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