What gives fireworks their different colors? Section 5-1 The Atom and Unanswered Questions Recall...

What gives fireworks their different colors?

The Atom and Unanswered Questions

• Recall that in Rutherford's model, the atom’s mass is concentrated in the nucleus and electrons move around it.

• The model doesn’t explain how the electrons were arranged around the nucleus.

• The model doesn’t explain why negatively charged electrons are not pulled into the positively charged nucleus.

The Atom and Unanswered Questions (cont.)

• In the early 1900s, scientists observed certain elements emitted visible light when heated in a flame.

• Analysis of the emitted light revealed that an element’s chemical behavior is related to the arrangement of the electrons in its atoms.

The Wave Nature of Light

• Visible light is a type of electromagnetic radiation, a form of energy that exhibits wave-like behavior as it travels through space.

• All waves can be described by several characteristics.

The Wave Nature of Light (cont.)

• The wavelength (λ) is the shortest distance between equivalent points on a continuous wave.

• The frequency (ν) is the number of waves that pass a given point per second.

• The amplitude is the wave’s height from the origin to a crest.

The Wave Nature of Light (cont.)

The Wave Nature of Light (cont.)

• Wavelengths represented by λ (lambda).

• Expressed in meters

• Frequency represented by v (nu)

• Expressed in waves per second

• Hertz (Hz) is SI unit = one wave/second

• Speed of light represented by c

• This is a constant value in a vacuum

The Wave Nature of Light (cont.)

• The speed of light (3.00 108 m/s) is the product of its wavelength and frequency c = λν.

• λ and v are inversely proportional

The Wave Nature of Light (cont.)

• Light from a green leaf is found to have a wavelength of 4.90 x 10-7 m (or 490 nm or 4,900Å) Note: Å = ångström = 10-10 m. What is the frequency of the light?• c = λν where c= 300 million meters/second

• c/λ = ν

• 3.00*108 m/s / 4.90 x 10-7 m = ν

• ν = 6.12 * 1014 Hz

The Wave Nature of Light (cont.)

• Sunlight contains a continuous range of wavelengths and frequencies.

• A prism separates sunlight into a continuous spectrum of colors.

• The electromagnetic spectrum includes all forms of electromagnetic radiation.

The Wave Nature of Light (cont.)

Visible Spectrum

Color Frequency Wavelength

violet 668–789 THz 380–450 nm

blue 631–668 THz 450–475 nm

cyan 606–630 THz 476–495 nm

green 526–606 THz 495–570 nm

yellow 508–526 THz 570–590 nm

orange 484–508 THz 590–620 nm

red 400–484 THz 620–750 nm

The Particle Nature of Light

• The wave model of light cannot explain all of light’s characteristics.

• German physicist Max Planck observed in 1900 that matter can gain or lose energy only in small, specific amounts called quanta.

• A quantum is the minimum amount of energy that can be gained or lost by an atom.

The Particle Nature of Light

• Energy of a quantum:

• Equantum = hv

• Planck’s constant (h) has a value of 6.626 10–34 Joules ● second.

• Found that energy can only be emitted or absorbed in whole number multiples of hv (e.g. 3hv or 8hv).

The Particle Nature of Light (cont.)

• Albert Einstein proposed in 1905 that light has a dual nature.

• A beam of light has wavelike and particlelike properties. Think of light as a stream of tiny packets of energy called photons.

• A photon is a particle of electromagnetic radiation which carries a quantum of energy, but has no mass. Thus:

Ephoton = h

Ephoton represents energy of lighth is Planck's constant. represents frequency.

The Particle Nature of Light (cont.)

• The photoelectric effect is when electrons are emitted from a metal’s surface when light of a certain frequency shines on it. Thus, depends on Ephoton of light, not intensity (brightness).

• Calculate the quantum of energy associated with purple light of 380 nm.

• v = c/λ = 3*108 m/s / 3.80 x 10-7 m = 7.9 x 1014 Hz

• Ephoton = h = 6.626 10–34 J*sec x (7.9 x 1014/sec)

= 5.2 x 10-19 J

The Particle Nature of Light (cont.)

