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Atomic Structure. Chapter 7: Describe the properties of electromagnetic radiation . Understand the origin of light from excited atoms and its relationship to atomic structure. Describe the experimental evidence for wave-particle duality. Describe the basic ideas of quantum mechanics .

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atomic structure

Atomic Structure

Chapter 7:

Describe the properties of electromagnetic radiation.

Understand the origin of light from excited atoms and its relationship to atomic structure.

Describe the experimental evidence for wave-particle duality.

Describe the basic ideas of quantum mechanics.

Define the three quantum numbers and their relationship to atomic structure.

electromagnetic radiation
Electromagnetic Radiation
  • Radiation is _____________!
  • List forms of electromagnetic radiation:

_______________ ___________

_______________ ___________

  • Maxwell Theory (1831-1879): describe all forms of radiation in terms of ________

________________________________.

  • Einstein Theory (1879-1955): light has _______________________________.
wave properties
Wave Properties

wavelength

Visible light

Ultraviolet radiation

electromagnetic radiation4
Electromagnetic Radiation

Frequency – hertz (s-1)

Speed = wavelength (m) x frequency (s-1)

c = l x v

what is the frequency of orange light which has a wavelength of 625 nm
What is the frequency of orange light, which has a wavelength of 625 nm?

Students should be familiar with conversion of units and conversion between l and v.

the visible spectrum of light
The Visible Spectrum of Light
  • Long wavelength --> ______ frequency

_____ energy

  • Short wavelength --> _____ frequency

_____ energy

energy and frequency
Energy and Frequency
  • Max Planck (1858-1947): the energy of a vibrating systems is proportional to the frequency of vibration.
  • The proportionality constant

h = Planck’s constant

= 6.6260693 x 10-34 J s

E = h v

radiation given off by a heated body
Radiation given off by a Heated Body
  • Planck solved the “___________________”.
  • Vibrations are _________ – only vibrations with specific frequencies are allowed.
  • There is a distribution of vibrations in a object.
quantization of energy
Quantization of Energy
  • An object can gain or lose energy by absorbing or emitting radiant energy in QUANTA.
  • Energy of radiation is proportional to frequency.

Light with large l (small v) has a _____ E.

Light with a short l (large v) has a ____ E.

E = h v

photoelectric effect
Photoelectric Effect
  • Experiment demonstrates the _______ _____________________________.

No e- observed until light of a certain minimum E is used.

photoelectric effect11
Photoelectric Effect
  • Classical theory said that E of ejected

electron should increase with increase

in light frequency—not observed!

  • No e- observed until light of a certain

minimum E is used.

  • If the frequency is above the minimum,

the number of e- ejected depends on

light intensity.

  • Einstein explained the photoelectric effect: light consists of “__________” particles called PHOTONS – _______________.
  • The energy of each photon is proportional to the ______________of radiation (Planck’s relation).
  • The greater the intensity of light, the more photons are available to strike per unit of time.
slide12
Show that the energy of a mol of blue photons (l = 400 nm) is higher than the energy of a mol of red photons (l=685 nm)
using planck s equation

~

= h c v

Using Planck’s Equation
  • As frequency (v) increases, energy (E) __________.
  • As wavelength (l) decreases, energy (E) _________.

E = h v

v = c/l

E = h v = h c

l

(wavenumber)

Students should be familiar with frequency, wavelength, and energy calculations.

photosynthesis
Photosynthesis
  • Chlorophylls absorb blue and red light and carotenoids absorb blue-green light, but green and yellow light are not effectively absorbed by photosynthetic pigments in plants; therefore, light of these colors is either reflected by leaves or passes through the leaves. This is why plants are green.
spectrum of excited hydrogen gas
Spectrum of Excited Hydrogen Gas
  • Excited atoms emit light of only certain wavelengths. –Evidence of ____________________.
  • Line Emission Spectra of Excited Atoms.
  • The wavelengths of emitted light depend on ______________________________.
which mathematical expression represents the regular patterns of emission

1

l

1

22

1

n2

(

)

= R

Which Mathematical Expression represents the Regular Patterns of Emission?
  • Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919) developed an equation:
  • Rydberg equation – to calculate the _________________

__________________

__________________.

  • Rydberg constant = R

R = 1.0974 x 107 m-1

when n > 2

n = 3 , l =red line

n = 4 , l = green line,

Etc. Balmer Series

atomic view of the early 20 th century
Atomic View of the Early 20th Century

An electron (e-) traveled about the nucleus in an orbit.

