0 Time υ = frequency λ = wavelength. Electromagnetic spectrum Visible light.

22
Time 0 maximum minimum crest trough crest frequency Number of crests or troughs pass this point in one second. 1Hz = 1 per second = 1/s = s -1 0 Time E lectrom agnetic R adiation Electrom agnetic energy is energy carried through space orm atter by m eansofwavelike oscillations. These oscillationsare system atic fluctuations in the intensityofelectrical and m agnetic forces. Electrom agnetic radiation -The rhythm icchanges w ith tim e and the successive series ofthese oscillationsthrough space. These oscillationsare popularly called the Lightw ave . Distance 0 Amplitude wavelength υ = frequency λ = wavelength

Transcript of 0 Time υ = frequency λ = wavelength. Electromagnetic spectrum Visible light.

Time

0

maximum

minimum

crest

trough

crest

frequency Number of crests or troughspass this point in one second.1Hz = 1 per second = 1/s = s

-1

0

Time

Electromagnetic Radiation

Electromagnetic energy is energy carried throughspace or matter by means of wavelike oscillations.These oscillations are systematic fluctuations in theintensity of electrical and magnetic forces.

Electromagnetic radiation - The rhythmic changeswith time and the successive series of theseoscillations through space. These oscillations arepopularly called the Light wave.

Distance

0

Am

plitu

de

wavelength

υ = frequency

λ = wavelength

Electromagnetic spectrum

Visible light

Properties of Waves

traveling waves - wave crests and troughs moveacross the surface of an ocean or lake

standing waves - wave crests and troughs do notchange position such as the string of a musicalinstrument

The crest or point of maximum amplitude occur atone position

points of zero amplitude or nodes occur at theends of the string

standing waves lead naturally to “quantumnumbers”

L n L length of string

λ2

λ2L

n

constructive interference

In phase

out of phase

Destructive Interference

wavelength x frequency = speed

λ x Hz = m/s

The speed of light in a vacuum is

c = 3.00 x 108 m · s -1

orλ x = c

Example: What is the frequency in Hz of yellow light thathas a wavelength of 625 nm.

υ

υ =c

625 nm =

3.00 x 10

625. x 10

m · s -18

-9 m = 4.80 x 10 s-114

Energy of Electromagnetic Radiation

Light travels in tiny quantized packets of energy. These packets are called photons. Each photon pulseswith a frequency, υ, and travels at the speed of light, c.

Energy of a photon = E = h υ

h is called Planck’s constant and has a value of

h = 6.626 x 10-34

J · s

Energy of Electromagnetic Radiation

In 1900, the German physicist Max Planck, theorized thatlight travels in tiny quantized packets of energy and thatthese packets travel at the speed of light, c , and pulse witha frequency, . Later in the century these packets weregiven the name photon.

Using the ideas of Planck, Albert Einstein confirmed thatthe energy of a photon is proportional to its frequency.

E = h

The h is called Planck’s constant and has the value

h = 6.626 x 10-34 J s

Example: Calculate the energy of 532 nm green light.

E = h 532 nm

=532. x 10

3.00 x 10 m · s -18

-9m

h c

=(6.626 x 10

-34 J·s)

=

υ

υ

· s

3.74 x 10 -19 J

υ

Atomic Spectra and the Bohr Model of the Hydrogen Atom

Continuous spectrum - Is the continuous unbrokendistribution of all wavelengths and frequencies.

Atomic or Emission spectrum - a series of lines at only afew wavelengths. Atoms absorb or emit radiation atspecific wavelengths.

Hydrogen line spectra - hydrogen is the simplest element. A proton and an electron. Its spectrum actually consists ofseveral series of lines. Figure 1 (a similar series is shownin Figure 7.7 of the text) shows a portion of the serieswhich occurs in the visible region. Other series occur inthe ultraviolet and Infrared. What we see from this is thatthe transitions are between quantized energy levels. In1885 J. J. Balmer found an equation which could fit all thehydrogen lines in all the series.

The Rydberg constant is an empirical constant meaning itwas chosen to give values for lambda which are close tothe experimentally determined ones. R H = 109,678 cm

-1.

n 2 must be larger than n1 (to give a positive value for lambda).

1 1

R

1

n nH12

22

n2 can be any value from 2 to infinity and n 1

can be any

value from 1 to infinity.

The Bohr Model of the Hydrogen Atom

In 1913 the German physicist Niels Bohr, proposed thefirst theoretical model of the hydrogen atom. He likenedhis model to that of a planet circling about the sun. Whatwas important about this model is that it placed restrictionson the orbits and energies of that an electron could have ina given orbit

+

Energy of the electron is

E = -b

n 2

J 18-2

42

22

42

10 x 2.18 b h

me2 b

hn

me2 - E

One electron system

E = =-b

n

-b

nh2

12E Eh 1

E = b1

n

1

nE =

hc

12

h2

1

= b

hc

1

n

1

n12

h2

Rh = 109,678 cm-1bhc

=109730 cm, -1

Absorption of Energy

Emission of Energy

Photons (Light packets) are quantized, travel at the speedof light, c , and travel with a frequency, .

Energy is proportional to frequency E = h υ.

Atoms absorb or emit radiation at specific wavelengths

The Bohr model is similar to a planet orbiting the sun andsatisfies the Rydberg equation fairly well.

The Bohr model is useless for any atom larger thanhydrogen.

