Bonding: Important Terms and Hybridization

Before we get started on this day's lesson, it would greatly benefit you if you re-read these posts:

Types of Bonds
Atomic Structure (electronic configurations in particular)

Done that? Good.

Let's go over some important terms:

Now if you recall, covalent bonds are formed due to the overlapping of atomic orbitals containing unpaired electrons with opposite spins. Such an orbitals are referred to as bond pairs, i.e they can participate in bonding.

An orbital which cannot participate in bonding, i.e one with paired electrons is called a lone pair.

Now, it is only logical that the strength of a bond directly correlates to the extent of overlapping. Greater the overlapping, stronger is the bond.

Orbitals can overlap in 2 ways:

(i) axial overlapping (along the axis): this results in the formation of a sigma(σ) bond.

(ii) sideways overlapping: results in the formation of a pi (π) bond. A pi bond is representative of a diffused electron cloud above and below the sigma bond that is shared by the two bonded atoms.

Note: That only one sigma bond can be formed between two atoms. The first bond formed is always a sigma bond.

Bond order: the no. of bonds present between atoms in a molecule.

a) Single Bond (eg. C-C): 1σ bond
b) Double Bond (eg. C=C ): 1σ + 1π bond
c) Triple Bond (eg. C≡C): 1σ + 2π bond

Bond Length: Is the average distance between the nuclei of two bonded atoms.

Study the energy diagram given below to better understand this phenomenon.

H2 Bond length

Quick Tip: Bear in mind that when two atoms approach one another, there are attractive (between electrons and nucleus) and repulsive (inter-electronic and inter-nuclear) forces at play. Initially the atoms move closer under the influence of attractive forces and as they move closer their potential energy decreases (generally, energy is released during bond formation). They reach a certain minimum distance at which attractive and repulsive forces are evenly matched. If the atoms move any closer, repulsive forces will dominate and cause the energy diagram to spike (as can be seen on the left). Since lower energy states are preferred by all systems, atoms are thus held a certain distance apart, where the the attractive and repulsive forces are evenly balanced and energy level is minimum. This minimum distance is called the bond length.

Bond Angle In water molecule

Remember: Bond Strength ∝ Bond Order ∝ 1/Bond length

Bond Angle: Angle Subtended by the bonded molecules.

Bond Disassociation Energy: Energy required to break a certain bond and take the bonded atoms to their gaseous states.

Okay, let us consider the water molecule. If we were to remove the Hydrogen on the right, we would need to expend a certain amount of energy, says, BE-1. Now, it is only natural that the oxygen atom bereft of a hydrogen atom would hold on more dearly to the second hydrogen on the left. So now if we were to remove the second hydrogen we would have to supply a slightly greater amount of energy (BE-2)

BE-2 > BE-1

So for the sake of convenience, we take the average of the two Bond Disassociation Energies and call it Bond Energy.

Bond Energy (O-H) = (BE-1+BE-2)/2

That pretty much covers all you need to know to follow whatever comes next.

Hybridization <This Shit IS IMPORTANT>

Central Atom: atom forming the maximum no. of bonds.

Orbitals of the central undergo hybridization ( in layperson language, it refers to the mixing of atomic orbitals) to form hybrid orbitals which overlap with "normal" orbitals of neighboring atoms to form bonds.

Conditions: i) Orbitals should have the same or almost the same energy.
ii) Hybrid orbitals formed should also have similar energy levels.
iii) Number of orbitals remains the same.
iv) Both bond pairs and lone pairs can take part in hybridization.

Types of Hybridization 

sp hybridization: forms 2 sp hybrids, each with 50% s and 50% p character.

sp² hybridization: forms 3 hybrid orbitals, each with 33.33% s and 66.66% p character.

sp³ hybridization: forms 4 orbitals each with 25% s character and 75% p character.

sp³ d hybridization: 5 orbitals with, 20% s, 60%p and 20% d character.

Sp³d² hybridization: 6 orbitals with 16.66% s, 50% p and 33.33% d character.

(in case you haven't already noticed, the letters (s,p,d etc.) indicate the orbitals participating in hybridization.)

Formation of Hybrid Orbitals

SP hybridization 

in BeCl₂ Beryllium is sp hybridized. 

