# Chem 105 Chpt 7 Lsn 21 1 CHAPTER 7 Atomic Structure Road Map Test 2 Extra credit Collection Road Map...

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CHAPTER 7Atomic StructureRoad MapTest 2 Extra credit Collection

Chapter 01

Equationsspeed of light = wavelength x frequency c = X = 3.00 x 108 m/sE = nh = nh(c/) n= positive integerPlancks constant(h) = 6.626 x 1034 J sEatom = Eemitted (or absorbed) radiation = nh

Rydberg equation = Rn2 > n1R = 1.096776 x 107 m-1 E = Efinal Einitial = 2.18 x 1018 JEphoton = Estate A Estate B = h

Chapter 01

Old Dead DudesPlanck blackbody radiation; hot glowing object; emit or absorb certain discrete quanta of energyBohr one electron model; spectral lines explained; e- motion restricted to fixed orbitsEinstein explained photoelectric effect - flow of current when monochromatic light of sufficient energy hits an objectRydberg predicted energy levels

Chapter 01

Practice Problem 21-1 The frequency of electromagnetic radiation of wavelength 5.6 mm isA) 5.4 x 107 HzB) 1.9 x 10-11 HzC) 5.4 x 1010 HzD) 1.1 x 108 HzE) none of the above

Chapter 01

Practice Problem 21-1 Answer The frequency of electromagnetic radiation of wavelength 5.6 mm isA) 5.4 x 107 HzB) 1.9 x 10-11 HzC) 5.4 x 1010 HzD) 1.1 x 108 HzE) none of the above

Chapter 01

Practice Problem 21-2 (7.12) Answer7.12 540 nm (10-9m/1nm)= 5.4 107 m E = = =

= 3.7 1019 J/photonThis radiation does not have enough energy(6.7 x 10-19 J/atom) to activate the switch. This is also true for radiation with wavelengths greater than 540 nm.

Chapter 01

Bohr ModelEnergy of atoms quantized; photon emitted when e- decreases in orbit Spectral line from emissionEmission - higher to lower energy stateAbsorption lower to higher energy state n = quantum numberLower n: smaller radiusof orbit (space e- circling in)Ground state: n=1Excited state: n>1Quantum staircase

Chapter 01

7.20 Which of these electron transitions correspond to absorption of energy and which to emission?n = 2 to n = 4n = 3 to n = 1n = 5 to n = 2n = 3 to n = 4AbsorptionEmissionEmissionAbsorbtion

Chapter 01

The Bohr explanation of the three series of spectral lines.n=1 ultravioletNumerous atoms with different excitation states (n) and subsequent of emissionn=2 visiblen=3 infrared

Chapter 01

Practice Problem 21.3 How much energy is absorbed when an electron is excited from the first level to the fourth?

Chapter 01

Practice Problem 21.3 Answer How much energy is absorbed when an electron is excited from the first level to the fourth?2.04 x 10-18 J

Chapter 01

Practice Problem 21.4 Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 3 to n = 1 energy level, based on the Bohr theory.A) 2.92 x 1015 s-1B) 1.94 x 10-18 s-1C) 3.21 x 1015 s-1D) 3.05 x 10-15 s-1E) Not enough information given to calculate answer.

Chapter 01

Practice Problem 21.4 Answer Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 3 to n = 1 energy level, based on the Bohr theory.A) 2.92 x 1015 s-1B) 1.94 x 10-18 s-1C) 3.21 x 1015 s-1D) 3.05 x 10-15 s-1E) Not enough information given to calculate answer.

Chapter 01

The Quantum-Mechanical Model of the AtomAcceptance of the dual nature of matter and energy and of the uncertainty principle culminated in the field of quantum mechanics, which examines the wave motion of objects on the atomic scale. In 1926, Erwin Schrdinger derived an equation that is the basis for the quantum-mechanical model of the hydrogen atom.

Chapter 01

The Quantum-Mechanical Model of the Atom: The Atomic Orbital and the Probable Location of the ElectronEach solution to the equation is associated with a given wave function, also called an atomic orbital. Its important to keep in mind that an orbital in the quantum-mechanical model bears no resemblance to an orbit in the Bohr model: an orbit was an electrons path around the nucleus, whereas an orbital is a mathematical function with no direct physical meaning.

Chapter 01

Quantum Numbers and Atomic OrbitalsAn atomic orbital is specified by three quantum numbers.n the principal quantum number; distance from nucleus (size); n = 1,2,3l the angular momentum quantum number; shape; l = 0 to n-1ml the magnetic moment quantum number; orbital orientation; ml =-l to +l.