Atomic Emission Spectra • Since the energy of a beam of light is related to

its frequency, we can determine its energy by measuring its frequency or wavelength.

• Thus the color of light (i.e. wavelength) tells us about its energy level.

• For example, light in a neon sign is produced when electricity is passed through a tube filled with neon gas and excites the neon atoms.

• The excited neon atoms emit light to release energy. Only colors related to the quantum of energy released will be generated.

Atomic Emission Spectra (Discrete)

Atomic Emission Spectra (cont.)

• The atomic emission spectrum of an element is the set of wavelengths of the electromagnetic waves emitted by the atoms of the element.

• Each element’s atomic emission spectrum is unique.

Atomic Emission Spectra (cont.)

• The Emission Spectra for Calcium (top) and Sodium (bottom).

A. A

B. B

C. C

D. D

Assessment

What is the smallest amount of energy that can be gained or lost by an atom?

A. electromagnetic photon

B. beta particle

C. quantum

D. wave-particle

A. A

B. B

C. C

D. D

Assessment

What is a particle of electromagnetic radiation with no mass called?

A. beta particle

B. alpha particle

C. quanta

D. photon

Bohr's Model of the Atom

Bohr's Model of the Atom

• Bohr correctly predicted the frequency lines in hydrogen’s atomic emission spectrum.

• His new model built a relationship between location of electrons and their energy levels.

• The lowest allowable energy state of an atom and its electrons is called its ground state.

• When an atom gains energy, it is said to be in an excited state.

Bohr's Model of the Atom (cont.)

• Bohr suggested that an electron moves around the nucleus only in certain allowed circular orbits.

Bohr's Model of the Atom (cont.)

• Each orbit was given a number, called the quantum number.

Bohr's Model of the Atom (cont.)

• Hydrogen’s single electron is in the n = 1 orbit in the ground state.

• When energy is added, the electron moves to the n = 2 orbit or higher (excited state).

• When the electron is no longer excited by an outside force, it drops back down to a lower energy level.

• When it “falls” it emits its extra energy in the form of electromagnetic radiation.

Bohr's Model of the Atom (cont.)

Bohr's Model of the Atom (cont.)

• Bohr’s atomic model attributes hydrogen’s emission spectrum to electrons dropping from higher-energy to lower-energy orbits closer to the nucleus.

∆E = E higher-energy orbit - E lower-energy orbit = E photon = hν = hc/λ

• Bohr determined that the energy of each level was:

E = -2.178 x 10-18 J x (Z2 / n2)

• Where Z = the nuclear charge (= +1 for Hydrogen) and

• n = orbit level

Electron Energy Transformations

• If an electron moves from n=6 to n =1 (ground state), energy released would equal:

• n=6: E6 = -2.178 x 10-18 J x (12/62) = -6.050 x 10-20 J

• n=1: E1 = -2.178 x 10-18 J x (12/12) = -2.178 x 10-18 J

• ∆E = energy of final state – energy of initial state

• ∆E = (-2.178 x 10-18 J) – (-6.050 x 10-20 J) =

= -2.117 x 10-18 J (atom released energy)

λ = hc/ ∆E = (6.626x10-34J*s x 3.0x108m/s) / -2.117 x 10-18 J

= 9.383 x10-8 m or 93.83nm (ultraviolet light emitted)

Electron Energy Transformations

Bohr's Model of the Atom (cont.)

• Bohr’s model explained the hydrogen’s spectral lines, but failed to explain any other element’s lines and their chemical reactions.

• The behavior of electrons is still not fully understood, but substantial evidence shows they do not move around the nucleus in circular orbits like planets.

The Quantum Wave Mechanical Model

• While the Bohr model was not perfect, its idea of quantum energy levels was on the right track.

• Louis de Broglie (1892–1987) noted that Bohr’s quantized energy orbits had similarities to “standing” waves.

• He proposed that electron particles also behaved like waves as they moved around the nucleus.

The Quantum Wave Mechanical Model (cont.)

• The next figure illustrates that waves with fixed endpoints, like the vibrations of a guitar string, can only vibrate in certain wavelengths (or else they don’t “fit”).

• Waves going around a circle can only vibrate in whole-number wavelengths.