Be in  ground state: 2s² 

One of the 's' electrons is excited and moves to the p orbital

Be excited state: 2s¹ 2p¹

Now, the s and the p orbitals undergo hybridization to form two sp-orbitals, with an unpaired electron in each.

Consider Chlorine. The chlorine atom is in the ground state and has the electronic configuration: 3s² 3p⁵

It is evident that the chlorine atom has an unpaired electron in a p-orbital. 

Now, the sp-hybridized berylium atom overlaps with two chlorine atoms forming the compound BeCl₂

Sp² hybridization

in BCl₃  Boron is sp²  hybridized.

B in the ground state: 2s² 2p¹

One of the 's' electrons is excited and moves to the p orbital. 

B in the excited state is now: 2s¹ 2p²

Now, the s and the 2 p orbitals undergo hybridization to form three sp²-orbitals, with an unpaired electron in each. Each of these hybrid orbitals bonds with the chlorine p-orbital with a bond pair (unpaired electron).

      

      

Sp³ hybridization

Carbon in CCl₄  is sp³  hybridized.

The process is pretty much the same.

C in ground state: 2s² 2p²

C in the excited state: 2s¹ 2p³

Four hybrid orbitals are thus formed, with an unpaired electron in each. These then overlap with the Chlorine p-orbital with a bond pair.

Sp³d hybridization

P in the ground state:  3s² 3p³ 3d⁰
P in the excited state: 3s¹ 3p³ 3d¹

Five hybrid orbitals are formed, with an unpaired electrons in each. Each of these then overlap with the Chlorine p-orbital with a bond pair (i.e unpaired electron). Note: that the axial chlorine atoms project out of the plane of the molecule.

Sp³d² hybridization

 S in the ground state:  3s² 3p⁴ 3d⁰

 S in the excited state: 3s¹ 3p³ 3d²

6 hybrid orbitals are formed with unpaired electrons in each which in turn bond with orbital of fluorine atom with a bond pair. 4 fluorine atoms arrange themselves along the vertices of  a square in the plane of the molecule and two project outwards

Sp³d³ hybridization

I in the ground state: 5s² 5p⁵ 5d⁰
I in the excited state: 5s¹ 5p³ 5d³

7 hybrid orbitals are formed with unpaired electrons in each which in turn bond with orbital of fluorine atom with a bond pair. 5 Fluorine atoms arrange themselves along the vertices of a pentagon in the plane of the molecule and two axial atoms project outwards.

Okay that does it for today. In the next post I shall deal with VSEPR theory and arrangement of molecules in 3-D space.

_____________

That's all Folks!

The Passive Observer Out!

What The Fact...Fire!

What is Fire?

"Fire" is rapid oxidation of a substance in an exothermic process (combustion). A fire is started when a combustible material combines with sufficient quantities of an oxidizer ( such as oxygen or an oxygen rich compound. Non-oxygen oxidizers can replace oxygen).



The flame is the visible portion of the fire and comprises excited gas/fuel/unburnt particulate matter.

Energy released by the exothermic process is sufficient to excite the electrons in some of constituent atoms and transient intermediates comprising the flame. The excited electrons then fall back to the ground state releasing the absorbed energy as visible light.

Quick Tip: Okay, picture this, an electron walks into a party and drinks a lot. (The brewskis equal energy.)
Now he gets super hammered (i.e goes to a higher energy state) and then later throws up (i.e returns to the ground state). Now if we assume that the electron drank nothing but beer and if we ignore the trace amounts of gastric juice, saliva, and his lunch in his vomit, we can safely say that beer (energy) he egested is equal to the beer (energy) he ingested.

The color of the flame depends primarily on two factors: blackbody radiation and spectral band emission

Typically, in case of complete combustion the excited gas molecules emit pale blue light due to energy transitions (explained above). This is the reason why most gas flames are blue in color.

However, in case of incomplete combustion, the yellow/orange/red color of the flame is due to incandescence of soot particles which glow red hot.

As you may already know that all bodies with temperature above absolute zero (0 K)  emit certain electromagnetic radiation corresponding to their temperature.

(Humans emit electromagnetic radiation too, so does your cat and your dog and everything you see around you. The reason we aren't suffused with an incandescent glow is because we are too "Cool" to radiate visible light, rather, we emit infrared radiation..oh yeah!)

