ch.2 - the quantum-mechanical model of the...

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CHEMISTRY - TRO-STRUCTURE & PROPERTIES 2E

CH.2 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM

CONCEPT: THE NATURE OF LIGHT

Visible light represents a small portion of the continuum of radiant energy known as _______________________________.

The visible light spectrum ranges from ______________ to ______________ .

Its wave properties of electromagnetic radiation are described by two independent variables:

_________ (ν, Greek mu) is the number of waves you have per second and is expressed in units of ______ or ________.

__________ (λ, Greek lambda) is the distance from one crest of a wave to the other and is expressed in units of _______.

Relationship between frequency & wavelength



PRACTICE: THE NATURE OF LIGHT

A. Based on the images of different electromagnetic waves, answer each of the following questions.

I. II.

III.

a) Which electromagnetic wave has the longest wavelength?

b) Which electromagnetic wave has the greatest energy?

c) Which electromagnetic wave has the lowest frequency?

d) Which electromagnetic wave has the largest amplitude?



CONCEPT: INTERCONVERSION OF LIGHT UNITS

The speed of a wave, is the product of ν and λ. In a vacuum, all forms of electromagnetic radiation travel at 3.00 x 108 ,

which is a physical constant called the _________________________________ (c).

c = ν · λ

EXAMPLE: Even the music we listen to deals with how energy travels to get to our car radio. If Power 96 broadcasts its

music at 96.5 MHz (megahertz, or 106 Hertz) find the wavelength in μm and Ao

of the radio waves.

PRACTICE: Calculate the frequency of the red light emitted by a neon sign with a wavelength of 663.8 nm.



CONCEPT: ENERGY AND MATTER

Light travels at different speeds as it passes through different media in a phenomenon known as _____________________.

Light passing through the opening of a slit creates a semicircular wave in a phenomenon known as ___________________.

If the light wave passes through two adjacent slits then the semicircular waves can interact with one another .

• ___________________ inteference ______ amplitude. � ___________________ inteference ______ amplitude.



CONCEPT: THE PARTICLE NATURE OF LIGHT

The physicists Max Planck and Albert Einstein theorized that light was made of small “packets” of electromagnetic energy.

• Each “packet” of energy referred to as a ________________ .

• The energy could be expressed with the following equation: ∆E = hv

_____________________ constant is represented by the variable of h and is equal to 6.626 x 10-34 J · s.

EXAMPLE: After a night out last Halloween dressed up as Charlie Sheen I came home and microwaved some day old

pizza. If the microwave I used emitted a wavelength of 3.25 cm, answer the following questions.

a) What is the energy of one photon of this microwave radiation?

b) What is the energy of one mole of this photon?

PRACTICE: Rank the following in terms of decreasing energy: Gamma energy, visible light 1 (∆E = 4.39 x 10-19 J),

microwave and visible light 2 (λ = 595 nm).



CONCEPT: THE PHOTOELECTRIC EFFECT

Albert Einstein theorized that light was quantized into small “packets” or “bundles” of energy.

• A single particle of this quantized “packet” of electromagnetic energy was later named a ________________.

According to the Photoelectric effect, when photons with enough energy hit the surface of a metal electrons are emitted.

– Energy is directly proportional to ____________________ rather than its ____________________.

– The Photoelectric Effect only happens with photons over a certain _______________ frequency.

EXAMPLE: Illustrate what happens when a photon of sufficient energy strike the surface of a metal.

Real-life Application:



CONCEPT: THE WAVE NATURE OF LIGHT

Up to this point we have discussed light as “packets” or particles of energy that travel through a given space, now we will

look at light as it travels as a uniform wave through a given space.

According to the ______________________ equation matter behaves as though it moves in a wave. To calculate the

wavelength of matter we simply use the following equation:

EXAMPLE: Find the wavelength (in nm) of a proton with a speed of 7.33 x 109 . (Mass of an proton = 1.67 x 10-27 kg)

PRACTICE: What is the speed of an electron that has a wavelength of 895 μm? (Mass of a electron = 9.11 x 10-31 kg)

λ =hmν

λ =

h =

m =

ν =



CONCEPT: HEISENBERG’S UNCERTAINTY PRINCIPLE

The nature of an electron is both unique and difficult to understand because it can behave as both a(n) _____________ and a(n) _____________.

• The _____________ of an electron is related to its wave nature, while its _____________ is related to its particle nature.

• Weiner Heisenberg introduced the term of _________________________ to describe how an electron could be observed as either a particle or wave, but not both.

• By extension we also couldn’t know both the _____________ or _____________ of an electron.

To illustrated this dual nature of an electron Heisenberg created his Uncertainty or Indeterminacy Principle and its associated formula:

Δx ⋅ Δp ≥ h4π

h =

Δx =

Δp =

EXAMPLE: An electron has an uncertainty in its position of 630 pm. What is the uncertainty in its velocity?