υ

Wave Properties of Matter and Wave Mechanics

Bohr’s model fails because the classical laws ofphysics do not apply to particles as tiny as theelectron.

Classical physics fails because atomic particles arenot as our senses perceive them

Under the appropriate circumstances small particlesbehave not as particles, but as waves

In 1924 Louis De Broglie proposed the idea of matterwaves, where their wavelength is give by

λ = hmv

Example: What is the wavelength of a 100 kg personrunning at 3.0 meters per second

λ =h

100 3.00 m · s -1kg

=(6.626 x 10

-34·s) = 2.21 x 10 -36 m

mv

J =kg m2

s 2

kg m2

s 2

Electron waves in Atoms

Wave mechanics - the theory concerning waveproperties of matter

Serves as the basis of all current theories ofelectronic structure

Quantum mechanics - the term is used becausewave mechanics predicts quantized energy levels

Erwin Schrödinger, an Austrian, is the first toapplied the concept of the wave nature of matterto the explanation of electronic structure. (1926)

Quantum mechanics says that the electron waves inan atom are standing waves and like the violin thesestanding waves can have many waveforms or wavepatterns. We will call these waveforms orbitals

Orbitals are described by a wave function usuallyrepresented by the symbol, ψ ( Greek letter , psi )

Wave function describes the shape of the electronwave and its energy

Energy changes within an atom are simply theelectron changing from one waveform and energy toanother

The lowest energy state is called the ground state

The Principle Quantum Number, n

The principle quantum number is called n. All orbitalswhich have the same value of n are said to be in thesame shell.

n ranges from n = 1 to n = ∞shells are also sometimes related by letterbeginning for no particular reason with K.

n is related to the size of the of the electron wave(how far it extends from the nucleus). The higherthe value of n, the larger is the electrons averagedistance from the nucleus.

As n increases the energies of the orbitalsincrease

Bohr’s theory only took n into account, andworked because hydrogen is the only element inwhich all the orbitals have the same value of n

The Secondary Quantum Number, l

The secondary quantum number divides the shellsinto groups of orbitals called subshells

n determines the values allowed for lfor a give value of n l can range from

l = 0 to l = (n - 1) when n = 1 l = 0

n = 1 l = 0n = 2 l = 0, 1n = 3 l = 0, 1, 2n = 4 l = 0, 1, 2, 3n = 5 l = 0, 1, 2, 3, 4 n = 6 l = 0, 1, 2, 3, 4, 5n = 7 l = 0, 1, 2, 3, 4, 5, 6

Subshells could be identified by their value of l, but toavoid confusion between n and l they are given lettercodes

l determines the shape of the subshell

subshells within a shell differ slightly in energy

Energy —>l = 0 1 2 3 4 5

s p d f g h

The Magnetic Quantum Number , ml

ml divides the subshells into individual orbitals

ml has values from -l to +l

when l = 0 ml = 0

when l = 1 ml = -1, 0, +1

when l = 2 ml = -2, -1, 0, +1, +2

when l = 3 ml = -3, -2, -1, 0, +1, +2, +3

Electron Spin Quantum Number , ms

Electron spin is based on the fact that electronsbehave like tiny magnets

Spin can be in either of two directions

N

S N

S

Spin quantum number ms can have values of +1/2 or -1/2

QuantumNumber

Allowed Values Name and Meaning

n 1, 2, 3, ...…, Principal quantum number: orbitalenergy and size

l (n-1), (n-2), ...., 0 Secondary Quantum number:orbital shape (and energy in amulti-electron atom), letter namefor subshell (s, p, d, f)

ml l, (l -1), ..., 0, ..., (-l +1), -l Magnetic quantum number: orbital orientation

ms 1/2, -1/2 Electron spin quantum number: spin up (+1/2) or spin down (-1/2).

Pauli Exclusion principle - The Pauli exclusion principlestates that no two electrons in the same atom can havethe same values for all four quantum numbers (n, l, ml, ms)

Aufbau - Add electrons 1 at a time, tp the lowestavailable orbital.

Hund’s Rule - When electrons are placed in orbitals ofthe same energy they try to move as far away away fromeach other as possible.

3s

4s

3p

4p

3s

3d

5s

5p4d

6s

6p5d 4f

7s6d 5f

2s2p

n = 2, l = 1, m l = -1n = 2, l = 1, m l = 0n = 2, l = 1, m l = 1

n = 2, l = 1, m l = -1

1sn = 2, l = 1, m l = -1

Ene

rgy

Approximate energy level diagram

1s

2s

2p

1s

2sH

Electron Configuration

1s1 He 1s2

1s

2sLi 1s2 2s1

1s

2sBe 1s2 2s2

1s

2sB 1s2 2s2 2p1

2p

1s

2sC 1s2 2s2 2p2

2p

1s

2sN 1s2 2s2 2p3

2p

1s

2sO 1s2 2s2 2p4

2p

1s

2sF 1s2 2s2 2p5

2p

1s

2sNe 1s 2 2s2 2p6

      Magnetic properties of Atoms

    When two electrons occupy the same orbital the must have different values of ms.

         Atoms with more electrons spinning in one direction than in the other are said to contain unpaired electrons. The magnetic effects do not cancel and these atoms behave as tiny magnets which can be attracted to an      external magnetic field.  These atoms are said to be paramagnetic.    

         Diamagnetic substances are those in which all the electrons are paired.

         Paramagnetism is a measurable property.