Temperature as you know is a measure of the motion of particles constituting matter, and since some of the particles constituting any object will carry charge their movement will lead to the release of electromagnetic radiation i.e light.

The Shape of the Flame

The familiar teardrop shape of a candle flame, here on earth is due to buoyant convection of gas molecules.
The rising hot gases also carry unburnt soot particles to the top of the flame, which make the flame appear yellow.

However, in micro-gravity  convection currents are absent and the flame appears somewhat spherical, spreading out in all directions. The flame also appears blue because the soot particles settle down, instead of  being carried to the top of the flame by convection currents.



Starting A Fire

The match head of a modern "safety match" is typically composed of  potassium chlorate, with a little sulfur and some form of siliceous filler and glue. Some heads contain antimony(III) sulfide to make them burn more vigorously. Safety matches ignite due to the extreme reactivity of phosphorus with the potassium chlorate in the match head.

The main reactant on the striking surface on modern matchboxes is red phosphorous. Safety matches ignite due to the reaction between potassium chlorate and phosphorous. The striking surface also consists of some  amount of abrasive material like powdered glass.

DIY Strike Anywhere Matches: Strike anywhere matches are hard to come by (especially here in India) so here's how you can make some at home.

What you need: a) Sand paper
                         b) Several matchboxes
                         c) Matchsticks

Using the sandpaper, sand off the red phosphorous from the striking surface of a couple of matchboxes ( you may need about 5-10)

Collect the red phosphorous in a container and mix it with some water. Dip the match heads in the mixture and coat them liberally, after which you can leave them out to dry. Once the water has evaporated, test the matches by striking against any rough surface.


Starting a fire without a match

Combustion, ultimately, is a chemical reaction. Here's a nifty way to start a fire you using chemistry.

Add glycerin to some potassium permanganete, give it about 30 seconds to initiate and Voila, Fire!

What happens here is the glycerin is oxidized extensively by the potassium permanganete and the resulting reaction is highly exothermic and produces a flame.


___________________________

That's all Folks!

The Passive Observer Out!


Confused? Reduction-Oxidation..dafuq?

Do some quick reading

Redox Reactions

The Periodic Table

The periodic table is a system in which elements are organized on the basis of their atomic numbers, electron configurations, and recurring chemical properties. 

Several scientists, Newland, Doberneir, Meyer, Mendeleev..among others, tried to come up with such a system. 

Mendeleev came up with the first widely recognized periodic table in which he arranged elements in horizontal rows and vertical columns and grouped elements with similar chemical properties together.

As the story goes, the idea for his periodic table struck Mendeleev when he was playing with himself (playing cards, you perv..a game called solitaire or patience).

click to enlarge

Mendeleev concluded that chemical properties of an element are a periodic function of their atomic masses. He also predicted the existence of germanium, gallium and scandium. 

Sure there were a few issues with his work.

Problems:

1. Mendeleev couldn't account for the isotopes of an element. (isotopes of an element have the same atomic number but different atomic masses.). For example, an isotope of carbon is 14C. This would have to be accommodated along with nitrogen. But 14C shows properties similar to those of carbon (12C). 

2. In order to ensure that elements in a column have similar chemical properties, Mendeleev was forced, in a few cases, to put an element of slightly higher atomic weight ahead of one of slightly lower atomic weight. Thus, tellurium (atomic weight 127.6) had to be put ahead of iodine  (atomic weight 126.9) in order to group Iodine with other halogens on the basis of similar chemical properties.

But his system worked well (for the most part) and he had an awesome beard, and he has a brand of  vodka named after him..so he gets the The Passive Observer seal of approval.


The modern periodic law differs from Mendeleev's and states that chemical properties of an element are periodic functions of their atomic number.

In the modern periodic table (pictured below) the rows are called "periods" and the columns are called "groups"

click to enlarge

Groups 1 and 2 (alkali metals and alkaline earth metals) constitute the s-block with their valence electrons occupying the s-orbital. Their outer electronic configuration is ns^1-2

Groups 13-18 constitute the p-block. Their outer electronic configuration is  ns² np^1-6

Groups 3 to 12 constitute the d-block (also called the transition elements) and are characterized by the filling of inner d-orbitals. These elements have the general outer electronic configuration (n-1)d^1-10 ns^0-2

Quick-Tip: Think Power Rangers.

