Chem 105 Chpt 7 Lsn 21Chem 105 Chpt 7 Lsn 21

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CHAPTER 7Atomic

StructureRoad MapRoad Map

Test 2 Extra credit CollectionTest 2 Extra credit CollectionRoad MapRoad Map

Test 2 Extra credit CollectionTest 2 Extra credit Collection

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EquationsEquationsspeed of light = wavelength x frequencywavelength x frequency

c = λ X = 3.00 x 108 m/sE = nh = nh(c/= nh(c/) ) n= positive integerPlanck’s constant(h) = 6.626 x 10–34 J sEatom = Eemitted (or absorbed) radiation = nh

Rydberg equationRydberg equation = R = R nn22 > n > n11

R = 1.096776 x 10R = 1.096776 x 1077 m m-1-1 ΔE = EΔE = Efinal final – E– Einitial initial = –2.18 x 10–18 J= –2.18 x 10–18 J Ephoton = Estate A – Estate B = hν

speed of light = wavelength x frequencywavelength x frequency c = λ X = 3.00 x 108 m/s

E = nh = nh(c/= nh(c/) ) n= positive integerPlanck’s constant(h) = 6.626 x 10–34 J sEatom = Eemitted (or absorbed) radiation = nh

Rydberg equationRydberg equation = R = R nn22 > n > n11

R = 1.096776 x 10R = 1.096776 x 1077 m m-1-1 ΔE = EΔE = Efinal final – E– Einitial initial = –2.18 x 10–18 J= –2.18 x 10–18 J Ephoton = Estate A – Estate B = hν

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Old Dead DudesOld Dead Dudes

Planck – blackbody radiation; hot Planck – blackbody radiation; hot glowing object; emit or absorb certain glowing object; emit or absorb certain discrete quanta of energydiscrete quanta of energy

Bohr – one electron model; spectral lines Bohr – one electron model; spectral lines explained; eexplained; e-- motion restricted to fixed motion restricted to fixed orbitsorbits

Einstein – explained photoelectric effect Einstein – explained photoelectric effect - flow of current when monochromatic - flow of current when monochromatic light of sufficient energy hits an objectlight of sufficient energy hits an object

Rydberg – predicted energy levelsRydberg – predicted energy levels

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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

Practice Problem 21-1

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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

Practice Problem 21-1 Answer

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Practice Problem 21-2 (7.12) Answer

7.12 540 nm (107.12 540 nm (10-9-9m/1nm)= 5.4 m/1nm)= 5.4 10 10–7–7 m m

EE = = = = = =

= 3.7 = 3.7 10 10–19–19 J/photon J/photon

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

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Bohr ModelBohr Model

Energy of atoms quantized; Energy of atoms quantized; photon emitted when ephoton emitted when e-- decreases in orbit decreases in orbit

- Spectral line from Spectral line from emissionemissionEmission - higher to lower Emission - higher to lower

energy stateenergy stateAbsorption – lower to higher Absorption – lower to higher

energy state energy state n = quantum numbern = quantum number- Lower n: smaller radiusLower n: smaller radiusof orbit (space eof orbit (space e-- circling in) circling in)- Ground state: n=1Ground state: n=1- Excited state: n>1Excited state: n>1 Quantum staircaseQuantum staircase

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7.20 Which of these electron 7.20 Which of these electron transitions correspond to transitions correspond to absorption of energy and which absorption of energy and which to emission?to emission?

(a)(a) n = 2 to n = 4n = 2 to n = 4

(b)(b) n = 3 to n = 1n = 3 to n = 1

(c)(c) n = 5 to n = 2n = 5 to n = 2

(d)(d) n = 3 to n = 4n = 3 to n = 4

AbsorptionAbsorption

EmissionEmission

EmissionEmissionAbsorbtion

AbsorptionAbsorption

EmissionEmission

EmissionEmissionAbsorbtion

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The Bohr explanation of the three series of spectral lines.

n=1 n=1 ultravioletultravioletn=1 n=1 ultravioletultraviolet

Numerous atoms with Numerous atoms with different excitation states (n)different excitation states (n) and subsequent and subsequent of emission of emission

Numerous atoms with Numerous atoms with different excitation states (n)different excitation states (n) and subsequent and subsequent of emission of emission

n=2 n=2 visiblevisiblen=2 n=2 visiblevisible

n=3 n=3 infraredinfraredn=3 n=3 infraredinfrared

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

Practice Problem 21.3

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

Practice Problem 21.3 Answer

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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-1 B) 1.94 x 10-18 s-1

C) 3.21 x 1015 s-1 D) 3.05 x 10-15 s-1

E) Not enough information given to calculate answer.

Practice Problem 21.4

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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-1 B) 1.94 x 10-18 s-1

C) 3.21 x 1015 s-1 D) 3.05 x 10-15 s-1

E) Not enough information given to calculate answer.

Practice Problem 21.4 Answer

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The Quantum-Mechanical Model of the Atom

Acceptance 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 Schrödinger derived an equation that is the basis for the quantum-mechanical model of the hydrogen atom.

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The Quantum-Mechanical Model of the Atom: The Atomic Orbital and the Probable Location of the Electron

Each solution to the equation is associated with a given wave function, also called an atomic orbital. It’s 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 electron’s path around the nucleus, whereas an orbital is a mathematical function with no direct physical meaning.