1. Any orbit should be possible and so is any energy.

2. But a charged particle moving in an electric field should emit energy.

End result should be matter self-destruction!

bohr model
Bohr Model
  • Niels Bohr (1885-1962) connected the observation of the spectra of excited atoms with the quantum ideas of Planck and Einstein.
  • Based on Rutherford’s work – electrons are arranged in space outside the atom.
  • Bohr model shows electrons moving in a circular orbit around the nucleus.
  • Bohr postulated:

1.- An electron could occupy only __________ ___________or energy levels in which it is stable.

2.-The energy of the electron in the atom is ______________.

atomic spectra and bohr
Atomic Spectra and Bohr
  • n ___________ quantum number
  • n is a _________________ having values of 1, 2, 3 and so on.
  • The energy of attraction between oppositely charged bodies (negative electron and positive nuclear proton) has a negative value. The value becomes more negative as the bodies move closer together (Coulomb’s law).
  • As the value of n increases, the energy becomes less negative, the distance of the electron from the nucleus increases.

Rh c

n 2

Potential energy of electron

in the nth level

= En = -

atomic spectra and bohr22

n = 2

2

E = -C (1/ 2

)

n = 1

2

E = -C (1/1

)

Atomic Spectra and Bohr
  • Only orbits where n = integral number are permitted.

If e-’s are in quantized energy states, then ∆E of states can have only certain values. This explain sharp line spectra.

ground state and excited state
Ground State and Excited State
  • Ground state: The state of an atom in which all electrons are in the ______________________.
  • Excited state: The state of an atom in which at least one electron is ______________________ ____________________.
cc alculate d e for an e of the h atom falling from high energy level n 2 to low energy level n 1
CC alculateDE for an e- of the H atom “falling” from high energy level (n = 2) to low energy level (n = 1).
atomic spectra and bohr25
Atomic Spectra and Bohr
  • The amount of energy that must be absorbed by the atom so that an electron can move from the first to the second energy state is 3/4RhC or 984 kJ/mol of atoms – no more or less – energy levels in the H atom are quantized – only certain amounts of energy may be absorbed or emitted.
  • When an electron “falls” from a level of higher n to one of lower n, ________ energy. The negative sign indicates energy is _________, 984 kJ must be _______ per mole of H atoms.
  • The energy ________ is observed as ______ – This is the source of the lines observed in the emission spectrum of H atoms. – The basic explanation holds for the spectra of other elements.
atomic spectra and bohr26
Atomic Spectra and Bohr

1

1

  • The origin of atomic spectra is the movement of _________ between quantized energy states.
  • Electron is excited from a lower energy state to a higher one – Energy is ________.
  • Electron moves from a higher energy state to a lower one – Energy is _________.

(

)

-

∆E = Efinal – Einitial = -R h c

n2final

n2initial

electronic transitions in an excited h atom
Electronic Transitions in an Excited H Atom
  • If electrons move from energy states n >1 to the n =1 state – emission lines have energies in the UV region (Lyman series).
  • If electrons move from energy states n >2 to the n =2 state – emission lines have energies in the VIS region (Balmer series).
  • If electrons move from energy states n >3 to the n =3 state – emission lines have energies in the IR region.
calculate the wavelength of the photon emitted if an electron in the h atom moves from n 4 to n 2
Calculate the wavelength of the photon emitted if an electron in the H atom moves from n = 4 to n =2
flaws in bohr s theory
Flaws in Bohr’s Theory
  • Bohr’s model of the atom explained only the spectrum of H atoms and of other systems having one electron (such as He+).
  • The idea that electrons are particles moving about the nucleus with a path of fixed radius, like that of the planets about the sun, is no longer valid.
wave mechanics
Wave Mechanics

Louis de Broglie (1892-1987) proposed that all moving objects have _______ _________________(1924).