Whoever came up with this system, must've been a fan of this show

Now look at the dismembered two rows, the lanthanoids  and actinoids, they are called the f-block or inner transition elements and their general outer electronic configuration is (n-2)f^1-14(n-1)d^0-1 ns²

 Locating an element

Quick Tip: Count from the nearest noble gas.

For instance, if I asked you to locate Bismuth, atomic no. 83 (and well no peeking at the periodic table)
The closest noble gas happens to be Radon, atomic no. 86, located in period 6 group 18. Therefore bismuth, atomic no. 83 is present in period 6 and group 15 (moving 3 spaces back).

Let's try Silver, atomic no. 47. (again don't sneak a peek at the periodic table). The nearest noble gas happens to be Xenon, atomic no. 54, which is located in group 18 period 5. Therefore Ag is present in  period 5, (and moving back 7 spaces) group 11.


Number of Elements in a Period

Each row (period) corresponds to the filling of a new energy level. 

In the first period, n=1 and the 1s orbital is filled. Since the 1s orbital can accomodate a total of 2 electrons, the first period also houses 2 elements (H and He)

In the second period, n=2. Thus, the 2s and 2p orbitals are filled. Therefore the 2^nd period accommodates a total of 8 elements (since the 2s and 2p orbitals can together accommodate 8 electrons (6+2) )

Similarly in the 3^rd period 3s and 3p orbitals are filled and it can accommodate 8 elements.

In the 4^th period the 4s, 3d and 4p orbitals (refer to aufbau principle) are filled and it can thus accommodate a total of 2+10+6= 18 elements.

Similarly the 5^th period corresponds to the filling of 5s 4d and 5p orbitals and thus accommodates 18 elements.

The 6^th period corresponds to the filling of the 6s 4f 5d and 6p orbitals and can thus accommodate a total of 32 elements.

Similarly for the 7th period , the following orbitals are available 7s 5f 6d 7p  and it can accommodate a total of 32 elements.

Hydrogen and Helium

Hydrogen has one s-electron and can be placed in group 1 with other alkali metals. Hydrogen can also gain an electron to attain stable gas configuration and thus at times behaves like group 17 (halogens) elements. 

Helium, has the electronic configuration 1s² and strictly speaking should be a part of the s-block, but since it has a completely filled valence shell its chemical properties are akin to those of other group 18 (noble gases) elements.

Nomenclature of Elements with Atomic Number Greater than 100


Ready-Reference Chart

Digit             Name                   Abbreviation

0                   nil                                  n
1                   un                                  u
2                   bi                                   b
3                   tri                                   t
4                  quad                               q
5                  pent                                p
6                  hex                                 h
7                  sept                                s
8                  oct                                 o
9                  enn                                e  

Therefore an element with atomic number 116 would be called Ununhexilium (Uuh)


________________________

That's all folks!

Stay tuned for a follow-up post on periodic trends.

till then, The Passive Observer Out

Atomic Structure: The Quantum Mechanical Model

The Story So Far: "Atomic Structure: The Story"

Basically we covered how several scientists tried (and failed) to come up with a satisfactory atomic model.

Then came along Schrodinger (you can learn more about him and his cat here and here and check out this minute-physics video here ), and he came up with this fancy equation we now know as "Schrodinger's Equation" (surprise, surprise!)

 It is a three dimensional, second differential, time- dependent equation. (Jargon..ignore this)

<DO NOT IGNORE ANY OF THIS>

For a system such as an atom or molecule whose energy does not change with time, Schrödinger’s equation can be written as,   

Now this equation was solved to obtain quantum numbers (among other things....but we won't get into that right now). 

Quantum Numbers: Out of the 4 quantum numbers only the first 3 were obtained from Schrodinger's Equation and infact only the first three are needed to define an Orbital.

 n = principal Quantum Number. (Orbit)

 l = azimuthal Quantum Number. (Sub-shell)

m_l = magnetic Quantum Number. (Orbital)

m_s = spin Quantum Number.