CONCEPT: THE ATOMIC MODEL

An atom is composed of __________ subatomic particles.

In the center of an atom there is the ________________ .

• It contains the subatomic particles: _____________ and _____________.

• Spinning around it we find the third subatomic particle: the _____________.

• PROTONS are _________________ charged subatomic particles.

• ELECTRONS are _________________ charged subatomic particles.

• NEUTRONS are _________________ charged subatomic particles.

________ Model helped to explain what happened when an electron absorbed or released energy within a hydrogen atom.

After the hydrogen electron absorbed sufficient energy and becomes __________ it would jump to a higher energy level.

• Eventually it would return to its _____________________ and release the energy it absorbed as heat or light.

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PRACTICE: THE ATOMIC MODEL

EXAMPLE: Calculate the energy of the 4th electron found in the n = 2 state of the boron atom in kilojoules per mole.

PRACTICE 1: Which of the following transitions (in a hydrogen atom) represents emission of the longest wavelength?

a) n = 4 to n = 2 b) n = 3 to n= 4 c) n = 1 to n = 2 d) n = 6 to n = 5 e) n = 2 to n = 5

PRACTICE 2: Which of the following transitions represents absorption of a photon with the largest energy?

a) n = 3 to n = 1 b) n = 2 to n = 4 c) n = 1 to n = 2 d) n = 6 to n = 3 e) n = 1 to n = 4



CONCEPT: ATOMIC EMISSION

When an electron absorbs enough energy it goes from a ___________ numbered shell to a ___________ numbered shell.

• The electron eventually releases or emits the energy it took in and goes from a ___________ numbered shell to a

___________ numbered shell.

If the electron goes from a higher numbered shell to the 1st shell it is referred to as a _____________________ Series.

1

∞

If the electron goes from a higher numbered shell to the 2nd shell it is referred to as a _____________________ Series.

2

∞

If the electron goes from a higher numbered shell to the 3rd shell it is referred to as a _____________________ Series.

3

∞



PRACTICE: ATOMIC EMISSION

EXAMPLE: What is the wavelength of a photon (in nanometers) emitted during a transition from n = 4 to n = 2 state in the

hydrogen atom?

PRACTICE: Classify each of the following transitions as either a Lyman, Balmer or Paschen series.

a) n = 3 to n = 1 b) n = 6 to n = 1 c) n = 3 to n = 2 d) n = 6 to n = 3 e) n = 4 to n = 2



CONCEPT: QUANTUM MECHANICAL PICTURE OF THE ATOM

The main atomic sub-levels are the s, p, d and f. Each atomic sub-level has a set number of atomic or electron orbitals.

Each electron orbital can hold up ________ electrons.

The s sub-level contains one electron orbital _______

The p sub-level contains three electron orbitals

_______ _______ _______

The d sub-level contains five electron orbitals

_______ _______ _______ _______ _______

The f sub-level contains seven electron orbitals

_______ _______ _______ _______ _______ _______ _______



CONCEPT: QUANTUM NUMBERS OF AN ATOMIC MODEL

An atomic orbital is characterized by three quantum numbers.

The __________________ quantum number deals with the atomic orbital’s size and energy. It tells us the relative distance

of the electron from the nucleus. It uses the variable ___________ and provides the shell number of the electron.

EXAMPLE: Calculate the principal quantum number of each atomic sublevel.

a. 7p b. 5s c. 3d d. 4f

The electron capacity of each shell can be determined by using the formula: ____________________ .

Electron Shell (n) Maximum Number of Electrons

1

2

3

4

The _______________________ quantum number deals with the shape of the atomic orbital. Each atomic orbital has a

specific shape.

• It uses the variable ___________ and formula _______________________.

Each atomic sub-level has an L value associated with it.

Sublevel s p d f g

L value 0 1 2 3 4

The ________________________________ quantum number deals with the orientation of the orbital in the space around

the nucleus. It is a range of the previous quantum number: -l to +l. It uses the variable ___________.

Sublevel s p d f

L value 0 1 2 3

ML value

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PRACTICE: QUANTUM NUMBERS OF AN ATOMIC MODEL

EXAMPLE 1: What l or ml values are allowed if n = 2? How many orbitals exist for n = 2?

EXAMPLE 2: How many electrons can have the following quantum sets?

a) n = 4

b) n = 3, l = 1

c) n = 4, mL = -2

d) n = 5, l = 2, mL = -2

PRACTICE 1: Provide the n, l and ml value for each of the given orbitals.

a. 6p n = l = mL =

b. 4d n = l = mL =

c. 5f n = l = mL =

PRACTICE 2: State all the l and mLvalues possible if the principle quantum number is equal to 3.

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CONCEPT: THE FOURTH QUANTUM NUMBER

An electron in an atom is described completely by a set of four quantum numbers.

• The first three describe its ____________________ and the fourth describes its ________________.

