Looking for a Tutor Near You?

Post Learning Requirement »
x

Choose Country Code

x

Direction

x

Ask a Question

x

x
x
For better view click here
x
Hire a Tutor
DISCOVER

Atomic Structure Notes-Chemistry

Loading...

Published in: Chemistry | IIT JEE Mains
22,662 Views

Atomic Structure Notes.

Akhilesh K / Lucknow

4 years of teaching experience

Qualification: M.Sc (NIT Rourkela - 2019)

Teaches: All Subjects, English, Mathematics, Science, Chemistry, Physics, Algebra, IIT JEE Mains, AIPMT, NEET

Contact this Tutor
  1. Atoms , The atom is mostly empty space. 'Two regions. ' NucleuS - protons and neutrons. Electron cloud- region where you might find an electron. Subatomic particles Relative Name Symbol Charge mass 1/1 840 Electron Proton Neutron p+ no +1 mic structure notes O 1 1 Actual mass (g) I x 10-28 1.67 x 10-24 1 67 Y 10-24
  2. Bohr's Model Fifth Fourth Third Second First Nucleus Orbit Nucleus Energy Levels Electron Further away from the ntJCIelJS means more energy. There is no "in between" energy atomic structure notes
  3. 'Few difficulty Bohr model had 'The spectra of larger atoms. At best/ it can make some approximate predictions about the emission spectra for atoms with a single outer-shell electron 'The relative intensities of spectral lines 'The existence of fine and hyperfine structure in spectral lines. 'The Zeeman effect - changes in spectral lines due to external magnetic fields Bohr model: A semiclassical mode!
  4. Wave-particle duality nature of light Classical physics- A system can absorb or emit any amount of energy. Plank' hypothesis- Energy absorbed or emitted by a black body is restricted to the relation E = hv Consequences: 1. Photoelectricity (Eistein, 1906) 2. Theories of atomic spectra (Bohr, 1913) atomic structure notes
  5. Photoelectric Effect Photoelectrons Emission of electrons from metals when exposed to ultraviolet) radiation. atomic structure notes
  6. Explanation (EINSTEIN 1905) Threshold frequency vo given by = hv O For v > vo the kinetic energy of the emitted electron Photoelectron (e-) EK(e-) Free, stationary electron Bound electron atomic structure notes 6
  7. Line Spectrum of Hydrogen atom when subjected to higher temperature or a electric discharge emit electromagnetic radiation From Bohr model: 2 n 1 AE-hv-13.6 —i n Paschen Series (Infrared) Lyman Series (Uttaviolet) 2 n 2 'Balmer Series (Vlts&) 410.2 nm violet 1 656.3 nm red 434.1 nmt at violet 486.1 nm bluegreen ctrl +1 Ira - 1 n; R = Rydberg Constant 109677.6 cm-I 7
  8. Wave particle duality of material particles Louis de Broglie (electron has wave properties) Werner Heisenberg (uncertainty Principle) Erwin Schrodinger (mathematical equations using probability, quantum numbers) de Broglie wavelength of electrons h/p Consequence: Electrons produce diffraction pattern when passed through thin diffraction grating (Davison and Germer) atomic structure notes
  9. Electron Motion Around Atom Shown as a de Broglie Wave atomic structure notes 9
  10. Schrödinger's equation, what is it ? Newton's law allows you to describe motion of mechanical systems and mathematically predict the outcome of the system. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome. The Schrodinger equation gives the quantized energies of the system and gives the form of the wavefunction so that other properties may be calculated. atomic structure notes 10
  11. The wave equation developed by Erwin Schrodinger in 13 at About the Wavefunction 1926 h2 3 2 2 2m 13 x The wavefunction is assumed to be a single-valued function of position and time, which is sufficient to get a value of probability of finding the particle at a particular position and time. The wavefunction is a complex function, since it is its product with its complex conjugate which specifies the real physical probability of finding the particle in a particular state. single-valued probability amplitude at (x, t) proba il- of finding particle at at time t atomi' rUCU notes prow e t e wavefunction is normalized.
  12. WAVEFUNCTION (W) (PSI) Classically, the state of a system is described by its position and momentum In Quantum theory, the state of a system is described by its wavefunction Trajectory Wavefunction a ormcs ruc ure no es