An Orbital is the region in 3 dimension space where there is maximum probability of finding an electron (since we cannot ascertain for sure the exact position of an electron (refer: Hesienberg's Uncertainty and Dual Nature of Matter)

Quick Tip: Quantum numbers are like the address of an electron. Just like your address has a house number, a street name, a city name and an area code..quantum nos. are used to describe the orbit, subshell and orbital (i.e the region where you are likely to find an electron...his house that is).

But..eh Shit Happens. 

Principal Quantum Number (n)

The principal quantum number n describes the average distance of the orbital from the nucleus — and the energy of the electron in an atom. It can have positive integer (whole number) values: 1, 2, 3, 4, and so on. The larger the value of n, the higher the energy and the larger the orbital. 

The Angular Momentum Quantum Number (l)

The angular momentum quantum number l describes the shape of the sub-shell  

The angular momentum quantum number l can have positive integer values ranging from 0 to n–1. F

The value of l defines the shape of the orbital, and the value of n defines the size.

Ready Reference Chart #1

Value of l     Subshell

0                    s

1                    p

2                    d

3                    f

4                    g

Ready Reference Chart #2

Value of n       Value(s) of l                  Sub-shells

n=1;                 l=0                            1s

 n=2;                l=0, 1                        2s                2p

 n=3;                l=0, 1, 2                    3s                3p                3d

 n=4;                l=0, 1, 2                    4s                4p                 4d              4f

No. of subshells = n

The Magnetic Quantum Number (m_l )

This number tells us about the orientation of the orbitals in 3-dimensional space. 

 The values allowed are integers from –l to 0 to +l. 

For example, if the value of l = 1 (p orbital), you can write three values for this number: –1, 0, and +1. 

This means that the p subshell has 3 orbitals, each with the same energy but different orientation.

Shapes and Orientation of Various Orbitals

An orbital can accommodate maximum of 2 electrons with opposite spins. 

So if an orbital is thought of as a house, then no more than two people can live in that house and the two people live on different floors cause they can't stand each other.

Numbers of orbitals in any sub-shell = (2l+1)

The Spin Quantum Number (m_s )

This describes the spin of an electron. 

The spin quantum number has 2 values +1/2 and -1/2

+1/2 = electron spins clockwise (spin up) and is indicated by an arrow pointing upwards (↑).

-1/2 = electron spins anticlockwise (spin down), indicated by arrow pointing downwards (↓).

[By convention when there is only electron, it is taken as  +1/2]

The Electron Balance Sheet

Numbers of sub-shells in any orbit = n

Numbers of orbitals in any sub-shell = (2l+1)

Max no. of e- in any orbital = 2

Max. no. of e- in any sub-shell = 2(2l+1)

No. of orbitals in any orbit = n²               

Max. No. of electron in any orbit =  2n²

Filling in Electrons

While filling in electrons we follow the following rules:

1. Pauli exclusion principle

No two electrons in an atom can have the same value for all the 4 quantum numbers. 

2.Hund’s rule of maximum multiplicity

Pairing of electrons in a sub-shell will not take place until all the orbitals are at least half filled. 

Half filled and fully filled orbitals have extra stability, because half filled and fully filled orbitals allow electrons to jump about and in doing so they expend energy (exchange energy) and lower energy equals greater stability.

3.Aufbau Principle

Electrons are filled in sub-shells in increasing order of energy.

For Hydrogen atom, the energy is given by the principle quantum no. n, whereas for other atoms, energy of subshell is given by (n+l) values. 

Orbitals with lower values of (n+l) have lower energy. If two sub-shells have the same value of (n+l), then the one with lower value n has lower energy.

Order of filling in subshells. superscript indicates max. no. of electrons that can be accommodated in a subshell

DIY: Write down the electronic configuration of the first 40 elements in the periodic table...do that and you'll get the hang of it. 

Be careful with chromium and copper.

Chromium expected electronic config. :  [Ar] 4s² 3d⁴

But remember Hund's rule (yes, the one from up there).."half filled orbitals have maximum stability.

So one of the s electrons is excited and sent to the d-orbital which now has 5 electrons (half filled, since the d-subshelll can accommodate a maximum of 10 electrons)

So Chromium's real electronic config. :  [Ar] 4s¹ 3d⁵

Same thing goes for copper. Copper's electronic configuration is :  [Ar] 4s¹ 3d¹⁰   (instead of [Ar] 4s² 3d⁹  )

Here's the first 20 to get you started.

