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**Chapter41 All About Atoms**

Atoms are the basic building blocks of matter that make up everyday objects. A desk, the air, even you are made up of atoms! There are 90 naturally occurring kinds of atoms. Scientists in labs have been able to make about 25 more.

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**41-1 The Mass and Size of the Atom**

The Mass of the Atom The absolute atomic mass matom can therefore be obtained by measuring Avogadro’s number: The present best value for NA is With the value of NA ,we can write:

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**The Size of the Atom Determining the Atomic Size from the Covolume**

The Van der Waals equation for one mole of a real gas states The quantity b is equal to the fourfold volume of the particles Determining the Atomic Size from the Gases movement is the distance,the N is again the particle number density

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**41-2 Some Properties of Atoms**

Basic properties of atoms: 1. Atoms are stable. 2. Atoms combine with each other. Atoms Are Put Together Systematically The numbers of elements in the six periods are: 2, 8, 8, 18, 18, 32.

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**Results of Mass Spectrometry**

In atomic physics,mass spectrometers are primarily of interest as instruments for analysing the isotopic composition of chemical elements An element often has several isotopes,for example chlorine:an isotope with mass number 35 occurs with an abundance of 75.4%;the other stable isotope with mass number A=37 has na abundance of 24.6%.The resulting relative atomic mass of the isotope mixture is Arel= There are elements with only one stable isotope,for example ; and others with two stable isotopes, and finally there are elements with many stable isotopes.

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**Atoms Emit and Absorb Light**

The light is emitted or absorbed as a photon with energy: Atoms Have Angular Momentum and Magnetism In quantum physics,each quantum state of an election in an atom involves an angular momentum and magnetic dipole moment that have opposite directions. (those vector quantities are said to be coupled)

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**The Einstein-de Haas Experiment**

This clever experiment designed to show that the angular momentum and magnetic moment of individual atoms are coupled. Observation of the cylinder’s rotation verified that the angular momentum and the magnetic dipole moment of an atom are couple in opposite directions. Moreover,it dramatically demonstrated that the angular momenta associated with quantum states of atoms can result in visible rotation of an object of everyday size.

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**41-3 Electron Spin Table 41-1 Electron States for an Atom Related to n**

Quantum Number symbol Allowed Values Related to Principal n 1,2,3…… Distance from the nucleus Orbital 0,1,2……(n-1) Orbital angular momentum Orbital magnetic 0,±1,±2, ……± Orbital angular momentum(z component) Spin s Spin angular momentum Spin magnetic All states with the same value of form a shell. All states with the same values of n and l form a subshell. All states in a subshell have the same energy. There are 2n2 states in a shell. There are 2(2 +1)states in a subshell

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In quantum physics,spin angular momentum is best thought of as a measurable intrinsic property of the election. Table 41-1,shows the four quantum numbers n,l, ml, and ms, that completely specify the quantum states of the electron in a hydrogen atom.The same quantum numbers also specify the allowed states of any single election in a multielectron atom.

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**41-4 Angular Momenta and Magnetic Dipole Moments**

Orbital Angular Momentum and Magnetism The magnitude L of the orbital angular momentum of an electron in an atom is quantized;it can have only certain values: The “ - ” in this relation means that is directed opposite an orbital magnetic dipole moment

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**The magnitude of must also be quantized and give by**

The components of the orbital magnetic dipole moment are quantized and give by is the Bohr magneton:

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**The components Lz of the angular momentum are also quantized,and they are given by**

we can extend that visual aide by saying that makes a certain angle with the z axis: We can call the semi-classical angle between vector and the z axis.

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**Spin Angular Momentum and Spin Magnetic Dipole Moment**

The spin magnetic dipole moment ,which is related to the spin angular momentum The magnitude of also be quantized and give by The magnitude S of the spin angular momentum of any electron,whether free or trapped,has the single value given by

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**The electron is said to be spin up**

The electron is said to be spin down Neither nor can be measured in any way.however,we can measure their components along any given axis---call it the z axis.the components of the spin angular momentum are quantized and given by The components of the spin magnetic dipole moment are also quantized

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**Orbital and Spin Angular Momenta Combined**

Define a total angular momentum which is the vector sum of the angular momenta of the individual electrons. the number of electrons in a neutral atom is the atomic number Z. For a neutral atom Instead, the effective magnetic dipole moment for the atom is the component of the vector sum of the individual magnetic dipole moments in the direction of

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**41-5 The stern-Gerlanch Experiment**

In the Stern-Gerlanch experiment,as it is now know,silver is vaporized in an oven, and some of the atoms in that vapor escape through a narrow slit in the oven wall,into an evacuated tube.Some of those escaping atoms then pass through a second narrow slit,to form a narrow beam of atoms. The beam passes between the poles of an electromagnet and then lands on a glass detector plate where it forms a silver deposit. The Experimental surprise Stern and Gerlach found was that the atoms formed two distinct spots on the glass plate,one spot above the point where they would have landed with no deflection and the other spot just as far below that point.This two-spot result can be seen in the plots of Fig.41-9,which shows the outcome of a more recent version of the Stern-Gerlach experiment.

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When the field was turned off,the beam was,of course, undeflected and the detector recorded the central-peak pattern shown in Fig.419. Fig.41-9 Results of a modern repetition of the Stern-Gerlach experiment. When the field was turned on,the original beam was split vertically by the magnetic field into two smaller beams,one beam higher than the previously undeflected beam and the other beam lower.As the detector moved vertically up through these two smaller beams,it recorded the two-peak pattern show in Fig.41-9.

