Lesson 2 notes

DALTON'S ATOMIC THEORY

• elements are made up of small indivisible particles called atoms
• atoms can neither be created nor destroyed - chemical reaction involves only the rearrangement of atoms and the same number of atoms must be present before and after the chemical reaction
• atom is the smallest particle which takes part in a chemical reaction
• same element - same properties
• different elements- different properties
• explained law of conservation of mass, law of constant proportions and law of multiple proportions
• DRAWBACKS -
• isotopes - same element have different atomic mass
• isobars - different elements have same atomic mass
• indivisibility - can be split into protons, electrons and neutrons
• failed to explain results of important experiments

JJ THOMPSON'S CATHODE RAY EXPT.

• cathode ray tube - glass containing 2 thin pieces of metal called electrodes sealed in it
• when a potential difference of 10,000V is passed through a gas at very low pressure - electrical discharge is observed
• stream of particles move from negative electrode (cathode) to positive electrode (anode)
• these were called cathode rays
• RESULTS -
• cathode rays start from cathode and move to the anode
• consist of negatively charged particles called electrons
• when these particles hit a screen coated with ZnS, they produce fluorescence
• get deflected from their path in the presence of an electric or magnetic field
• produce heating effect when made to strike a metal foil
• produce X-rays when hit tungsten, copper, molybdenum
• high penetration power
• ionise the gas through which they pass
• charge to mass ration - 1.76 into 10 o the power 11 coloumb/kg
• electrons - universal constituent of all atoms since e/m ratio for different gases remained the same (irrespective of gas)

GOLDSTEIN'S DISCHARGE TUBE EXPT.

• passed high voltage between the electrons of a discharge tube
• perforated cathode
• RESULTS -
• some rays were coming from the side of the anode and passed through the perforated cathode
• consist of positively charged particles formed by the ionization of gas particles by cathode rays
• charge to mass was maximum when gas used was hydrogen
• e/m ratio varies with the gas unlike in the case of cathode rays

DISCOVERY OF NEUTRONS

• bombarding boron or beryllium with neutrons

PLUM PUDDING MODEL

• all positive charge and mass of atoms are distributed throughout the volume of the atom and negatively charged particles are embedded in them such that the atom remains neutral
• only explained the neutrality of atom
• DRAWBACKS
• could not justify Rutherford's alpha particles scattering experiment

RUTHERFORD'S ALPHA SCATTERING EXPT.

• narrow beam of alpha particles to fall on a thin gold foil and studied the path with ZnS screen
• ZnS screen gives off a visible flash when hit by alpha particles
• alpha particles were emitted by radioactive substances
• alpha particles - di-positive He ions (mass - 4; 2 unit +ve charge)
• very high penetrating power
• expected observations
• all particles would pass through the gold foil
• if penetration power was less, they would be deflected slightly
• actual observations -
• majority - went through
• some - deflected by small angles
• very few - deflected completely
• conclusions -
• most alpha particles went through - most of the atom is empty
• few were deflected - indicated the presence of heavily charged positive body
• 1 in 20,000 particles were reflected by 180 degrees - volume occupied by heavily positively charged body is very small compared to volume of atom

RUTHERFORD ATOMIC MODEL

• all positive charge and mass of an atom is concentrated in a very small region called nucleus
• size of nucleus is very small compared to nucleus
• diameter of nucleus - 10 to the power -13 ; diameter of atom - 10 to the power -8
• most of space inside the atom is empty
• electrons revolve around the nucleus
• centrifugal force due to rotation counterbalances the force of attraction between positive and negative
• radius of nucleus = 1.25 into 10 to the power -15 into cube root of A
• defects -
• exact positions of electrons not mentioned
• electron should lose energy continuously in the form of EMR (due to acceleration). then it should have a decrease in velocity and spiral into the nucleus in 10 to the power -8 seconds

ELECTROMAGNETIC WAVES

• a wave which is created when mutually perpendicular electric and magnetic fields interact with each other
• line formed by the intersection of perpendicular electric and magnetic fields is the direction of propagation of EMW
• properties -
• do not require a medium for propagation
• not affected by electric or magnetic fields
• wavelength - distance between 2 consecutive troughs or crests
• frequency - number of times a wave passes through a given point in a second
• wave number - number of waves per unit length
• amplitude - height of crest or depth of trough
• time period - time needed for a complete wave to pass through a point

ELECTROMAGNETIC SPECTRUM

• arrangement of different EMR in order of increasing or decreasing frequency
• increasing wavelength : gamma rays < X-rays < UV < Visible spectrum < IR < Microwave < FM < AM < Long radio waves

PLANCK'S QUANTUM THEORY OF ENERGY OF EMW

• EMW has both particle and wave nature (dual nature of EMW)
• when EMW interact with macroscopic particles - behave as a wave; else - particle
• energy of an EMW is quantized (total energy which can be supplies by an EM is a multiple of a small number)
• energy of EMW is in the form of packets
• each packet - quantum of energy
• when EMW belongs to visible spectrum, these packets of energy are called photons
• energy of a quantum is directly proportional to its frequency
• in microscopic world - particles absorb quanta one by one
• in macroscopic world , E = n.h.c/lambda

