Chapter 40 All About Atoms In this chapter we continue with a primary goal of physics―discovering and understanding the properties of atoms. 100 years ago researchers struggled to find experiments that would prove the existence of atoms. Today, thanks to scientific and technological progress, we can manipulate atoms in amazing ways: we can image individual atoms using scanning tunneling microscopy; we can drag them on surfaces to make quantum corrals, and even hold an individual atom indefinitely in a trap in order to study its properties when isolated. (40-1)

Basic Properties Atoms are stable. Essentially all atoms have remained unchanged for billions of years. Atoms combine with each other. Atoms stick together to form molecules and stack up to form rigid solids. Even though atoms are mostly empty space, their interactions allow you to stand on a floor without falling through! These basic properties can be explained by quantum mechanics Some Properties of Atoms (40-2)

Some Properties of Atoms Fig Subtler Properties Atoms Are Put Together Systematically. There are repetitive (periodic) patterns in the properties of different atoms that allow them to be organized into a periodic table. Ionization energy vs. atomic number (number of protons in nucleus) Six periods with 2, 8, 8, 18, 18, and 32 atoms in each period, respectively. These numbers are predicted by quantum mechanics. (40-3)

Some Properties of Atoms Subtler Properties, cont’d Atoms Emit and Absorb Light: Atoms Have Angular Momentum and Magnetism: Fig “Orbit” of each electron (more correct to think in terms of angular momentum of electronic state) can produce a magnetic moment. (40-4)

Some Properties of Atoms Subtler Properties, cont’d Einstein-de Haas Experiment: Fig Angular momentum and magnetic moment of atoms are coupled. Aligning magnetic moments of iron atoms using an external magnetic field causes the iron cylinder to rotate in a direction opposite to the now-aligned angular momenta of the iron atoms (conservation of angular momentum). (40-5)

40-3 Electron Spin Trapped or free, electrons have intrinsic spin angular momentum S (spin). This is a basic characteristic like the electron’s mass or charge. This leads to two additional quantum numbers that are required to fully specify the electronic state: s (magnitude of the spin, which is always ½ for electrons) and m s (the component of spin along the z-axis). Electron States for an Atom Quantum Number Symbol Allowed Value Related to Principal n 1, 2, 3, … Distance from nucleus Orbital l 0, 1, 2, …, ( n-1) Orbital angular momentum Orbital magnetic m l - l, -( l -1 ), …+( l -1), + l Orb. ang. mom. (z-component) Spin s ½ Spin angular momentum Spin magnetic m s ± ½ Spin ang. mom. (z-component) Table 40-1 States with same n form a shell. States with same value for n and l form a subshell. (40-6)

Orbital Angular Momentum and Magnetism 40-4 Angular Momenta and Magnetic Dipole Moments Orbital Angular Momentum: Orbital Magnetic Dipole Moment: (40-7)

Orbital Angular Momentum and Magnetic Dipole Moments Fig Bohr magneton (40-8)

Fig Spin Angular Momentum and Spin Magnetic Dipole Moment S, the magnitude of the spin angular momentum, has a single value for any electron, whether free or trapped: where s (=½) is spin quantum number of the electron. The spin magnetic dipole moment  s is related to S and is given by: (40-9)

Fig Orbital and Spin Angular Momentum Combined (40-10)

40-5 Stern-Gerlach Experiment Fig Magnetic Deflecting Force on Silver Atom Stronger B Weaker B z (40-11)

Stern-Gerlach Experiment, cont’d Experimental surprise Fig Silver atoms Meaning of Experiment: (40-12)

40-6 Magnetic Resonance Fig (40-13)

For fixed radio frequency light, when B ext = hf/2m z - B int → absorption occurs. B int is different for protons in different molecules, so the resonance B ext will be different for protons in different molecules (local environment). Resonances provide a fingerprint of what (and where in the case of Magnetic Resonance imaging) different proton-containing molecules are present in the material studied. The net magnetic field that a proton experiences consists of the vector sum of the externally applied magnetic field B ext and internal fields B int Magnetic Resonance, cont’d Fig magnetic dipole moments of atoms and nuclei near the proton→ B int (40-14)

40-7 Pauli Exclusion Principle No two electrons confined to the same trap (or atom) can have the same set of values for their quantum numbers Multiple Electrons in Rectangular Traps 1. One-dimensional trap. Two quantum numbers n=1, 2, 3… (wavefunction state along L ) and m s = +½ or -½. 2. Rectangular corral. Three quantum numbers n x = 1, 2, 3… (wavefunction state along L x ), n y = 1, 2, 3… (wavefunction state along L y ), and m s = +½ or -½. 3. Rectangular box. Four quantum numbers n x = 1, 2, 3… (wavefunction state along L x ), n y = 1, 2, 3… (wavefunction state along L y ), n z = 1, 2, 3… (wavefunction state along L z ), and m s = +½ or -½. (40-15)

