241 F17-Ch2a 1-per-page PDF

Preview

Summary

Download 241 F17-Ch2a 1-per-page PDF

Description

Chapter 2

© Drs. XO, PHB, CWR

Atomic Structure

CHEM 241 Fall 2017 Ch.2 − p.1

Note: General Chem. textbooks do not go into sufficient detail on these topics. SELF-STUDY: SLIDES WITH SS ON THEM MUST BE STUDIED IN DETAIL BEFORE CLASS. IN CLASS, THEY WILL BE CLARIFIED ONLY, +/- EXERCISES.

© Drs. XO, PHB, CWR

Early Attempts to Find Patterns

SS

CHEM 241 Fall 2017 Ch.2 − p.2

Chemists looked for patterns in physical & chemical properties to make it easier to remember and understand the elements. Atomic structure was not yet understood. John Döbereiner (1817) - “Triads” He noticed groups of three elements with similarities, e.g. calcium, strontium, barium; and sulphur, selenium, tellurium; and chlorine, bromine, iodine. (http://en.wikipedia.org/wiki/Johann_Wolfgang_Döbereiner)

John Newlands (~1865) – “Law of Octaves” The first person to notice that there seemed to be a repetition of properties every 8 elements if placed in order of atomic mass. (http://www.tutorvista.com/content/science/science-ii/periodic-classification-elements/newlands-octaves.php)

Notes

Groups of the 8th elements

Do

Lithium,

Sodium

Potassium

Re

Beryllium

Magnesium

Calcium

Me

Boron

Aluminum

Fa

Carbon

Silicon

So

Nitrogen,

Phosphorus

La

Oxygen

Sulphur

Ti

Fluorine

Chlorine

The Mendeleev Periodic Table

© Drs. XO, PHB, CWR

SS

    (Dimitri Ivanovich Mendeleev) He also arranged the elements in order of increasing and began a new row when the next element was similar in properties to a previous one (1869). For example: •

Lithium, sodium and potassium form chlorides, MCl, which are soluble in water.

•

They have oxides, M2O, which give hydroxides in water. I

II A B

III A B

IV A B

V A B

VI A B

VII A B

Li

Be

B

C

N

O

F

Na

Mg

Al

Si

P

S

Cl

K

Ca

A

B

(http://en.wikipedia.org/wiki/Dmitri_Mendeleev)

VIII B

CHEM 241 Fall 2017 Ch.2 − p.3

The Mendeleev Periodic Table (cont.)

© Drs. XO, PHB, CWR

SS

CHEM 241 Fall 2017 Ch.2 − p.4

•

He left gaps for yet to be discovered elements, e.g. scandium, which he named “eka-boron”, and which was first isolated in 1879 (Lars Fredrik Nilson).

•

The next element titanium, already isolated in 1825 (Berzelius), is a metal, unlike silicon. Although both elements form dioxides and tetrachlorides, Ti also forms a trichloride. Mendeleev put it in subgroup IVB. II A B

III A B

IV A B

V A B

VI A B

VII A B

Li

Be

B

C

N

O

F

Na

Mg

Al

Si

P

S

Cl

K

Ca

A

I

B

Sc

Ti

VIII B

The Mendeleev Periodic Table (cont.)

© Drs. XO, PHB, CWR

SS

CHEM 241 Fall 2017 Ch.2 − p.5

•

The following elements needed to be put in the B subgroups, and iron, cobalt and nickel are sufficiently similar that Mendeleev put all three together in VIIIB.

•

The elements gallium and germanium, which Mendeleev called “eka-aluminum” and “eka-silicon” were unknown, so he left two gaps.

• •

The sequence recommenced in subgroup A, with arsenic, etc. The radioactive element, technetium, does not occur naturally (so he left a gap). II A B

III A B

IV A B

V A B

VI A B

VII A B

Li

Be

B

C

N

O

F

Na

Mg

Al

Si

P

S

Cl

K

Ca

A

I

B

Zn Ga

Cu Rb

Sc Ge Y

Sr Ag

Ti

Cd

In

V

Sn

Se

As Zr

Cr

Nb Sb

Mn Fe Co Ni Br

Mo Te

VIII B

Tc Ru Rh Pd I

The Mendeleev Periodic Table (cont.)

© Drs. XO, PHB, CWR

SS

CHEM 241 Fall 2017 Ch.2 − p.6

Problems: • Order of increasing atomic mass did not always work (e.g. Te & I), even after efforts to correct erroneous values. •

The necessity for A and B subgroups was troubling.