POSTULATES OF PLANCK'S THEORY

• sources of EMW emit or absorb energy discontinuously in the form of small packets
• smallest packet of energy - quantum
• energy of a quanta is directly proportional to frequency
• a body can absorb or emit energy in whole number multiples of the energy of one quantum (quantization of energy)
• each particle can absorb only one quantum of energy at a time
• one quantum of energy cannot be shared by two particles

BOHR'S MODEL

• for hydrogen like species
• applied Planck's Quantum theory and said that while revolving around the nucleus an electron does not lose energy
• electron does not gain or lose energy on its own
• whenever hydrogen like species interact with EMW it absorbs/emits energy in the form of quanta (which will be quantized)

POSTULATES OF BOHR'S MODEL

• atom consists of a dense stationary nucleus at the centre
• electron revolved around the nucleus in circular orbits without emitting energy
• electron does not fall or fly away - centrifugal force balances the force of attraction between electrons and nucleus
• electron can revolve around only those orbits which have an angular momentum mvr as an integral multiple of h by 2 pi
• since electron neither loses nor gains energy, the orbits are called stationary states
• each stationary state is associated with a definite amount of energy known as energy levels
• greater the distance from the nucleus greater the energy of the energy level
• electron continues to move without losing energy - ground state or normal state
• if suitable EMW is supplied, electron gets excited and jumps to the next energy level. the amount of energy absorbed is equal to the difference in energies of the 2 concerned levels

ENERGY OF ELECTRON-NUCLEUS SYSTEM

• energy at infinite distance at rest - zero (by definition)
• to bring it closer to nucleus - some work must be done to electron
• as electron is brought closer to nucleus, PE decreases due to attractive forces between nucleus and electron
• KE increases
• whenever attractive forces develop, PE always decreases ; PE increases when repulsive forces increase
• thus, total energy decreases, KE increases and PE decreases

BOHR'S MODEL MERITS AND DEMERITS

• MERITS -
• accounted for stability and gave line spectra for hydrogen and hydrogen-like species
• accurate experimental values
• concept of stationary state of electron explains emission and absorption spectra
• DEMERITS -
• does not account for spectra of non-hydrogen species
• when source of spectrum is placed in electric and magnetic field - split further into lines - failed to account for this splitting of spectral lines in the presence of magnetic field (Zeeman's effect) and electric field (Stark effect)
• treated the particle as only a particle instead of wave and particle
• Heisenberg's uncertaintly pricniple
• did not give any justification for mvr=h/2pi

ATOMIC SPECTRA

• light coming from a source can be split into its constituent wavelengths by a prism
• such a collection of dispersed light giving its wavelength composition is called a spectrum
• types - absorption and emission

ABSORPTION AND EMISSION SPECTRUM

• ABSORPTION SPECTRUM
• a band of EMW is incident on an atom - incident waves
• EMW obtained after passing through the atom - transmitted waves
• on dispersion of transmitted waves, some wavelengths are missing in the transmitted waves as compared to the incident waves
• these wavelengths are absorbed by the atoms
• absorption spectrum - spectrum obtained after absorption of EMW by the atom
• absorbed wavelengths appear as dark lines in the spectrum
• energy absorbed in the form of EMW is used by the electrons of the atom to move onto a higher energy level
• EMISSION SPECTRUM
• sample of atoms in the excited state tend to lose energy in the form of EMW to attain more stability by lowering its energy
• emission spectrum - spectrum of waves obtained when a sample of atoms get de-excited
• IMPORTANT
• number of wavelengths in the emission spectrum is always greater than or equal to the dark lines in the absorption spectrum

HYDROGEN SPECTRUM

• electron -- absorbs energy -- higher energy level -- de-excited -- emission spectrum -- lower and more stable energy level
• rydberg's formula gives the wavelength of the emitted waves
• each transition of the electron corresponds to a different line of the spectrum having a definite wavelength
• the entire spectrum consists of different series of lines named after their discoverers
• lyman, Balmer, Paschen, Brackett, Pfund, Humphrey

PHOTOELECTRIC EFFECT

• emission of electrons from a metal when EMW of appropriate wavelength strikes it
• photoelectrons - electrons that are ejected
• potassium and caesium - visible light ; other metals - UV
• when energy in the form of EMW is incident on metals, the electrons absorb the energy and use it to overcome the attrattional forces
• once sufficient energy is supplied - electrons are ejected from metal
• emission is dependent on high frequency

CONCLUSIONS OF PHOTOELECTRIC EFFECT

• electrons are ejected when EMW of sufficiently high frequency strikes them
• in order to be ejected from metal surface, electrons can absorb only one quantum of energy. if the energy is high enough, they will get ejected
• if energy is insufficient, electron will not get ejected irrespective of intensity of EMW
• threshold energy or work function - minimum energy which must be possessed by a quantum in order to eject electrons
• threshold frequency - minimum frequency of EMW which can cause emission
• as the intensity of EMW having frequency greater than the threshold frequency, the number of electrons ejected also increases. as number of electrons ejected increases, rate of flwo of electrons also increases. thus as intensity increases, photo current also increases