Chapter 01

n = LEVELSSmaller n, the lower the energy level the greater the probability of the electron being closer to the nucleusl = orbital shapel = 0ssphericall = 1pdumb bell & crash and burn, Fig 7.18l = 2dcloverleaf, Fig 7.19l = 3ftoo complicated

Chapter 01

The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic OrbitalSublevel (subshell) : designate the orbital shape. Each sublevel has a letter designation: = 0 is an s sublevel = 1 is a p sublevel. = 2 is a d sublevel. = 3 is an f sublevel.Orbital. Each allowed combination of n, , and m values specifies one of the atoms orbitals. Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation . The total number of orbitals for a given n value is n2.Smart People Dont Fail

Chapter 01

The Quantum-Mechanical Model of the Atom: Shapes of Atomic OrbitalsOrbitals with Higher ValuesOrbitals with = 3 are f orbitals and must have a principle quantum number of at least n = 4. There are seven f orbitals (2 + 1 = 7), each with a complex, multi-lobed shape.

Chapter 01

The Quantum-Mechanical Model of the Atom: Energy Levels of the Hydrogen AtomThe energy state of the H atoms depends on the principal quantum number n only.

Chapter 01

CLASSICAL THEORYMatter particulate, massiveEnergy continuous, wavelikeObservationTheorySummary of the major observations and theories leading from classical theory to quantum theory.

Chapter 01

Practice Problem 21.5 Determining Quantum Numbers for an Energy LevelSOLUTION:PLAN:Follow the rules for allowable quantum numbers found in the text.l values can be integers from 0 to n-1; ml can be integers from -l through 0 to + l.For n = 3, l = 0, 1, 2For l = 0 ml = 0For l = 1 ml = -1, 0, or +1For l = 2 ml = -2, -1, 0, +1, or +2There are 9 ml values and therefore 9 orbitals with n = 3.

Chapter 01

Practice Problem 21.6 Determining Sublevel Names and Orbital Quantum Numbers SOLUTION:PLAN:PROBLEM:Give the name, magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers:(a) n = 3, l = 2(b) n = 2, l = 0(c) n = 5, l = 1(d) n = 4, l = 3Combine the n value and l designation to name the sublevel. Knowing l, we can find ml and the number of orbitals.nlsublevel namepossible ml values# of orbitals(a)(b)(c)(d)325420133d2s5p4f-2, -1, 0, 1, 20-1, 0, 1-3, -2, -1, 0, 1, 2, 35137

Chapter 01

Practice Problem 21.7 What is wrong with this picture, or complete the name.nlml name1101p

4314d

32-2?

???2s

210?

31-23p

Chapter 01

The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic OrbitalThe energy states and orbitals of the atom are described with specific terms and associated with one or more quantum numbers.Level (n). The atoms energy levels, or shells, are given by the n value: the smaller the n value, the lower the energy level and the greater the probability of the electron being closer to the nucleus.

Chapter 01

The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic OrbitalSublevel (). The atoms levels contain sublevels, or subshells, which designate the orbital shape. Each sublevel has a letter designation: = 0 is an s sublevel = 1 is a p sublevel. = 2 is a d sublevel. = 3 is an f sublevel.

Chapter 01

The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic OrbitalOrbital (m ). Each allowed combination of n, , and m values specifies one of the atoms orbitals. Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation .

Chapter 01

Practice Problem 21-8 What value or values of m are allowable for an orbital with = 2?A) 0B) 2C) -1D) none of the aboveE) all of the above

Chapter 01

Practice Problem 21-8 Answer What value or values of m are allowable for an orbital with = 2?A) 0B) 2C) -1D) none of the aboveE) all of the above

Chapter 01

The Quantum-Mechanical Model of the Atom: Shapes of Atomic OrbitalsThe s OrbitalAn orbital with = 0 has a spherical shape with the nucleus at its center and is called an s orbital.The 2s orbital (Figure 7.17B) has two regions of higher electron density. Between the two regions is a spherical node, a shell-like region where the probability drops to zero.

Chapter 01

Practice Problem 21-9 The nodes for a 3s atomic orbital areA) two points near the nucleus and another point at an infinite distance from the nucleus.B) three spherical solids.C) one plane and two spheres.D) two concentric circles.E) two concentric spheres.

Chapter 01

Practice Problem 21-9 Answer The nodes for a 3s atomic orbital areA) two points near the nucleus and another point at an infinite distance from the nucleus.B) three spherical solids.C) one plane and two spheres.D) two concentric circles.E) two concentric spheres.

Chapter 01

The Quantum-Mechanical Model of the Atom: Shapes of Atomic OrbitalsThe p OrbitalAn orbital with = 1 has two regions (lobes) of high probability, one on either side of the nucleus, and is called a p orbital. In Figure 7.18, the nucleus lies at the nodal plane