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Quantum Numbers and Atomic Orbitals

.An atomic orbital is specified by

three quantum numbers.

n the principal quantum number; distance from nucleus (size); n = 1,2,3…

ll the angular momentum quantum number; shape; l = 0 to n-1

ml the magnetic moment quantum number; orbital orientation; – ml =-l to +l

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n = LEVELSn = LEVELSSmaller n, the lower the energy level the Smaller n, the lower the energy level the

greater the probability of the electron greater the probability of the electron being closer to the nucleusbeing closer to the nucleus

ll = orbital shape = orbital shapel = 0l = 0 ss sphericalsphericall = 1l = 1 pp dumb bell & crash and burn, Fig 7.18dumb bell & crash and burn, Fig 7.18l = 2l = 2 dd cloverleaf, Fig 7.19cloverleaf, Fig 7.19l = 3l = 3 ff too complicated too complicated

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The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital

Sublevel (subshell) : designate the orbital shape. Each sublevel has a letter designation: ℓ = 0 is an s sublevel ℓ = 1 is a p sublevel. ℓ = 2 is a d sublevel. ℓ = 3 is an f sublevel.

Orbital. Each allowed combination of n, ℓ, and mℓ values specifies one of the atom’s 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 Don’t Fail

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The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals

Orbitals with Higher ℓ ValuesOrbitals with ℓ = 3 are f orbitals and

must have a principle quantum number of at least n = 4. There are seven f orbitals (2ℓ + 1 = 7), each with a complex, multi-lobed shape.

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The Quantum-Mechanical Model of the Atom: Energy Levels of the Hydrogen Atom

The energy state of the H atoms depends on the principal quantum number n only.

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CLASSICAL THEORYCLASSICAL THEORY

Matter particulate,

massive

Energy continuous,

wavelike

Since matter is discontinuous and particulate perhaps energy is discontinuous and particulate.

Observation Theory

Planck: Energy is quantized; only certain values allowed

blackbody radiation

Einstein: Light has particulate behavior (photons)photoelectric effect

Bohr: Energy of atoms is quantized; photon emitted when electron changes orbit.

atomic line spectra

Summary of the major observations and theories leading from classical theory to quantum theory.

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Practice Problem 21.5 Determining Quantum Numbers for an Energy Level

SOLUTION:

PLAN:

PROBLEM: What values of the angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals are allowed for n = 3?

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, 2

For l = 0 ml = 0

For l = 1 ml = -1, 0, or +1

For l = 2 ml = -2, -1, 0, +1, or +2

There are 9 ml values and therefore 9 orbitals with n = 3.

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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.

n l sublevel name possible ml values # of orbitals

(a)

(b)

(c)

(d)

3

2

5

4

2

0

1

3

3d

2s

5p

4f

-2, -1, 0, 1, 2

0

-1, 0, 1

-3, -2, -1, 0, 1, 2, 3

5

1

3

7

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Practice Problem 21.7 What is wrongWhat is wrong with this picture, or with this picture, or completecomplete the the

name.name.nn ll mml l namename11 11 00 1p1p

44 33 11 4d4d

33 22 -2-2 ??

?? ?? ?? 2s2s

22 11 00 ??

33 11 -2-2 3p3p

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The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital

The energy states and orbitals of the atom are described with specific terms and associated with one or more quantum numbers.1.Level (n). The atom’s 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.

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The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital

2. Sublevel (ℓ). The atom’s levels contain sublevels, or subshells, which designate the orbital shape. Each sublevel has a letter designation:a. ℓ = 0 is an s sublevelb. ℓ = 1 is a p sublevel.c. ℓ = 2 is a d sublevel.d. ℓ = 3 is an f sublevel.

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The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital

3. Orbital (mℓ ). Each allowed combination of n, ℓ, and mℓ values specifies one of the atom’s orbitals. Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation .

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What value or values of mℓ are allowable for an orbital with ℓ = 2?A) 0B) 2C) -1D) none of the aboveE) all of the above

Practice Problem 21-8

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What value or values of mℓ are allowable for an orbital with ℓ = 2?A) 0B) 2C) -1D) none of the aboveE) all of the above

Practice Problem 21-8 Answer

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The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals

The s OrbitalAn orbital with ℓ = 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.

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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.

Practice Problem 21-9

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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.

Practice Problem 21-9 Answer

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The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals

The p OrbitalAn orbital with ℓ = 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 of this dumbbell-shaped orbital. Keep in mind that one p orbital consists of both lobes and that the electron spends equal time in both.

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The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals

The p OrbitalSince there are three mℓ values, these

describe the three mutually perpendicular orientations in space. Unlike an s orbital, each p orbital does have a specific orientation in space. The ℓ = 1 value has three possible mℓ values: –1, 0, and +1, which refer to three mutually perpendicular p orbitals. They are identical in size, shape, and energy, differing only in orientation.

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The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals

The d OrbitalAn orbital with ℓ = 2 is called a d

orbital. There are five possible mℓ values for the ℓ = 2 value: –2, –1, 0, +1, +2.

Thus, a d orbital can have any one of five orientations, as shown in Figure 7.19.

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The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals

Orbitals with Higher ℓ ValuesOrbitals with ℓ = 3 are f orbitals and

must have a principle quantum number of at least n = 4. There are seven f orbitals (2ℓ + 1 = 7), each with a complex, multilobed shape; Figure 7.20 shows one of them.

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According to the quantum-mechanical model, how many orbitals in a given atom have n = 3?A) 4B) 7C) 9D) 10E) 18

Practice Problem 21-10

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According to the quantum-mechanical model, how many orbitals in a given atom have n = 3?A) 4B) 7C) 9D) 10E) 18

Practice Problem 21-10 Answer

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