Tip: Noble gases are like checkpoints. To abbreviate the electronic configuration of an element the electronic configuration of the preceding noble gas is taken out and put in brackets, since all but the last few subshells of any element are identical to those of the noble gase, and the outer electronic configuration of the element is put down.

Therefore, Sodium's electronic configuration can be written as [Ne]3s¹

Electronic Configuration of Ions

For cations, remove electrons from the outermost shell irrespective of the order in which the shell was filled. 

The number of electrons removed is equal to the charge on the cation.

For anions, add electrons equal to the charge on the anion.

^{_________________________}

That's all Folks!!

The Passive Observer Out!

Atomic Structure: The Story

Disclaimer: This post reads like a story...nothing heavy here. Sit back and relax.

The idea of  "atoms" as fundamental, indivisible particle of nature is Old..very old...Think ancient greece and ancient India....yup that old. In fact the word "atom" comes from the ancient Greek adjective atomos, meaning 'indivisible'. 


John Dalton was one of the first people to propose that atoms are responsible for chemical interactions and he put for the following postulates in atomic theory

1. Elements are made of extremely small particles called atoms.
2. Atoms of a given element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties.
3. Atoms cannot be subdivided, created, or destroyed.
4. Atoms of different elements combine in simple whole-number ratios to form chemical compounds.
5. In chemical reactions, atoms are combined, separated, or rearranged.

And he had it right, for the most part at least.

Discovery of Sub-atomic Particles

Enter Sub-atomic particles. Now these buggers shook up the scientific community..

Cathode Rays and The Discovery Of Electrons 

Now atoms were thought of as indivisible particles untill the JJ Thomson discovered the electron. He did so by studying cathode rays in a Crookes tube. Now a Crookes tube is an evacuated glass tube with electrodes on either end and a coating on phosphorescent material on one side. Now, when a voltage was applied across the electrodes the phosphorescent material began to glow and Thomson concluded that this glow was due to certain rays originating at the cathode and thus he called them cathode rays (GENIUS!!).

Now on further experimentation, the following characteristics of cathode rays were observed.

Characteristics of cathode rays

1) Cathode rays originate at the cathode and consist of a stream of negatively charged particles.

2) Cathode rays travel in straight lines (they cast shadows of objects placed in their path).

3) Cathode rays possess high energy.

4) The e/m(specific charge) ratio of cathode rays remained constant.

5) The rays are deflected by an electromagnetic field.

Charge of an  =1.6×10-19 C (calculated by milikan)

Mass of an  =9.1×10-31 kg

 e/m ratio 1.758×10¹¹ C/kg

Anode (Canal) Rays  & The Discovery of Protons

Canal (Anode) rays were called so as they originated in the region between the anode and cathode.

(Thank you Mr. Point Out the Obvious...these physicists could've made use of some imagination when they came up with these names).

 They consisted of positively charged ions and moved towards the negatively charged cathode. They were produced as a result of the interaction between cathode rays and gaseous atoms. During such interactions, the energy of the cathode rays was imparted to the gaseous atom resulting in knocking out of one or more electrons from the gaseous atom. This process lead to the formation of positively charged ions and these positively charged ions constituted the anode rays. Unlike cathode rays the e/m ratio of anode rays did not remain a constant and varied with the gas that was taken in the tube.

 When Hydrogen gas was taken inside the tube and a voltage was applied, the hydrogen molecule split into hydrogen atoms which then interacted with the cathode rays and lost their lone electron it. The particle thus obtained was the "Proton". 

Tidbits: The mass of proton is approx 1837 times that of an electron. Protons were discovered by Goldstein.

Discovery of Neutrons

A thin strip of beryllium was bombarded with α-particles and it was found that new rays were coming out which consisted of particles having unit mass but no charge. The particles were named "neutrons" and James Chadwick was responsible for this discovery. Protons and neutrons together are collectively known as nucleons

 So now that we have all the fundamental particles on hand, let's start putting together "The Atom"

Now the first atomic model was given by Thomson and was called the "Plum Pudding Model" (finally!!).
So anyway, the electrons in this model were embedded in a sphere of positive charge, kinda like raisins in a pudding and hence the name. Unfortunately, this model of the atom was inconsistent with later experimental observations.

