Chapter 7Quantum

Theory of the Atom

Waves

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•A wave is a continuously repeating change or oscillation in matter or in a physical field.

التذبذب • او باستمرار المتكرر التغير هو الموجة. الفيزيائي المجال في او المادة في

•Light is an electromagnetic wave, consisting of oscillations in electric and magnetic fields traveling through space.

من • تتكون كهرومغناطيسية موجات هو الضوءوالمغناطيسية االلكترونية المجاالت في تذبذب

. الفراغ في تنتقل والتي

Waves•A wave can be characterized by its wavelength and frequency.

وتعرف • وذبذباتها باطزالها الموجات وصف يمكنموجتين قمتي بين المسافة وهي المبدا ب

متجاورتين؟•Wavelength, symbolized by the Greek letter lambda, , is the distance between any two identical points on adjacent waves.

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Waves•Frequency, symbolized by the Greek letter nu, , is the number of wavelengths that pass a fixed point in one unit of time (usually a second). The unit is 1/S or s-1, which is also called the Hertz (Hz).

عدد • وهو نيو اليوناني بالحرف له يرمز الترددزمن وحدة في ثابتة نقطة في تمر التي الوجات

. الهيرتز وتسمى ثانية تكون ما غالبا واحدة

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Waves•Wavelength and frequency are related by the wave speed, which for light is c, the speed of light, 3.00 x 108 m/s. الموجة بسرهة مباشرة عالقة لها

• c =

•The relationship between wavelength and frequency due to the constant velocity of light is illustrated on the next slide.

السرعة • من تنتج والتردد الموجة طول بين العالقة. الالحقة الشريحة في موضح للضوء الثابتة

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Waves

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When the wavelength is reduced by a factor of two, the frequency increases by a factor of two.سرعة تقل عندما

مساوي 2بعاملالتردد يزداد

2بمقدار

Example 1

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•What is the wavelength of blue light with a frequency of 6.4 × 1014/s?

= 6.4 × 1014/sc = 3.00 × 108 m/s

c = so = c/

= 4.7 × 10-7 ms

110x6.4

s

m10x3.00

λ14

8

c

Example 2

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•What is the frequency of light having a wavelength of 681 nm?

= 681 nm = 6.81 × 10-7 mc = 3.00 × 108 m/s

c = so = c/

= 4.41 × 1014 /s

m10x6.81s

m10x3.00

7

8

c

Waves•The range of frequencies and wavelengths of electromagnetic radiation is called the electromagnetic spectrum.

تسمى • الكهرومغناطيسي لالشعاع الموجات واطوال الترددات معدلالطيف

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Example 3

•When frequency is doubled, wavelength is halved.

•The light would be in the blue-violet region.

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Waves•One property of waves is that they can be diffracted—that is, they spread out when they encounter an obstacle about the size of the wavelength.

عندما • وتنتشر تتشتت انها هي الموجات خواص احدىهذه اثبت وقد الموجة طول بحجم بعائق تصطدم

اوائا في النظرية هذه تعززت وقد يونغ، توماس النظرية. عشر التاسع القرن

•In 1801, Thomas Young, a British physicist, showed that light could be diffracted. By the early 1900s, the wave theory of light was well established.

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Photoelectric Effect•The wave theory could not explain the photoelectric effect, however.

وهي • الفوتوضوئية تأثير تفسر لم الموجة نظريةاخرى مادة اي او معدن سطح من الكترونات انبعاث

. عليها الضوء يشع عندما

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Photoelectric Effect•The photoelectric effect is the ejection of an electron from the surface of a metal or other material when light shines on it.

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“Particles” of Light

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•Einstein proposed that light consists of quanta or particles of electromagnetic energy, called photons. The energy of each photon is proportional to its frequency:

الطاقة • من ككم او كجسيمات الضوء نظريةتلك وسمى اينشتاين افترضها الكهرومغناطيسية

الناتجة الطاقة بان افترض وقد بالفوتونات الجسيمات: التالية المعادلة حسب تردده و تتناسب فوتون كل عن

•E = h•h = 6.626 × 10-34 J s (Planck’s constant)

Photoelectric Effect

•Einstein used this understanding of light to explain the photoelectric effect in 1905.

تأثير • لتوضيح الضوء عن المفهوم هذا اينشتاين استخدمالكهروضوئية

•Each electron is struck by a single photon. Only when that photon has enough energy will the electron be ejected from the atom; that photon is said to be absorbed.