For light: (1) E = mc2

(2) E = h v = h c / l

wave mechanics calculate the broglie wavelength
Wave Mechanics –Calculate the Broglie Wavelength

Baseball (115 g) at 100 mph

e- with velocity = 1.9 x 108 cm/sec

It is possible to observe wave-like properties only for particles of extremely __________, such as protons, neutrons, and electrons.

l= h

m v

the uncertainty principle
The Uncertainty Principle
  • Erwin Schrödinger, 1887-1961 : developed ________________or ______________.
  • Werner Heisenberg, 1901-1976 : The uncertainty principle – it is impossible to fix both the ______________ electron in an atom and its ________ with any degree of certainty.
  • Max Born, 1882-1970 : if the energy of an electron in an atom is known with a small uncertainty, there will be large uncertainty in its position in the space about the atom's nucleus.
  • We can assess only the likelihood, or probability, of finding an electron with a given energy within a given region of space.
schr dinger s wave functions
Schrödinger's Wave Functions
  • The behavior of the electron in the atom is best described as a standing wave – In a vibrating string, only certain vibrations can be observed = only certain wave functions are allowed for the electron in the atom.
  • Each wave function () is associated with an allowed energy value, En, for the electron.
  • Then, from 1 and 2, the energy of the electron is quantized – only certain values of energy.

Wave motion:wave length and nodes

4. In contrast to Bohr’s theory – quantization is imposed as a postulate.

schr dinger s wave functions34
Schrödinger's Wave Functions

5. The is related to the probability of finding the electron within a given region of space = _______________.

6. Energy is known precisely – position is given by a probability. The region of space in which an electron of a given energy is most probably located is called its _______________.

7. The solution to the Schrödinger's equation, for an electron, in a 3-D space, are 3 integer numbers = quantum numbers n, l, and ml. These numbers have only certain combination of values.

quantum numbers
Quantum numbers
  • n, Principal quantum number = 1, 2, 3, …

Determines the ________ of the electron. Also related to size of orbital.

En = - Z2h R / n2

Electrons with the same n value are in the same electron ______ or same electron _________.

  • l, Angular Momentum quantum number = 0, 1, 2, 3, …, n-1

Determines the ______ at which electrons circulate about the nucleus. Related to orbital __________.

Electrons with the same l value are in the same _______ and have the same orbital _____ (______). All orbitals in the same subshell have the same ___________.

  • ml, Magnetic quantum number = 0, ±1, ± 2, ± 3, …, ±l

Determines the _____________ of the orbital motion of the electron. (Clockwise or counterclockwise). Related to ___________ in space of the orbitals within a subshell, this gives the ___________ of orbitals in a subshell.

See Table 7.1 (p 319)

quantum numbers and orbitals
Quantum numbers and Orbitals

Number of subshells in a shell = n

Number of orbitals in a subshell = 2l + 1

Number of orbitals in a shell = n2

l =0 (s) ; l =1 (p) ; l =2 (d) ; l =3 (f)

Name of orbital = value of n and letter code for l

If n=1 ; l = n-1 = 0 ; ml = 0

Only 1 subshell (s); only 1 orbital (1s)

If n=2 ; l = 0, 1 ; ml = +1, 0, -1

There are 2 subshells (s and p)

4 orbitals (the 2s, and three 2p (3 orientations)

orbitals
Orbitals
  • Electron orbitals are probabilities – represented as ____________________.
orbitals38
Orbitals

surface density plot

or radial distribution plot

  • For the s orbital, the probability of finding an electron is the same at the same distance from the nucleus – the 1s orbital is ____________ in shape.
  • Quantum mechanics – electron has wave properties – the maximum amplitude of the electron wave occurs at 0.053 nm from the nucleus.
  • Bohr’s radius = 0.059 nm
orbitals39
Orbitals
  • The p orbitals have 1 nodal surface – zero probability of finding an electron.
  • Number of nodal surfaces = value of l
  • There are three p orbitals in each p subshell: ml = +1, 0, -1
  • Refer to orbitals according to the axes along which the lobes lie: px, py, pz
orbitals40
Orbitals
  • The d five orbitals, l=2 have 2 nodal surfaces (may not be flat).
  • What type of orbital is designated n = 4, l = 3, ml =-3?

a. 4s

b. 4p

c. 4d

d. 4f

e. none

orbitals41
Orbitals

Students should be familiar with definitions of quantum numbers and orbital types.

practice
Practice
  • Which of the following represent valid sets of quantum numbers?
  • n=3, l=3, ml= +1
  • n=5, l=1
  • n=6, l=5, ml=1
  • n=4, l=3, ml=-4
remember
Remember
  • Go over all the contents of your textbook.
  • Practice with examples and with problems at the end of the chapter.
  • Practice with OWL tutors.
  • W ork on your assignment for Chapter 7.
  • Practice with the quiz on the cd or online service.