<Sorry JJ, you did good though, that's why they gave you the Nobel prize....don't worry, it's okay to be wrong>


Rutherford's Scattering Experiment and Rutherford's Model: 

Rutherford bombarded a gold foil with alpha particles ( He 2+ ions) and placed a fluorescent screen of zinc sulphide behind the foil, which produced a tiny flash of light whenever it was hit by an alpha particle.

He then made the following observations:

1) Most of the alpha particles passed through the foil undeflected.
2) A small fraction of them were deflected by small angles. A few, however bounced back.

This forced Rutherford to conclude that "The Atom" was mostly empty space, Yes, empty space as most of the alpha particles passed without any deflection, and that there was a region of concentrated positive charge within the atom. These results were inconsistent with Thomson's model which suggested that the mass of the atom was uniformly distributed.

Rutherford's model of the atom was akin to a solar system, where the nucleus i.e region of positive charge was positioned at the center and the electrons moved around it in orbit.

Well, he was wrong too. Now, basic physics, a body moving in a circular orbit undergoes acceleration even if it is moving with a constant velocity. And, according to Maxwell's electromagnetic theory a charged body (like an electron) when accelerated would emit radiation. Thus an electron in orbit will release energy and its orbit will continue to shrink untill it spirals into the nucleus and the atom collapses. (which would take approximately 10^-8 seconds...and that is not a lot of time..so, yeah thank god rutherford got it wrong).

Quick Tip: Picture a child made to run around a tree, initially he is full of energy and runs large circles but after a while as he gets tired (i.e looses some of his energy) he starts running smaller and smaller and smaller circles and eventually, well, he collapses.

(No children were harmed in the making of this post.)

The next Big Thing was the BOHR MODEL. But we'll get to that in a minute...maybe more than a minute, but background is important people.

So Buildup to the Bohr Model:

A Particle or a Wave...?

Wave Nature:

James Maxwell suggested that when electrically charged particles move under acceleration, alternating electrical and magnetic fields are produced and these fields are transmitted as electromagnetic waves/radiation. He also made the connection that light waves were also associated with these electromagnetic oscillations.

c=vλ , where c is speed of electromagnetic radiation (all em radiations travel at a constant speed of 3.0 x 10^8 m/s in vacuum) v is frequency and λ the wavelength.

Particle Nature:

Now, this guy called Planck comes around and says that all atoms can emit(or absorb) energy in discrete packets called quantum i.e atoms don't emit or absorb energy in a continuous manner. He also gave the following relation:

E=hv, where E is energy emitted/absorbed, h is planck's constant and v is frequency of electromagnetic radiation.

The particle nature could explain phenomenon like black-body radiation and photoelectric effect satisfactorily, however was inconsistent with the known wave behavior of light. 

So the scientists had no choice but to accept the fact that light has both wave and particle like characteristics.

[A few key topics like the photoelectric effect, spectra and line spectrum of hydrogen and Rydberg's formula have been omitted in this post. I promise I will cover them later, but I advise you to look them up yourself.]


Bohr Model:

Bohr put forth the following Postulates:


1) An Atom consists of central positive part called nucleus around which the electrons are revolving in selected circular orbits .These orbits are associated with definite energies and are also called energy shells or energy levels. 

2)As long as the electron is in the orbit, its energy does not change with time.i.e. energy of an electron in a particular orbit remains constant. This is why these orbits are also called stationary states.


3)Electrons can occupy only those orbits where the angular momentum is an integral multiple of  .
    
i.e mvr= n.(h/2π)   where n=1,2,3,…..

Thus, Bohr quantized angular momentum.

4)Electrons can move only from one orbit (energy level) to another. 
     
 (Bohr frequency rule)  ∆E= E2-E1 = hv 

When electrons move a characteristic amount of energy is absorbed (when electrons move from lower to higher level) or emitted (when electrons move from higher to lower level). Since each orbit has a characteristic energy, emission and absorption of energy occur only in discrete values (equal to difference in two energy levels) and will correspond to a characteristic frequency and wavelength. Energy change is not gradual or continuous but is abrupt and this explains the fact that atomic spectra are discontinuous.