• And only ODD numbers of whole wavelengths can fit around a circle or orbit.

The Quantum Wave Mechanical Model (cont.)

• The de Broglie equation predicts that all moving particles, including baseballs and electrons, have wave characteristics.

represents wavelengthsh is Planck's constant.m represents mass of the particle. represents velocity.

• Since electrons can only move in specific wavelengths around the nucleus, and wavelength/frequency determines energy, we now have a mathematical reason for Bohr’s quantum energy levels.

The Quantum Wave Mechanical Model (cont.)

• Heisenberg showed it is impossible to take any measurement of an object without disturbing it.

• The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of an electron particle at the same time.

• The only quantity that can be known is the probability for an electron to occupy a certain region around the nucleus. These regions are called “Orbitals”.

The Quantum Wave Mechanical Model (cont.)

• Building on de Broglie’s work, Erwin Schrödinger derived an equation in 1926 that treated electrons as waves.

• His new model was called the quantum wave mechanical model of the atom.

• Schrödinger’s wave equation applied equally well to elements other than hydrogen, thus improving on the Bohr Model.

The Quantum Wave Mechanical Model (cont.)

• The Schrodinger wave function defines a three-dimensional region of electron location probability called the atomic orbital.

90%

ElectronProbability

• All the electrons for each element must occupy a specific orbital – there can be no overlap.

• The Quantum Model describes the different types and energies of orbitals using various:– Sizes– Shapes– Orientations– Spins

Every Electron needs an Orbital it can call Home

Atomic Orbitals

• Principal quantum number (n) indicates the relative size and energy of atomic orbitals.

• “n” specifies the atom’s major energy levels, called the principal energy levels.

• These are similar to Bohr’s orbit levels.

• n: 1-7 represent the seven principal energy levels for electrons of all known elements

Atomic Orbitals (cont.)

• Principal levels have multiple sublevels The number of sublevels = n and relate the shape of the orbital.

Atomic Orbitals (cont.)

• Each energy sublevel relates to orbitals of different shape. Spacial orientation can increase the number of sublevels.

Atomic Orbitals (cont.)

• Each Orbital has a unique set of “Quantum Numbers” defining its energy and position.

• ‘n’ = Principal Quantum Number (size /energy)

• ‘l’ = Angular Momentum Quantum Number. Shape of orbital. There are “n” shapes from 0 to n-1. Also referred to letters based on early spectral descriptions (0=s,1=p,2=d,3=f).

• ml = Magnetic Quantum Number. Orientation of orbital. Has values between –l and l .

• ms = Electron Spin Quantum Number. Electrons can spin in two directions: ½ and -½ or “up” and “down”

n l ml ms

(level) (shell)

(shape) (subshell)

(orientations) (spin)

1 0 1s 0 1 -1/2, +1/2 2 2

0 2s 0 1 -1/2, +1/2 2

1 2p -1,0,+1 3 -1/2, +1/2 6

0 3s 0 1 -1/2, +1/2 2

1 3p -1,0,+1 3 -1/2, +1/2 6

2 3d -2,-1,0,+1,+2 5 -1/2, +1/2 10

0 4s 0 1 -1/2, +1/2 2

1 4p -1,0,+1 3 -1/2, +1/2 6

2 4d -2,-1,0,+1,+2 5 -1/2, +1/2 10

3 4f -3,-2,-1,0,+1,+2,+3 7 -1/2, +1/2 14

Orbital Name

Quantum Numbers for first Four Levels of Orbitals

2

3

4

8

18

32

Number of Electrons

Electrons per level

Number of Orbitals

Quantum Numbers (cont.)

• What are the quantum numbers for the hydrogen’s lone electron in its ground state?

• n=1, l=0, ml=0, ms=1/2

• Usually written as: (1,0,0,1/2)

• Only certain quantum numbers are allowed

• If n=1, then can’t have l=3, for example.

• Would the following be allowed?

• (3,2,-3,1/2)• No: level n=3 can have ml=-2,-1,0,1,2 only

• (2,1,-1,-1/2)• Yes

Quantum Numbers (cont.)