•

Some new elements did not fit in an empty space (e.g. Lanthanides Ho & Sm), and there was an entire missing column (which one?). II A B

III A B

IV A B

V A B

VI A B

VII A B

Li

Be

B

C

N

O

F

Na

Mg

Al

Si

P

S

Cl

K

Ca

A

I

B

Zn Ga

Cu Rb

Sc Ge Y

Sr Ag

Ti

Cd

In

V

Nb Sb

Mn Fe Co Ni

Se

As Zr

Sn

Cr Br Mo Te 127.60

VIII B

Tc Ru Pd Rh I

126.90

© Drs. XO, PHB, CWR

• •

Establishing Atomic Structure

SS

CHEM 241 Fall 2017 Ch.2 − p.7

Once atomic structure was better understood, the elements were ordered by instead. The ability of this new periodic table to predict as-of-yet unknown elements made it (quickly) widely accepted by chemists.

The Modern Periodic Table

Pnictogens

© Drs. XO, PHB, CWR

SS

CHEM 241 Fall 2017 Ch.2 − p.8

© Drs. XO, PHB, CWR

The Mendeleev Periodic Table (question)

Which column was missing in Mendeleev’s periodic table? A. The transition metals B. The noble gases

D. The halogens

CHEM 241 Fall 2017 Ch.2 − p.9

© Drs. XO, PHB, CWR

Modeling the Structure of Hydrogenic Ions: the Bohr Atom SS

CHEM 241 Fall 2017 Ch.2 − p.10

As chemists we need to know about what the electrons are doing inside atoms. This helps us to understand a number of very basic atomic properties connected to ionic bonding, such as: Ionization enthalpy (ionization energy or potential), Electron attachment enthalpy (electron affinity) Ionic radius and various properties of atoms when they are found in covalent compounds or metals, such as: Other types of radii (atomic, covalent and van der Waals) Electronegativity And, of course, we need to understand the formation of covalent bonds between atoms. To make this a little easier, we start with the simplest possible atom, hydrogen, which has only one electron (and other “exotic” one-electron species, such as He+, Li2+, Be3+, which also have only one electron, but increasing numbers of protons in their nuclei, the hydrogenic ions.)

© Drs. XO, PHB, CWR

White light, from the sun or an incandescent filament is split into a rainbow - a continuous spectrum or continuum

Light coming from a gas discharge tube, for example one where a current is passed through hydrogen gas, produces a line spectrum

Atomic Line Spectra

SS

CHEM 241 Fall 2017 Ch.2 − p.11

Drs. XO, PHB, CWR

SS

Bohr Theory

The first attempt to devise a model of the atom to explain the line spectra was due to Niels Bohr (1885 – 1962). He based his theory on the Rutherford “planetary” model of the atom, and considered only circular orbits. To counter a principle of classical physics, that electrons in a circular path would emit radiation (energy) and spiral into the nucleus, he said that only certain orbits were allowed, those with radius & energy given by: 2 2

rn =

n h 4 π 2 me 2 Z

En = −ℜ

CHEM 241 Fall 2017 Ch.2 − p.12

p

hc n2

n=1 n=2 n=3

where n = 1,2,3, … , h = Planck’s constant, m = mass of the electron, e = charge of the electron, Z = charge of nucleus, c = speed of light,  = the Rydberg constant (a combination of the others).

• The number n is called the principal quantum number. • The energy is always negative, and as required by Coulomb’s law, becomes more negative the closer the electron is to the nucleus. • The value of En is most negative for n = 1, and becomes less negative as n increases. It goes to zero (no attraction of electron to nucleus) when n = . • The situation where n = 1 is called the ground state, and others are called excited states. An atom will want to be in its ground state, and will generally lose energy as electromagnetic radiation in order to get there.

Bohr Theory (cont.)

© Drs. XO, PHB, CWR

CHEM 241 Fall 2017 Ch.2 − p.13

Bohr theory predicts line spectra for hydrogen: If an electron moves from an orbit ninitial to an orbit nfinal where ninitial < nfinal, energy is absorbed. A photon of the correct energy can make this happen, or a violent collision with an electron or another atom. If the electron is not in the n = 1 ground state, it will eventually lose energy by emitting a photon (or photons) to get there. The energy of the photon emitted or absorbed is given by the general formula:

∆E = E final − Einitial = ℜhc

1 n 2final

−

1 n2initial

Using E = hν and c = λν, we can calculate λ and ν for the photon, to show that:

1

λ

=ℜ

1 n 2final

−

1 2 ninitial

SEE MOODLE: Dry Lab Experiment D1- Bohr Atom Simulation NB: (|expression| means take the absolute (+) value of the expression.)