• . يمتلك عندما فقط واحد بفوتون يضرب الكترون كلالذرة من االنبعاث من تمكنه كافية طاقة الفوتون ذلك

. امتص قد الفوتون ذلك ان القول 15 | 7ويمكن

Duality of Light الضوء ازدواجية

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•Light, therefore, has properties of both waves and matter. Neither understanding is sufficient alone. This is called the particle–wave duality of light.

من • خواصكل بين يجمع الضوء فان لذلك . الضوء فهم يمكن ال معا والموجات المادة

. فقط واحدة بخاصية

Example 4

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•The blue–green line of the hydrogen atom spectrum has a wavelength of 486 nm. What is the energy of a photon of this light? = 4.86 nm = 4.86 × 10-7 mc = 3.00 × 108 m/sh = 6.63 × 10-34 J s

E = h andc = so E = hc/

= 4.09 × 10-19 J

m10x4.86

s

m10x3.00Js6.63x10

λ 7

834

hc

E

The Quantum Atom الذري الكم

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•In the early 1900s, the atom was understood to consist of a positive nucleus around which electrons move (Rutherford’s model).

وااللكترونات • الذرة عن رذرفورد نموذج اكتشاف تم ان بعدحسب وهي نظرية معضلة النظرية تلك تركت والبروتونات

الدوران في يستمر المشحون الجسيم فان الزمن فيزياء . كهرومغناطيسي اشعاع شكل على طاقة دورانه في ويفقد

. الذرة استقرار حالة في ليست النظرية هذه ولكن•This explanation left a theoretical dilemma: According to the physics of the time, an electrically charged particle circling a center would continually lose energy as electromagnetic radiation. But this is not the case—atoms are stable.

The Quantum Atom

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•In addition, this understanding could not explain the observation of line spectra of atoms.

خطي • طيف وجود مالحظة سبب توضيح يستطع لم ايضاللذرة

•A continuous spectrum contains all wavelengths of light. للضوء الموجات اطوال كل على يحتوي المستمر الطيف

موجات • اطوال او محددة الوان فقط يري الخطي والطيف . لكل معين خطي طيف عنها ينتج العملية هذه للضوء محدد

نوعها حسب ذرة•A line spectrum shows only certain colors or specific wavelengths of light. When atoms are heated, they emit light. This process produces a line spectrum that is specific to that atom. The emission spectra of six elements are shown on the next slide.

Elemental Line Spectra

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Quantum Model of Hydrogen Atom

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•In 1913, Neils Bohr, a Danish scientist, set down postulates to account for•1. The stability of the hydrogen atom•2. The line spectrum of the atom

•: بوهر فرضيات•. الهيدرجين ذرة استقرار•. للذرة الخطي الطيف

Quantum Model of Hydrogen Atom•Energy-Level Postulate الطاقة مستويات فرضية•An electron can have only certain energy values, called energy levels. Energy levels are quantized. كل

الطاقة من محدد مستوى له الكترون

•For an electron in a hydrogen atom, the energy is given by the following equation: الهيدروجين معادلة

• RH = 2.179 x 10-18 J رويدبيرغ ثابت

• n = principal quantum number7 | 22

2H

n

RE

Quantum Model of Hydrogen Atom•Transitions Between Energy Levels•An electron can change energy levels by absorbing energy to move to a higher energy level or by emitting energy to move to a lower energy level.

طاقته • مستويات االلكترون يغير ان يمكنطاقة مستويات الى للتحرك الطاقة بامصاصاقل مستويات الى نزوله عند طاقة يشع او اعلى

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Quantum Model of Hydrogen Atom

•For a hydrogen electron the energy change is given by

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2i

2f

H

11Δ

nnRE

ifΔ EEE

RH = 2.179 × 10-18 J, Rydberg constant

Quantum Model of Hydrogen Atom•The energy of the emitted or absorbed photon is related to E: او االمتصاص تحدد الطاقة فرقية االشعاع

•We can now combine these two equations:

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2i

2f

H

11

nnRh

constant sPlanck'

Δ electron

h

hEEphoton

Quantum Model of Hydrogen Atom•Light is absorbed by an atom when the electron transition is from lower n to higher n (nf > ni). In this case, E will be positive.

المستوى • من االلكترون ينتقل عندما الذرة من الضوء يمتص . من الضوء ويشع موجب الطاقة فرق وتكون االعلى االقل

وتكون االقل الى االعلى المستوى من االنتقال عند الذرة. سالب الطاقة فرق

•Light is emitted from an atom when the electron transition is from higher n to lower n (nf < ni). In this case, E will be negative.

