BOHR MODEL (Approx 1913)

SCH4U CHEMISTRY

BOHR MODEL (approx 1913)

The Bohr model of the atom was based on the line spectra of the Hydrogen atom. The model also incorporated the concept developed by Einstein regarding the particle behaviour of light during emission or absorption (photon or quanta of energy).

Postulates:

1.Energy Levels

an electron can only have specific energy values in an atom

the path followed by the electrons is a circular orbit (spherical in 3-D)

these energies are called energy levels given the name Principal Quantum Number, n

the orbit closest to the nucleus is given n=1, with the lowest energy
as one moves outward the energies get larger and “n” increases (n=1,2,3,4,...)

an electron can only circle in one of the allowed orbits WITHOUT a loss of energy

2.Transition Between Energy Levels

an electron in an atom can only change energy by going from one energy level to another level, i.e. NOT in-between

light is emitted when an electron falls from a higher energy level to a lower energy level
an electron generally remains in its ground state – the lowest energy level possible (n=1 for hydrogen)
when an electron is given energy it can be bumped to a higher energy level called the excited state
as the electron drops from the excited state down to lower energy levels it emits light

Bohr was able to show that his model was able to match the Balmer series (Visible light, drop to n=2) and predict the Paschen series ( IR light , drop to n=3) and the Lyman series (UV light, drop to n=1)

Although the Bohr model could explain the behaviour of the hydrogen atom, it could not fully explain the behaviour of other atoms

QUANTUM NUMBERS

During and subsequent to Bohr’s work, others continued to probe the behaviour of light emitted or absorbed by the atom. As a result, additional components were added to Bohr’s model to improve its ability to explain the behaviours observed. This led to the introduction of quantum numbers, in addition to Bohr’s Principle Quantum Number.

Principal Quantum Number, n

Goes back to Bohr model which labeled the shells

Today called Principal Quantum Number, i.e. n=1,2,3……etc.

n=1 is closest to the nucleus with the lowest energy

Relates primarily to the main energy of an electron

e.g. Fig. 1 “energy staircase” where energy levels are like unequal steps

Secondary Quantum Number, l

Michelson found that the spectrum of H was composed of more than one line (experimental observation using spectrometry indicated that main lines of hydrogen spectra composed of more than one line – line splitting (Michelson, 1891)

Sommerfeld (1915) used elliptical orbits to extend the knowledge of the time by explaining Michelson’s work

He introduced the concept of there being additional electron subshells (or sublevels) that formed part of the energy levels and used the concept of the secondary quantum number to describe this concept

I.e. each energy “step” was a group of several little steps

“l” relates to the shape of the electron orbit and the number of values for l equals the volume of n

i.e. if n=3, then l=0,1,2

as letters:l = s, p, d, f, g

Magnetic Quantum Number, ml

it was observed that if a gas discharge tube was placed near a strong magnet, some single lines split into new lines

called normal Zeeman effect after Zeeman who 1st observed this (1897)

this was explained by Sommerfeld & Debye (1916) who thought that orbits may exist at varying angles and that the energies may be different when near strong magnets

for each value of l, ml can vary from –l to +l (each value represents a different orientation)

i.e. if l=1 then ml can be –1,0 or +1

if l=2 then ml can be –2,-1,0,+1, or +2

Summary: The magnetic quantum number ml , relates to the direction of the orbit of the electrons. The number of values of ml represents the number of orientations of the orbits that we can have.