CHEM 241 Fall 2017 Ch.2 − p.14

Energy Levels and Line Spectra

© Drs. XO, PHB, CWR

Energy

Quantum # (n)

0 -1/36 RH -1/25 RH -1/16 RH

Paschen series (IR)

-1/9 RH

∞ 6 5 4 3

Balmer series (visible transitions shown) -1/4 RH

2 Lyman series (UV)

Remember that the lines in the spectra are always associated with a transition between two energy levels. The energy associated with the n = 1 to n = ∞ transition, i.e. ejection of the electron from the atom, is called the ionization energy. The equations on the previous slides can be used to calculate all the energies and frequencies for this diagram. Try some!

1

λ

=ℜ

1 n 2final

−

1 n2initial

 = the Rydberg constant

-RH

1

= 1.097 × 107 m-1 (per H atom) = 2.179 × 10-18 J (per H atom) = 13.61 eV (per mole H atoms)

Drs. XO, PHB, CWR

Decline and Fall of Bohr Theory

CHEM 241 Fall 2017 Ch.2 − p.15

Bohr theory suffered from several defects that lead to its replacement by the one we use now: •

It predicted the line spectra of hydrogen and other one-electron ions; He+, Li2+, Be3+ etc, but could not handle species with two or more electrons.

•

It could not explain how atoms bond together.

•

There was no explanation for why only certain orbits were allowed.

•

The theory violated the newly postulated Heisenberg Uncertainty Principle because it tries to be too precise about where the electron is found. Electrons cannot be treated as simple particles. The Bohr Theory is now replaced by one which does not try to describe the motion of the electron exactly, but rather deals in probability, and we end up with a picture of the electrons in atoms as a diffuse clouds of specific shapes. The subject is called wave mechanics or quantum mechanics. Graphic adapted from http://csep10.phys.utk.eduastr162lectlightbohr.html

© Drs. XO, PHB, CWR

Wave Mechanics - Foundation

CHEM 241 Fall 2017 Ch.2 − p.16

There were several important steps in the evolution of the wave mechanical approach: Diffraction (1665) Electromagnetic radiation (light) is diffracted at gratings - a phenomenon easily understood by assuming wave properties for light. The Photoelectric effect (Einstein, 1905) Light striking certain metal and metalloids generates electrons. This effect is most easily understood by postulating that light can behave as photons particles of energy, hν. The de Broglie Equation (Louis de Broglie, 1924) E = mc2 E = h c =  h = Planck’s constant (6.626 x 10−34 J·s−1) The momentum of a photon: c = speed of light (2.998 x 108 m·s−1) E = energy of the photon or particle p = mc = (E/c2)c = E/c = h/c = h/  = photon frequency Therefore, for a photon:  = photon wavelength  = h/p v = particle velocity m = particle mass & for an atomic particle (e.g., an electron): p = particle momentum  = h/mv The wavelength of tiny particles is significant compared to their size.  Treat electrons as standing waves centred on nucleus, not particles in circular orbits.

Drs. XO, PHB, CWR

Wave Mechanics – Foundation (cont.)

CHEM 241 Fall 2017 Ch.2 − p.17

The Diffraction of an Electron Beam (Davisson and Germer, 1927) An electron beam can be diffracted by a suitable metal crystal just like light, confirming de Broglie's theory. The Heisenberg Uncertainty Principle (~1927) There is a theoretical limit on the exactness with which a particle can be “pinned down” (usually in terms of its position and momentum): x. p > h/2 where x is the uncertainty in position and p the uncertainty in momentum. The more accurately an electron’s energy is known, the less accurately its position is known. BUT: When treat ing an electron as a standing wave, it is possible to map out the probability of finding the electron at various locations . ( = the orbital concept – coming soon).

© Drs. XO, PHB, CWR

Standing Waves - The Vibrating String

CHEM 241 Fall 2017 Ch.2 − p.18

For a review of the properties of waves go here: http://faculty.concordia.ca/bird/java/Wave/Wave.html

The general equation of a sine wave on a string (at one extreme of its motion) is:  = sin(nx/l) where n can be 1 or 2 or 3 or … or . There is one eigenfunction for each value of n.

 = sin(1x/l)

 = sin(2x/l)

 = sin(3x/l)

Nodes: positions/lines/planes/surfaces where the wave’s function has a zero value. To find them, look for places where the mathematical sign of the function changes (an inflection point or line/plane/surface).