• What is the maximum number of electrons with quantum number of (n=5, l=4)?

• If l = 4, then can have 9 orbitals of ml = -4,-3,-2,-1,0,1,2,3,4

and within each orbital, can have two electrons of spin ½ and -½

• Thus there is room for 9x2 = 18 electrons

• These 18 electrons will have quantum numbers starting with (5,4)

1. 5,4,-4, ½

2. 5,4,-4, -½

3. 5,4,-3, ½

4. 5,4,-3, -½

5. etc.

Atomic Orbitals Summary

• Principal quantum number (n) = size and energy of atomic orbitals.

•n= 1-7 energy levels or “shells”• Subshells (l) = shape of atomic orbitals

•Subshell quantum no.: 0, 1, 2, 3

•Subshell orbital letters: s, p, d, f

• Orientation (ml): different directions increases the number of orbitals per level.

•Number of orbitals for each subshell: s=1; p=3; d=5; f=7.

A. A

B. B

C. C

D. D

Assessment

Heisenberg proposed the:

A. Atomic Emission Spectrum

B. Quantum Leap

C. Wave theory of light

D. Uncertainty Principle

A. A

B. B

C. C

D. D

Assessment

Who proposed that particles could also exhibit wavelike behaviors?

A. Bohr

B. Einstein

C. Rutherford

D. de Broglie

A. A

B. B

C. C

D. D

Assessment

Which atomic suborbitals have a “dumbbell” shape?

A. s

B. f

C. p

D. d

A. A

B. B

C. C

D. D

Assessment

Which set of quantum numbers are not allowed and why?

A. (2,1,-1,1/2)

B. (4,1,2,1/2)

C. (3,2,-2,-1/2)

D. (1,0,0,1/2)

If l=1, ml can only be from -1 to 1

A. A

B. B

C. C

D. D

Assessment

The set of quantum numbers (4,1,-1,1/2) has which orbital name?

A. 4s

B. 5s

C. 4p

D. 4d

Electron Configuration

• Determine how electrons are organized around the nucleus for each element =

“Electron Configuration”

• Apply the

• Pauli exclusion principle,

• the aufbau principle, and

• Hund's rule to properly determine electron configurations using orbital diagrams and electron configuration notation.

Ground-State Electron Configuration

• The arrangement of electrons in the atom is called the electron configuration.

• The aufbau principle states that each electron occupies the lowest energy orbital available.

Ground-State Electron Configuration (cont.)

• The Pauli exclusion principle states that a maximum of two electrons can occupy a single orbital, but only if the electrons have opposite spins.

• Hund’s rule states that single electrons with the same spin must occupy each equal-energy orbital before additional electrons with opposite spins can occupy the same energy level orbitals.

Ground-State Electron Configuration (cont.)

Electron Configuration (cont.)

• Some electron configurations don’t appear to follow the rules, such as those for chromium, copper, and several other elements.

• Their configurations reflect the increased stability of half-filled and completely filled sets of s and d orbitals.

• Chromium: 1s2 2s2 2p6 3s2 3p6 4s1 3d5

• Copper: 1s2 2s2 2p6 3s2 3p6 4s1 3d10

Electron Configuration (cont.)

• Noble gas notation – shorthand configuration.

Period Table Blocks – Valence Electrons

Valence Electrons

• Valence electrons are defined as electrons in the atom’s outermost orbitals—those associated with the atom’s highest principal energy level.

• Electron-dot structure consists of the element’s symbol representing the nucleus, surrounded by dots representing the element’s valence electrons.

Valence Electrons (cont.)

A. A

B. B

C. C

D. D

Assessment

In the ground state, which orbital does an atom’s electrons occupy?

A. the highest available

B. the lowest available

C. the n = 0 orbital

D. the d suborbital

A. A

B. B

C. C

D. D

Assessment

The outermost electrons of an atom are called what?

A. suborbitals

B. orbitals

C. ground state electrons

D. valence electrons

A. A

B. B

C. C

D. D

Assessment

Which Periodic Table Group will have its valence electrons in a s2 p3 configuration?

A. The Alkali Metals

B. The Halogens

C. The Noble Gases

D. Group 15