•An electron is ejected when nf = ∞. 7 | 26

Quantum Model of Hydrogen Atom

•Energy-level diagram for the hydrogen atom.

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Quantum Model of Hydrogen Atom

•Electron transitions for an electron in the hydrogen atom.

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Example 5

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•What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from n = 6 to n = 3?

ni = 6nf = 3RH = 2.179 × 10-18 J

6.626 x10 34J s 2.998 x108 m

s

-1.816 x10 19J

= -1.816 x 10-19 J

1.094 × 10-6 m

soλ

Δhc

E E

hc

Δλ

?E 2.179 x10 18J 1

32 1

62

2i

2f

H

11Δ

nnRE

Example 6

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Line Spectra

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•The red line corresponds to the smaller energy difference in going from n = 3 to n = 2. The blue line corresponds to the larger energy difference in going from n = 2 to n = 1.

n = 1

n = 2

n = 3

A minimum of three energy levels are required.

Quantum Evidence

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Planck

Vibrating atoms have only certain energies:

E = h or 2h or 3hEinstein

Energy is quantized in particles called photons:

E = hBohr

Electrons in atoms can have only certain values of energy. For hydrogen:

numberquantumprincipalJ,10x2.179 18H

2H

nR

n

RE

Matter Waves

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Light has properties of both waves and particles (matter).

االمواج • وهي للضوء مزدوجة خواص هناك كان اذاوالمادة

What about matter?المادة عالقة هي ما

Matter Waves

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•In 1923, Louis de Broglie, a French physicist, reasoned that particles (matter) might also have wave properties.

خواص • ايضا الجسيمات لدى بان بروغلي استنتجوكتلة الموجة طول بين ما عالقة اوجد وقد الموجة،

: يلي كما وسرعتها الجسيمات

•The wavelength of a particle of mass, m (kg), and velocity, v (m/s), is given by the de Broglie relation:

sJ10x6.626

λ

34

h

mv

h

Example 7

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•Compare the wavelengths of (a) an electron traveling at a speed that is one-hundredth the speed of light and (b) a baseball of mass 0.145 kg having a speed of 26.8 m/s (60 mph).

mv

hλ

Electronme = 9.11 × 10-31 kgv = 3.00 × 106 m/s

Baseballm = 0.145 kgv = 26.8 m/s

Example 7 (Cont)

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Electronme = 9.11 × 10-31 kg v = 3.00 × 106 m/s

Baseballm = 0.145 kg v = 26.8 m/s

s

m10x3.00kg10x9.11

sJ10x6.63λ

631

34

2.43 × 10-10 m

s

m26.8kg0.145

sJ10x6.63λ

34

1.71 × 10-34 m

Example 8

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protonelectron λλ

electronelectronelectronλ

vm

h

protonprotonprotonλ

vm

h

electronelectronvm

h

protonprotonvm

h

Example 8 (Cont)

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electron

proton

proton

electron

m

m

v

v

electronelectronvm protonprotonvm

kg 10 x 9.10938

kg 10 x 1.6726231-

-27

proton

electron v

v

310 x 5 1.8361proton

electron

v

v

proton. the of that times 1800 than

more is electron the ofvelocity The

Principal Quantum Number

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•Principal Quantum Number, nوهو • المدار، او الطاقة مستوى الى يعود الكمي الرقم

بشكل الذرة في االلكترون طاقة عليه تعتمد ماكذلك. اقل طاقة اصغر مدار nاساسي

•This quantum number, which refers to energy level or shell, is the one on which the energy of an electron in an atom primarily depends. The smaller the value of n, the lower the energy and the smaller the orbital.

•The principal quantum number can have any positive value: 1, موجبة . . . ,3 ,2 الكمي الرقم قيمة•Orbitals with the same value for n are said to be in the same shell. المستوى نفس لهم القيمة بنفس المدارات

Energy Levels (Shells)

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•Shells are sometimes designated by uppercase letters: رقمي وترتيب كبيرة بحروف المدارات تعرف

Lettern

K1

L2

M3

N4

. . .

What are Quantum Numbers?

Quantum number are a set of four values that define theenergy state of an electron in an atom.

Quantum number values are designated as n, l, m and s(s is often written as ms )

n is called the principal quantum number and rangesfrom 1, 2, 3, etc. (also refers to the energy level or shell

l represents the orbital type and depends on n. It rangesfrom 0 through n – 1. It often called the azimuthal

quantum number

m depends on l. It ranges from – l thru 0 to + l. It definesthe orbital orientation in space and is call the magnetic

quantum number.