Adding electrons to a rectangular trap: Use energy level diagram. Start at lowest energy level and move up as lower levels become filled. Finding the Total Energy Fig Filled levels Partially filled level Empty (unoccupied) level (40-16)

Four quantum numbers n, l, m l, and m s identify the quantum states of individual electrons in a multi-electron atom. Subshells are labeled by letters: l = spdfgh... Example: n = 3, l = 2→ 3 d subshell 40-9 Building the Periodic Table n l = 0 ( s ) l = 1 ( p ) l = 2 ( d ) m l = __ __ __ ____ __ __ __ __ 2__ __ __ __ 1__ Energy Neon: Z = 10→10 electrons 1 s 2 2 s 2 2p 6 (40-17)

Building the Periodic Table, cont’d n l =0 ( s ) l =1 ( p ) l =2 ( d ) m l = __ __ __ ____ __ __ __ __ 2__ __ __ __ 1__ Energy Sodium: Z = 11→11 electrons 1 s 2 2 s 2 2p 6 3 s 1 n l =0 ( s ) l =1 ( p ) l =2 ( d ) m l = __ __ __ ____ __ __ __ __ 2__ __ __ __ 1__ Energy Chlorine: Z = 17→17 electrons 1 s 2 2 s 2 2p 6 3 s 2 3 p 6 For smaller atoms such as these, one can assume that the energy only depends on n. degenerate (40-18)

Building the Periodic Table, cont’d Iron: Z = 26→26 electrons For atoms with a larger number of electrons, the interactions among the electrons causes shells with the same n but different l to have different energies (degeneracy lifted). 1 s 2 2 s 2 2p 6 3 s 2 3 p 6 3 d 6 4 s 2 Due to interactions, it takes less energy to start filling the 4 s subshell before completing the filling of the 3 d subshell, which can accommodate 10 electrons. (40-19)

X rays are short-wavelength ( m), high-energy (~keV ) photons. Photons in the visible range: ~ m; ~eV. Useful for probing atoms X Rays and Ordering of Elements Fig Fig Independent of target material (40-20)

1.Energetic electron strikes atom in target, knocks out deep-lying (low n value). If deep-lying electron in n = 1 ( K -shell), it leaves a vacancy (hole) behind. 2.Another electron from a higher energy shell in the atom jumps down to the K -shell to fill this hole, emitting an x-ray photon in the process. Characteristic X-Ray Spectrum Fig If the electron that jumps into the hole starts from the n = 2 ( L -shell), the emitted radiation is the K  line. If it jumps from the n = 3 ( M -shell), the emitted radiation is the K  line. The hole left in the n = 2 or n = 3 shells is filled by still higher lying electrons, which relax by emitting lower energy photons (higher lying energy levels are more closely spaced). (40-21)

Moseley (1913) bombarded different elements with x rays. Nuclear charge, not mass, is the critical parameter for ordering elements. Ordering Elements Fig (40-22)

Accounting for the Moseley Plot Ordering Elements, cont’d Energy levels in hydrogen: Approximate effective energy levels in multi-electron atom with Z protons (replace e 2 x e 2 with e 2 x ( e ( Z - 1) ) 2 : K  energy: K  frequency: (40-23)

Lasers have many uses: Small: voice/data transmission over optic fibers, CDs, DVDs, scanners Medium: medical, cutting (from cloth to steel), welding Large: nuclear fusion research, astronomical measurements, military applications 4.Laser light can be sharply focused: Can be focused into very small spot so that all the power is concentrated into a tiny area. Can reach intensities of W/cm 2, compared to 10 3 W/cm 2 for oxyacetylene torch Lasers and Laser Light 1.Laser light is highly monochromatic: Its spread in wavelength is as small as 1 part in Laser light is highly coherent: Single uninterrupted wave train up to 100 km long. Can interfere one part of beam, with another part that is very far away. 3.Laser light is highly directional: Beam spreads very little. Beam from Earth to Moon only spreads a few meters after traveling 4 x 108 m. (40-24)

40-12 How Lasers Work Fig Thermal distribution (Boltzmann): To get more stimulated emission than absorption,  x > N 0 → population inversion → not in thermal equilibrium (40-25)

Fig Helium-Neon Gas Laser Fig Thermal Equilibrium Population Inversion Fig (40-26)