Spin Quantum Number, ms

needed to explain additional spectral line-splitting & different kinds of magnetism

ferromagnetism-associated with substances containing Fe, Co & Ni

paramagnetism-weak attraction to strong magnets (individual atoms vs. collection of atoms)

paramagnetism couldn’t be explained until Wolfgang Pauli suggested that electrons spin on their axis (1925)

could spin only 2 ways (clockwise vs. counterclockwise) and he used only 2 numbers to describe this:

ms = +1/2 (clockwise) or –1/2 (counterclockwise)

opposite pairs of electron spins represent a stable arrangement

when electrons are paired – spin in opposite directions – the magnetic field is neutralized, while an individual electron spin can be affected by a magnet

ATOMIC STRUCTURE & THE PERIODIC TABLE

using the quantum numbers gives an ordered description of the electrons in a particular atom

the secondary quantum number, l, is presented as s, p, d, and f

to represent the shape of the orbitals

Value of l / 0 / 1 / 2 / 3
Letter designation / s / p / d / f
Name designation / sharp / principal / diffuse / fundamental

Electron orbitals

4 quantum numbers apply equally for the electron orbits (paths), as well as, electron orbitals (clouds) [see Fig. 1 & Table 2 on p. 185]

1st 2 quantum numbers (n & l) describe electrons that have different energies under normal circumstances in multi-electron atoms

the last 2 quantum numbers describe electrons that have different energies under special conditions (e.g. strong magnetic fields

we use a number for the main energy level and a letter for the energy sublevel

simpler to use 1s than n=1, l=0 and 2p is n=2, l=1…etc

if we needed the third quantum number ml we would need another designation, 2px, 2py, 2pz

Value of l / Sublevel symbol / Number of orbitals
0 / s / 1
1 / p / 3
2 / d / 5
3 / f / 7

Creating Energy-Level Diagrams

these diagrams indicate which orbital energy levels are occupied by electrons for an atom or ion

In fig.2 on p. 187, as atoms become larger & the main energy levels come closer, some sublevels may overlap

Generally the sublevels for a particular value of n, increase in energy in the order of s<p<d<f.

There are also some rules that apply to creating an energy-level diagram

Pauli Exclusion Principle - states that no 2 electrons in an atom have the same 4 quantum numbers (usually you place 1 electron with  and the other electron )

Aufbau Principle – an energy sublevel must be filled before moving into the next higher energy sublevel

Hund’s Rule – one electron is placed into each of the suborbitals before doubling up any pair of electrons

These are the “rules” that are followed until all the electrons have been placed in their proper place

(see Fig. 6 p. 188 for order diagram.)

1s, 2s, 2p,3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 6f, 7d, 7f.

Order of filling sub-shells:

7s7p7d7f7g

6s6p6d6f6g

5s5p5d5f5g

4s4p4d4f

3s3p3d

2s2p

The filling of sub-shells can also be shown on an energy level diagram as follows:

5p5p5p

4d4d4d4d4d

4p4p4p

3d3d3d3d3d

3p3p3p

2p2p2p

This method allows one to see the different energy levels in diagram form – energy is on the vertical axis. Each underline (orbital) can take up to 2 electrons – one electron  (clockwise spin) and the other electron  (counterclockwise spin)

Sample problem 4:

O = 8 electrons

5p5p5p

4d4d4d4d4d

4p4p4p

3d3d3d3d3d

3p3p3p

3s

2p2p2p



Fe = 26 electrons

5p5p5p

4d4d4d4d4d

4p4p4p

3d3d3d3d3d

3p3p3p

2p2p2p

Creating Energy-Level Diagrams for Anions

Are done the same way except add the extra electrons that corresponds to the ion charge to the total number of electrons before showing the distribution of electrons e.g. S has 16 electrons but S-2 has 18 electrons

Creating Energy-Level Diagrams for Cations

Draw the energy-level diagram for the neutral atom first, then remove the number of electrons needed (for the correct ion charge) from the orbitals with the highest principal quantum number

Homework:

Nelson 12 p. 191 #’s 1-4

Electron Configuration

Provide the same information in a more concise format

Examples:

O: 1s2 2s2 2p4

S-2: 1s2 2s2 2p6 3s2 3p6

Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6

Sample Problems p.192 & 193

Shorthand Form of Electron Configurations

There is an internationally accepted form of shorthand that can be used where the core electrons are expressed by the preceding noble gas and just adding the electrons beyond the noble gas

E.g. Cl: 1s2 2s2 2p6 3s2 3p5 becomes [Ne] 3s2 3p5

Homework:

Nelson 12 p. 194 #’s 6-11

Explaining the Periodic Table

Period / # of elements / Electron Distribution:
Groups: 1-2 13-18 3-12 -
Orbitals: s p d f
Period 1 / 2 / 2
Period 2 / 8 / 2 6
Period 3 / 18 / 2 6 10
Period 4-5 / 18 / 2 6 10
Period 6-7 / 32 / 2 6 10 14

Can use the filling of the subshells to explain the Periodic Table

Noble gases all have ns2 np6 in the outer shell of electrons

These types of patterns of configuration are seen in the representative elements

Transition elements can be explained as elements filling the d elements therefore the transition elements are sometimes referred to as the d block of elements

Lanthanides and actinides are explained by the filling of the f orbitals

Explaining Ion Charges

Zn: [Ar] 4s2 3d10 has 12 outer electrons but Zn+2: [Ar] 3d10 and it is unlikely that Zn would give up 10 electrons to go to 4s sublevel

Pb: [Xe] 6s2 4f14 5d10 6p2 lead can either lose 2 6p electrons to become Pb2+ or lose 4 electrons from the 6s and 6p orbitals to form Pb4+

Explaining Magnetism

To explain magnetism we can draw the electron configuration of a ferromagnetic element, e.g. Fe [Ar] 4s2 3d6 = 1 pair + 4 unpaired= unpaired electrons cause the magnetism?

Ruthenium which is right under iron is only paramagnetic (weakly magnetic)

Result occurs probably because the atoms form groups called domains that cause this type of magnetism

“Ferromagnetism is based on the properties of a collection of atoms, rather than just one atom”

Anomalous Electron Configurations

List on p.196 shows some anomalies in predictions of electron configurations

evidence suggests that half-filled and filled subshells are more stable (lower energy) than unfilled subshells

i.e. Cr: [Ar] 4s2 3d4 expected but in fact it is [Ar] 4s1 3d5

appears more important for d subshells and in the case of chromium an s electron is promoted to the d subshell to create two half-filled subshells

the justification is that the overall energy state is lower after the promotion of the electron

Homework: Nelson 12 p. 197 #’s 1-14

PROBABILITY MODEL

(WAVE MECHANICAL MODEL or

QUANTUM MECHANICAL MODEL)

DeBroglie (1924)

Proposed that moving electrons could be considered to behave like waves

experimentation showed that electrons can exhibit diffraction patterns like light – a key part of the wave model of light
derived expression relating wave properties to particle properties

ג = h/mvwhere:ג = wavelength of

particle wave

h = Planck’s Constant

m = mass of particle

v = speed of particle

for a baseball of m= 0.145 g with v=27 m/s

ג = 10-34 m

for an electron of m = with v=3.00x108 m/s

ג = 100 x 10-12 m (100 pm)

visible light has a wavelength range of 400 to 750 nm

Schrodinger’s Theory (1926)

extended wave properties of electrons to their behaviour in atoms and molecules

consider Bohr’s Model – electron orbits nucleus like the earth around the sun in a continuous path
in quantum mechanics – electron does NOT have a precise orbit in an atom

using principle of standing waves (wave theory) and the quantum numbers, Schrodinger was able to devise an expression, called the wave equation, that could identify the space an electron will occupy

Heisenberg’s Uncertainty Principle (1927)

Heisenberg claimed that it was impossible to know at the same time (absolutely), both the position and momentum of an electron in an atom

(Δx)(Δpx) ≥ h/4

where:Δx = uncertainty in position

Δpx = uncertainty in momentum

another way of saying this is:

“if you know where a particle is, you cannot know where it is going”

because of the interaction of photons of light with electrons, once one identifies where the electron is, then the light will excite the electron and send to a place unknown
nonetheless, one can make a statistical statement about where an electron is in an atom – one can indicate the probability of finding an electron at a certain point in an atom
to do this we can employ the wave equation
suggests that the atom does not have a definite boundary – unlike the Bohr model