S is the spin number and is either + ½ or – ½

Orbital Shape المدار شكل

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•Angular Momentum Quantum Number, lالنشط • الزاوي الكمي الرقم

•Sometimes called the azimuthal quantum number, this quantum number distinguishes orbitals within a given n (shell) having different shapes. االشكال من العديد له

•It can have values from 0, 1, 2, 3, . . . to a maximum of (n واحد .(1 – ناقص مدار رقم اخر وحتى صفر من قيمته

•For a given n, there will be n different values of l, or n types of subshells.

•Orbitals with the same values for n and l are said to be in the same shell and subshell.

الزاوي • الكمي والرقم القيمة نفس تحمل التي المداراتالقشرة بنفس تكون

Orbital Shape

•Subshells are sometimes designated by lowercase letters:

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l ≤Letter

0s

1p

2d

3f

. . .

Not every subshell type exists in every shell. The minimum value of n for each type of subshell is shown above.

n = 1 2 3 4

Orbital types defined by the azimuthal quantum number

l = 0 s type orbital

l = 1 p type orbital

l = 2 d type orbital

One orientation

Three orientations

Five orientations

l = 3f type orbital Seven orientations (not shown)

Orbital Orientation

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•Magnetic Quantum Number, ml المغناطيسي الكمي الرقم

•This quantum number distinguishes orbitals of a given n and l—that is, of a given energy and shape but having different orientations.

ولكن • محدد وشكل طاقة عند الزاوي والمدار المدار يميزمختلفة باتجاهات

•The magnetic quantum number depends on the value of l and can have any integer value from –l to 0 to +l. Each different value represents a different orbital. For a given subshell, there will be (2l + 1) values and therefore (2l + 1) orbitals.

Quantum Number Summary

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•Let’s summarize:•When n = 1, l has only one value, 0.

•When l = 0, ml has only one value, 0.

•So the first shell (n = 1) has one subshell, an s-subshell, 1s. That subshell, in turn, has one orbital.

Quantum Number Summary

•When n = 2, l has two values, 0 and 1.

•When l = 0, ml has only one value, 0. So there is a 2s subshell with one orbital.

•When l = 1, ml has only three values, -1, 0, 1. So there is a 2p subshell with three orbitals.

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Quantum Number Summary

•When n = 3, l has three values, 0, 1, and 2.

•When l = 0, ml has only one value, 0. So there is a 3s subshell with one orbital.

•When l = 1, ml has only three values, -1, 0, 1. So there is a 3p subshell with three orbitals.

•When l = 2, ml has only five values, -2, -1, 0, 1, 2. So there is a 3d subshell with five orbitals.

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Quantum Number Summary

•We could continue with n =4 and 5. Each would gain an additional subshell (f and g, respectively).

•In an f subshell, there are seven orbitals; in a g subshell, there are nine orbitals.

•Table 7.1 gives the complete list of permitted values for n, l, and ml up to the fourth shell. It is on the next slide.

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Summary

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Shells and Subshells in Hydrogen

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•The figure shows relative energies for the hydrogen atom shells and subshells; each orbital is indicated by a dashed-line.

•Spin Quantum Number, ms

•This quantum number refers to the two possible orientations of the spin axis of an electron.

•It may have a value of either +1/2 or -1/2.

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•Which of the following are permissible sets of quantum numbers?• n = 4, l = 4, ml = 0, ms = ½

• n = 3, l = 2, ml = 1, ms = -½

• n = 2, l = 0, ml = 0, ms = ³/²

• n = 5, l = 3, ml = -3, ms = ½

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(a) Not permitted. When n = 4, the maximum value of l is 3.

(b) Permitted.(c) Not permitted; ms can only be +½ or –½. (b) Permitted.

Orbital Shapes

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•Atomic Orbital Shapes•An s orbital is spherical.

•A p orbital has two lobes along a straight line through the nucleus, with one lobe on either side.

•A d orbital has a more complicated shape.

Orbital Sizes

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•The cross-sectional view of a 1s orbital and a 2s orbital highlights the difference in the two orbitals’ sizes.

Orbital Sizes

•The cutaway diagrams of the 1s and 2s orbitals give a better sense of them in three dimensions.

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p-Orbital Shape

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•The next slide illustrates p orbitals.

•Figure A shows the general shape of a p orbital.

•Figure B shows the orientations of each of the three p orbitals.

p-Orbitals

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d-Orbitals

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•The complexity of the d orbitals can be seen below