BLACK BODY EFFECT

• perfect black body which absorbs all the energy and emits back all the energy in the form of EMW
• irrespective of how much energy a black body is emitting in the form of EMW, it should emit the same distributions of frequencies
• as the temperature of the source increases and consequently, its tendency to emit energy increases, the peak wavelength (wavelength with the highest intensity) emitted by the black body decreases or frequency of EMW emitted increases

PARTICLE WAVE DUALITY OF MATTER

• proved by diffraction of a beam of fast moving electrons
• diffraction is a property of waves in which waves tend to bend around sharp edges

de-BROGLIE EQUATION

• calculated the wavelength of wave associated with a particle
• for waves, E=h nu
• for particles, E = mc^2
• equating these 2 , lambda = h/mv or lambda = h/p where p is the momentum of the particle
• rest mass of the photon - value of ma calculated in the above equation (h/c into lambda)

IN PHASE AND OUT OF PHASE

• consider an electron moving in a circular orbit
• if 2 ends of the electron wave meet to give a regular series of crests and troughs - in phase
• out of phase - irregular
• for the atom to be stable - in phase
• n' lambda = 2 pi r
• n' - number of waves made by the electron in that bohr orbit
• n'=n thus number of waves made by an electron in an orbit = orbit number

HEISENBERG'S UNCERTAINTY PRINCIPLE

• it is impossible to measure the position and the momentum of a particle simultaneously and accurately
• suppose we attempt to accurately pinpoint the position and velocity of an electron
• for this, we will have to use light
• as a result of being hit by the photon, the position is disturbed
• accuracy of measurement depends on wavelength (shorter wavelength; greater accuracy)
• but shorter wavelength means higher frequency and hence higher energy
• this high energy photon on striking the electron changes its velocity and direction

QUANTUM MECHANICAL MODEL

• based on particle and wave nature of the electron
• proposed by Erwin Schroiddnger
• does not talk about the exact location of an electron
• tries to define a region wherein the probability of finding an electron is maximum
• quantum numbers - the most basic quantities that are derived from the wave function

QUANTUM NUMBERS

• orbitals - region where the probability is greater than 95%
• all orbitqals are located around the nucleus
• different orbitals differ in terms of size, shape, orientation
• orbitals of different atoms differ in terms of size

PRINCIPLAL QUANTUM NUMBER (N)

• size of the orbital
• greater the n value, greater is the size of the orbital, farther the electron from the nucleus
• can take any integral values from 1 to infinite
• similar to the shell number
• maximum number of electrons is 2 n squared

AZIMUTHAL OR ANGULAR MOMENTUM (L)

• shape
• integral values from 0 to (n-1)
• different values of l, different shapes
• 0 - s (spherical)
• 1- p (dumbel)
• 2- d (double dumb-bell)
• 3 - f irregular

MAGNETIC QUANTUM NUMBER (ML)

• orientation
• integers ranging from -1 to +1
• each different value of m - diferent orientation
• number of values of m - number of orientations

SPIN QUANTUM NUMBER (S)

• used to distinguish electrons which reside in the same orbital
• move in a manner opposite to each other and hence opposite spins
• clockwise and anti-clockwise spins
• +1/2 and -1/2

S SUB SHELL

• l=0
• spherical and hence symmetrical in all 3 directions
• size depends on n value
• greater n value, larger the size

P SUB SHELL

• l=1
• dumb-bell shaped
• px,py and pz orbitals depending upon whether the density of an electron is maximum along the x,y or z axis
• directional character as not spherically symmetrical
• 3 p-orbitals having same valye of n have sae energy and are called degenerate orbitals

D ORBITALS (L=2)

• m=-2,-1,0,+1,+2
• 3 lie in between the axes and 2 lie on the axes
• 5 degenerate orbitals

RULES FOR WRITING ELECTRONIC CONFIG

• Aufbau principle - electrons are added one ny one to the various orbitals in order of increasing energy starting from the lowest energy
• Pauli's exclusion principle - no electron can have the same set of four quantum numbers
• Hund's rule of maximum multiplicity - electron pairing in p,d,f orbitals cannot occur until each orbital of a given subshell contains atleast one electroj. all electrons in a degenerate set of orbitals will have same spin

ELECTRONIC CONFIG

• number of electrons to be accomodated in a subshell = 2 into number of degenerate orbitals
• maximum number of orbitals in a shell - n squared

EXCEPTIONAL CONFIGURATIONS

• symmetrical distribution of electrons - effect is more dominant in d and f orbitals - half filled orbitals and fully filled orbotals are more stable
• exchange energy - whenever electrons with the same spin are present in degenerate orbitals
• electrons tend to exchange their positions and gain stability by losing energy
• energy released - exchange energy
• max number of echanges occur when the subshell is either half filled or full-filled
• exceptional elements - chromium, copper, silver, molybdenum