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27 Nov 2019

a) what are the largest and smallest values that the magneticquantum number m has in the Zn atom?
b) how many electrons have m = 0 in Zn?
c) in a particularly stable multi electron atom, the followingstates are fully occupied: n = 1; l=0; n=2; l=0,1,2; n=4; l=0,1,2;n=5; l=0,1. What is the Z value of this atom?

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Hubert Koch
Hubert KochLv2
28 Feb 2019

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

Related questions

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.

Consider a system consisting of N noninteracting atoms in asubstance at temperature T and volume V placed in an externalmagnetic field B pointing in the z direction. The magnetic energyof an atom can be taken as
e=-µiB
where µ is the magnetic moment of the atom. In this problem, wewill not consider the detailed contributions to the atomic magneticmoment from both the orbital and electron spin angular momentum;rather we will take the atomic magnetic moment to simply be givenby
µ=-gµBJ/?? in terms of the atomic g-factor, Bohr magneton, and thetotal angular momentum of the atom.

(a) Write the energy per atom noting that the magnetic field is inthe z direction. (b) Given that the magnitude and z component ofthe total angular momentum are
quantized, write the energy per atom in terms of the magneticquantum number mj , indicatingtherangeoftheallowedmjvaluesintermsofj,thequantumnumber associated with the magnitude ofthe total angular momentum. (For electron spin, j = 1/2 and mj = ±1/2.)
(c) How many values of mj are there?



The emergence of line spectra from a gas when a current passesthrough it was an observed phenomenon waiting for an explanation inthe early 20th century. The atomic line spectra coming fromelements such as hydrogen had been analyzed since the late 19thcentury. By studying the wavelength of the emerging radiation ofhydrogen, experimenters found (often by trial and error) that thewavelengths in those spectra were described by the formula

\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2}\right),
where R is known as the Rydberg constant. It has a value of R =1.097 \times 10^{7}\; \rm m^{-1}. The variables n_1 and n_2 areinteger numbers (n_1 = 1,2,3,4,\dots). As experiments continued,scientists began to see more and more characteristic lines emergingfrom the hydrogen spectrum. Each of them corresponded to awavelength predicted by this formula with some integer values forn_1 and n_2.

In 1913, Niels Bohr provided an explanation for the observationsmade in experiments by proposing that each electron in an atom hadonly certain allowable energy levels. Furthermore, he postulatedthat when an electron changed its energy level, it must emit orabsorb a single photon with the energy equal to the energydifference between the two levels.

With this interpretation, the variables n_1 and n_2 acquired newsignificance. Bohr's model predicted that n_2 was the initialenergy state of the atom (n_initial) and that n_1 was the finalstate of the atom (n_final). A photon with the predicted wavelengthwas created when an atom made a transition from its initial energystate to a lower final energy state. The equation now read

\frac{1}{\lambda} = R \left( \frac{1}{n_{\rm final}^2} -\frac{1}{n_{\rm initial}^2} \right).
Bohr's model also predicted that a photon of the appropriatewavelength (given by the same formula) could promote an atom from alower energy level to a higher one.

In this problem, we explore the photon characteristics necessaryfor transitions between energy levels in hydrogen and singlyionized {\rm He}^+, whose energy levels are accurately predicted bythe Bohr model.
What is the change in energy DeltaE of the hydrogen atom as theelectron makes the transition from the n=3 energy level to the n=1energy level?
Express your answer numerically in electron volts.

b. When an atom makes a transition from a higher energy level to alower one, a photon is released. What is the wavelength of thephoton that is emitted from the atom during the transition from n=3to n=1?
Express your answer numerically in angstroms.

c.

When the hydrogen atom makes the transition from the n=2 to the n=1energy level, it emits a photon. This photon can be absorbed by toa singly ionized helium atom ({\rm He}^+) in its second energylevel (n_{\rm initial} = 2), causing it to move to a higher energylevel. To what final energy level number n_final can the photonpromote the helium ion?

Note that {\rm He}^+ has two protons in its nucleus and a singleelectron.
Express your answer as an integer.

Please answer fully, Thank you
a.

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