© Drs. XO, PHB, CWR

2D Waves - Example Drumskins Animations of waves on drumskins http://faculty.concordia.ca/bird/c241/java/drums/drums_demo.html

These have circular nodes:

CHEM 241 Fall 2017 Ch.2 − p.19

© Drs. XO, PHB, CWR

2D Waves - Drumskins (cont.) These have transverse (linear) nodes:

These have both kinds of node:

CHEM 241 Fall 2017 Ch.2 − p.20

© Drs. XO, PHB, CWR

2-D Waves – Drumskins (question a)

How many transverse (linear) nodes does this vibration have? A.

One

C.

Three

D.

Four

E.

Five

CHEM 241 Fall 2017 Ch.2 − p.21

© Drs. XO, PHB, CWR

2-D Waves – Drumskins (question b)

CHEM 241 Fall 2017 Ch.2 − p.22

How many circular nodes, (including the outer ring) does this vibration have? A. One B. Two C. Three D. Four E. Five

© Drs. XO, PHB, CWR

Vibrations on a String − The Particle in a Box

If an oscillating string is anchored to the walls of a box of length a, only certain frequencies result in a symmetric standing wave.

Note: also see Dr.Bird’s version in Extra Slides at end (phrased differently) + see any Phys.Chem. text e.g., Noggle.

inside box, potential E V=0

V = 0

x

V =

CHEM 241 Fall 2017 Ch.2 − p.23





Differentiating  = sin(n  x / a) twice with respect to x : (reveals way wave’s curvature changes with position)

dψ = ( nπ / a ) cos( nπ x / a ) dx

then,

dψ = −( nπ / a ) 2 sin( nπx / a ) = − (n 2π 2 / a 2 )ψ 2 dx 2



For wave to oscillate nicely in box of length a : λ = 2a/n (1/2, 1, 3/2, 2… wavelengths fit in box) Subbing back into 2nd derivative equation:



d2 ψ 2 2 π λ / )ψ = −(4 2 x d NOTE: see Wikipedia “second derivative” for help visualizing…

Miessler Fig.2.3-2.4

Vibrations on a String − The Particle in a Box

© Drs. XO, PHB, CWR

CHEM 241 Fall 2017 Ch.2 − p.24

To make the wave represent a particle in a box (e.g. electron in an atom) instead of a string, we can substitute in its de Broglie wavelength:  = h/m v So:

d2 ψ π 2 / λ2 )ψ 2 = −(4 dx

d2 ψ 2 2 2 v π /h 2 )ψ 2 = −(4m dx

The equation is eventually supposed to represent an electron near a nucleus, so we treat it as (i) moving in some fashion & (ii) being attracted to the nucleus. So, using the total energy = kinetic energy + potential energy, we get: E = ½ m v 2 + V thus v 2 = (2/m)(E - V) Thus: d 2 ψ

dx

2

= −(8mπ /h )( E − V )ψ 2

2

(there is an eigenvalue E for each n) or

d2 ψ + (8mπ 2 /h 2 )( E − V )ψ = 0 2 dx

Of course, there is no such thing as a three-dimensional string, so there is no 3D equivalent of the equation describing the motion of such an object, nor is the sine wave “particle in a box” a fully appropriate model for a real atom. But…. In three dimensions, this equation becomes the Schrödinger equation:

∂ 2ψ ∂ 2ψ ∂ 2ψ 2 2 π /h )( E − V )ψ = 0 + + + (8m 2 2 2 ∂x ∂y ∂z

Drs. XO, PHB, CWR

Schrödinger’s Equation: eigenfunctions, eigenvalues & the meaning of Ψ

CHEM 241 Fall 2017 Ch.2 − p.25

For an electron and nucleus, the ∂ 2ψ ∂ 2ψ ∂ 2ψ potential energy V = e2/r, & the (8mπ 2 / h 2 )( E − e 2 / r )ψ = 0 2 + 2 + 2 + ∂x ∂y ∂z solutions to Schrödinger’s equation (wavefunctions) are not sine waves. To achieve a physically meaningful solution for a wavefunction ψ: 1. ψ must be single-valued (1 probability value for e- at any position at same E) 2. ψ must be continuous (no abrupt changes in probability from 1 point to another) 3. ψ approaches 0 as r →  (less likely to find e- farther from nucleus) 4. total probability of finding e- somewhere in space is 1 5. all orbitals in an atom (ψA, ψB, etc) must be orthogonal (axes ⊥ like px, py, pz) When the Schrodinger equation is solved, we obtain two things, which depen...