E2=energy of higher level  

E1=energy of lower level.

Bohr gave useful relationships for calculating the energy and radius of electron in an orbit.

As Z increases energy value becomes more –ve and radius decreases i.e.electrons will be held tightly to the nucleus

As n increases, r will increase i.e. the electron will be present away from nucleus).
Velocity of electron in orbit increases with increase in positive charge on nucleus and decreases with increase in the value of n. 

Advantage of Bohr’s model of atom

1)Bohr’s model of atom imparted certain degree of stability to the model of atom.
2)It was the first model of atom which incorporated the principles of quantum mechanics (Bohr quantized angular momentum and energy.)
3)Bohr’s model of atom was able to explain the spectra of hydrogen and H-like ions (hydrogenic ions) i.e. simple spectra.
4)Bohr’s model of atom gave certain useful relationship to calculate the energy of electron, radius of orbit etc.

Disadvantage of the Bohr’s model of atom

1)Bohr’s model of atom was two dimensional.
2)Bohr’s model was able to explain simple spectra but failed to explain complex spectra.
3)Bohr’s model of atom failed to explain Zeeman effect and Stark effect.
4)Bohr’s model of atom went against de Broglie relationship and Heisenberg’s uncertainty principle.
5)Bohr’s model could not explain bonding of atoms, or how molecules are formed from atoms and shapes of molecules.

(*Zeeman Effect-splitting of spectral lines in the presence of a magnetic field.

*Stark-Effect-splitting of spectral lines in the presence of an electric field) 

Towards the Quantum Mechanical Model (but not quite there yet...)

Seriously..make up your mind!

Now I am no expert, but quantum mechanics is brilliant and crazy shit, at the same time. Quantum mechanics answers a dozen question and raises a dozen questions, at once. Get it?

Quantum mechanics is where science transitioned from certainty to uncertainty. It told us that nothing can be known for sure and trying is simply a waste of time, everything exists everywhere and nothing exists anywhere at the same time.

Now the last two topics for this particular post:

de Broglie Relationship

Well take Plank's E= hv = hc/λ and equate it with Einstein's E=mc^2

λ= h/(mv) (de broglie relationship)

WhatTheFact....Now de broglie proposed that matter, like electromagnetic radiation, had both wave like and particle like characteristics, which is apparent from the relationship described above.

But, the wave nature of matter as you can see in the above relation, is inversely proportional to the mass.

So for macroscopic bodies like humans (or cats) our wave nature is negligible but for a tiny little thing, say an electron, displays significant wave character.

In fact, it has been proven experimentally that an electron beam undergoes diffraction, a characteristic phenomenon associated with waves. This fact has been put to use in the making of an electron microscope.

Heisenberg's Uncertainty Principle

Now Werner Heisenberg in 1927, comes around and says "It is impossible to determine simultaneously the exact position and exact momentum (or velocity) of an electron."

Now, How...?

Quick Tip: If I hand you a rectangular block and ask you to measure its dimensions, what would you use? a ruler, obviously. But what if I scale down and hand you a coin and ask you to measure its thickness, what would you use? You can't use a ruler, instead you will need an instrument graduated in units smaller than the thickness of the coin, like a vernier scale or a micrometer.

Similarly, in order to determine the position of an electron, we must use an instrument calibrate in units smaller than the dimensions of the electron (bear in mind that an electron is a point charge and essentially dimensionless..still play along) So to observe an electron we will "illuminate" it with light of a short wavelength (i.e wavelength smaller than the dimensions of the electron) but such radiation would posses a great amount of energy and this energy would be transferred to the electron, thus effecting a change in its velocity.

So we have been accurately determined the position of the electron but in doing so we have changed its velocity. If we use a light of longer wavelength then we can avoid the error in measuring its velocity but then we cannot accurately estimate its position.

Mathematically, the uncertainty can be given by the following equation:

Δx.Δp >/=  h/4π, where Δx is the uncertainty in position, Δp is uncertainty in momentum and h is planc's constant.

or Δx.Δv >/= h/4πm, where m is mass and Δv is the uncertainty in position.

_____________________

That's all folks!

Stay tuned for a part 2, in which I will deal with the quantum mechanical model of the atom, but here's the story thus far.

Cheers!

The Passive Observer Out