• The ____________ quantum number (mS) helps to discuss the rotational spin of the electron and has values of

either _________ and _________.

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According to the _________________________________: no two electrons in the same atom can have the same four quantum numbers.

EXAMPLE: State the electron configuration of boron and list the four quantum numbers of the 1st and the 5th electron.



CONCEPT: ATOMIC ORBITAL SHAPE The _______________________ quantum number deals with the shape of the atomic orbital. Each atomic orbital has a

specific shape.

• It uses the variable ___________ and formula _______________________.

Each atomic sub-level has an L value associated with it.

Sublevel s p d f g

L value 0 1 2 3 4

EXAMPLE: Based on the following atomic orbital shape, which of the following set of quantum numbers is correct:

a) n = 8, l = 1, ml = 12

b) n = 8, l = 2, ml = -2

c) n = 8, l = 0, ml = 1

d) n = 8, l = 0, ml = 0

PRACTICE: Based on the following atomic orbital shape, which of the following set of quantum numbers is correct:

a) n = 2, l = 1, ml = +1 , ms = - 1

b) n = 4, l = 1, ml = - 2 , ms = +12

c) n = 3, l = 1, ml = - 1, ms = 0

d) n = 2, l = 1, ml = + 1 , ms = – 12



8. Which of the following transitions (in a hydrogen atom) represent emission of the smallest or shortest wavelength?

a. n = 4 to n = 2

b. n = 3 to n= 4

c. n = 1 to n = 2

d. n = 7 to n = 5

e. n = 2 to n = 5



9. Which of the following transitions represent absorption of a photon with the highest frequency? a. n = 3 to n = 1

b. n = 2 to n = 4

c. n = 1 to n =2

d. n = 6 to n = 3

e. n = 1 to n = 3



10. Provide the n, l and ml value for each of the given orbitals. a) 7s n = b) 5d n =

l = l =

ml = ml =

c) 2p n = d) 4f n =

l = l =

ml = ml =



11. Which statement about the four quantum numbers is false? a. n = principal quantum number, n = 1 to ∞

b. l = azimuthal quantum number, l = 0,1,2, . . ., (n+1)

c. mL = magnetic quantum number, mL = (-l), . . .,0,. . ., (+l)

d. ms = spin quantum number, ms = + 12or − 1

2

e. The first three quantum numbers deal with the atomic orbitals except for the ms quantum

number, which deals with the electrons in the atomic orbitals.



12. Each of the following sets of quantum numbers gives information on a specific orbital. Find the error in each.

a. n = 4, l = 0 , ml = 1, ms = – 12

b. n = 5, l = 2 , ml = - 1, ms = 1

c. n = 7, l = 7, ml = - 5, ms = – 12

d. n = 0, l = 5, ml = - 3, ms = 12



14. How many electrons can have the following quantum sets? a) n = 4, mL = -1

b) n = 5, mL = 0 , mS = – 12

c) n = 9, l = 4, mS = – 12

d) n = 2, mS = 12



19. For n = 2, what are the possible sublevels? a) 0

b) 0, 1

c) 0, 1, 2

d) 0, 1,2, 3



16. Based on the following atomic orbital shape, which of the following set of quantum numbers is correct:

a) n = 2, l = 1, ml = 0

b) n = 3, l = 2, ml = –1

c) n = 4, l = 0, ml = +1

d) n = 1, l = 1, ml = 0




a) n = 3, l = 2, ml = 0, ms = – 12

b) n = 3, l = 1, ml = - 3, ms = 1

c) n = 4, l = 0, ml = 0, ms = – 12

d) n = 4, l = 2, ml = - 3, ms = 12




a) n = 3, l = 3, ml = 0, ms = 12

b) n = 1, l = 3, ml = -3, ms = 1

c) n = 7, l = 3, ml = - 4, ms = – 12

d) n = 6, l = 3, ml = -3, ms = – 12



25. Give the electron configuration for the following element and its ion. For the ion, state if it is paramagnetic or diamagnetic:

a. Ag

Ag+



26. Give the electron configuration for the following element and its ion. For the ion, state if it is paramagnetic or diamagnetic:

a. Cl

Cl+



27. Which of the following represents an “excited” state?

a) Cl: 1s22s22p63s23p5

b) Be: 1s22s2

c) Na: 1s22s2-2p63p1

d) N: 1s22s22p3



28. Give the set of four quantum numbers that represent the indicated electron in the following element:

a. Br (33rd electron) n = , l = , ml = , ms =




a. Ca (19th electron) n = , l = , ml = , ms =




a. Cu (27th electron) n = , l = , ml = , ms =




a. Mo3+ (38th electron) n = , l = , ml = , ms =



32. For a multi-electron atom, arrange the electron subshells of the following listing in order of increasing energy: 6s, 4f, 2p, 5d.



ch.2 - the quantum-mechanical model of the...

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