.

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