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**The Meaning of the Results**

It is not the magnetic deflecting force The potential energy U of the dipole in the magnetic field In Fig.41-8,the positive direction of the z axis and the direction of are vertically upward. Using (F=-dU/dx) for the z axis

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**which result in the two spots of silver on the glass.**

According to The component are for quantum numbers ms=±1/2. substituting into Eq gives us Then substituting these expressions for Uz in Eq.41-17,we find that the force component Fz deflecting the silver atoms as they pass through the magnetic field can have only the two values which result in the two spots of silver on the glass.

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Sample Problem 41-1 The separation between the two subbeams is twice this,or 0.16 mm. This separation is not large but is easily measured.

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**41-6 Magnetic Resonance The f required for the spin-flipping**

a condition called magnetic resonance. The f required for the spin-flipping Nuclear magnetic resonance is a property that is the basis for a valuable analytical tool, particularly for the identification of unknown compounds. Figure shows a nuclear magnetic resonance spectrum.

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**41-7 The Pauli Exclusion Principle**

Sample Problem 41-2 41-7 The Pauli Exclusion Principle Pauli exclusion principle : For elections,it states that No two elections confined to the same trap can have the same set of values for its quantum numbers. This principle means that no two elections in an atom can have the same four values for the quantum numbers n,l,ml, and ms. In other words,the quantum numbers of any two elections in an atom must differ in at least one quantum number.

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**41-8 Multiple Electrons in Rectangular Traps**

1.One –dimensional trap. width L quantum number n quantum number 2.Rectangular corral. widths Lx,Ly quantum numbers nx,ny quantum number 3.Rectangular box. widths Lx,Ly,Lz quantum numbers nx,ny,nz quantum number

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**Finding the Total Energy**

(a) Energy-level diagram for one electron in a square corral of widths L. (b) Two electrons occupy the lowest level of the one-electron energy-level diagram. (c) A third electron occupies the next energy level. (d) The system’s ground-state configuration,for all 7 electrons. (e) Three transitions to consider as possibly taking the 7-electron system to its first excited state. (f) The system’s energy-level diagram,for the lowest three total energies of the system.

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**nx ny ms 2 8 1 5 Total 32 *In multiples of**

Table 41-2 Ground-State Configuration nx ny ms Energy* 2 8 1 5 Total 32 *In multiples of

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**41-9 Building the Periodic Table**

The values of l are represented by letters: l = …… s p d f g h …… To table 41-1 Guided by the Pauli exclusion principle X Rays and the Numbering of the Elements The distribution by wavelength of the X rays produced when 35 kev electrons strike a molybdenum target.The sharp peaks and the continuous spectrum from which they rise are produced by different mechanisms.

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**The Continuous X-Ray Spectrum**

The Characteristic X-ray Spectrum The peaks arise in a two-part process (1) An energetic electron strikes an atom in the target and,while it is being scattered,the incident electron knocks out one of the atom’s deep-lying (low n value) electrons.If the deep-lying election is in the shell defined by n=1,there remains a vacancy,or hole,in this shell.

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**Accounting for the Moseley Plot**

(2)An electron in one of the shells with a higher energy jumps to the K shell,filling the hole in this shell.During this jump,the atom emits a characteristic x-ray photon. Accounting for the Moseley Plot The hydrogen atom is for n = 1,2,3,…… We can approximate the effective energy of the atom by energy of the atom by replacing the factor in Eq with or , That gives us

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**We may write the energy change as**

Then the frequency f of the line is Taking the square root of both sides yields C is a constant ( )

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Sample Problem 41-4 Sample Problem 41-5

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**41-11 Lasers and Laser Light**

1. Laser light is highly monochromatic. 2. Laser light is highly coherent. 3. Laser light is highly directional. 4. Laser light can be sharply focused. Laser light special characteristics: 41-12 How Lasers Work DEMO Here are three processes by which the atom can move from one of these states to the other : 1.Absorption Fig.19 (a)

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**2.Spontaneous emission. 3.Stimulated emission.**

In Fig.41-19(b) 3.Stimulated emission. In Fig.41-19(c) To produce laser light,we must have more photons emitted than absorbed.So there requires more atoms in the excited state than in the ground state,as in Fig.41-20b. However,since such a population inversion is not consistent with thermal equilibrium, we must think up clever ways to set up and maintain one.

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**The Helium-Neon Gas Laser**

Four essential energy levels for helium and neon atoms in a helium-neon gas laser.Laser action occurs between levels E2 and E1 of neon when more atoms are at the E2 level than at the E1 level.

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metastable state metastable state metastable state Four energy systems

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Sample Problem 41-6 (a) (b)

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**REVIEW & SUMMARY Some Properties of Atoms**

Angular Momenta and Magnetic Dipole Moments an orbital magnetic dipole moment

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is the Bohr magneton:

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**Spin and Magnetic Resonance**

Pauli exclusion principle : For elections,it states that No two elections confined to the same trap can have the same set of values for its quantum numbers. Building the Periodic Table The values of l are represented by letters: l = …… s p d f g h …… Guided by the Pauli exclusion principle

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**X Rays and the Numbering of the Elements**

Lasers and Laser Light

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