  13. WAVEFUNCTION (W) (PSI) 1. A wavefunction is a mathematical function (like sinx, ex). Like any mathematical function it can have large value at some place, small in other and zero elsewhere. It can be real or complex 2. A wavefunction contains all information about the system 3. The wavefunction is a function of Cartesian coordinate and time. ie. NJ (x/ Y/ z, t) 4. If the wavefunction is large at a point in space, the particle has a large probability at that point 5. The more rapidly a wavefunction changes from place to place, higher the K.E. of the particle it describes atomic structure notes 13
  14. WAVEFUNCTION (W) (PSI) A wavefunction describes the state of a system How? The state of a system is described by some measurable quantities such as mass, volume, momentum, position, Energy etc. These quantities are called observables How to determine the observables from wavefunction (W) By performing a set of well defined mathematically operations on W. These mathematical operations are called operators atomic structure notes 14
  15. Born interpretation The state of a system (particle) is completely specified by its avefunction W which is a probability amplitude an has the significance that (more generally IW12dV since W may be complex) represents the probability that the particle is located in the infinitesimal element of volume dV about the given point/ at time t. atomic structure notes 15
  16. NORMALIZATION As per Born interpretation, the probability of existence of the particle in the entire space should be 1. In mathematical term the wave function has to be normalized For one dimension N V dx=l Where N is the normalization constant atomic ti ct 1 e not
  17. In 1913 Niels Bohr came up with a new atomic model in which electrons are restricted to certain energy levels. Schrödinger applied his equation to the hydrogen atom and found that his solutions exactly reproduced the energy levels stipulated by Bohr. The result was amazing and one of the first major achievement of Schrödinger's equation and earned him the 1933 Nobel Prize in physics. Newton's Law: Conservation of Energy ( Harmonic Oscillator example)) Kinetic Energy + Potential Energy —rnv24 --kx2 = E 2 kx h? div 2 Time independent Schrodinger Equation ato
  18. Quantum conservation of Energy Schrodinger Equatio In a wave equation, physical variables takes the form of "operators" (H), Hamiltonian operator In three dimensions, -h2/2m (02 v/öx2 + 02 v/öy2 + Ö2VlÖZ2) + = at Time dependent Schrodinger Equation 2 2 2m ax atomic structure notes
  19. Eigen value equations (operator) (function)= (constant factor) (function) ax ax —ae = —16(Sin4x) atomic structure notes 19
  20. How to proceed urther? 'Let us test the Schrödinger equation for some simple physical systems! Some model systems at first — easy to test ! Hopefully, some quantum properties of matter will also be understood! 'If we can understand these 'simple systems' without doing any approximation and can derive 'exact solutions'/ then we shall proceed towards our major target — atoms and molecules 'Why we do not go right now to solve the Schrödinger equation for atoms and molecules? Because the mathematical solution for atoms and moleCUIes is complicated. atomic structure notes 20
  21. Characteristics of the wavefunctions 1. Wavelength = 2L/n 2. There are n-l nodes (interior points where the wave function passes through zero) in the wavefunction 3. The energy increases with increasing number of nodes. The ground state has no nodes. . The ground state energy is not 0/ but h2/8mL21 the zero point energy. This is a consequence of the uncertainty principle. atomic structure notes 21
  22. Applications of this model 1. Calculation of energy of It-electrons of conjugated olefins 2. Electrons in nano materials 3. Electrons present in cavities or color centers 4. Translational motion of ideal gas molecules atomic structure notes
  23. Hydrogen atom Hydrogen has special significance 'No approximation is required in solution of Schroedinger equation 'Can get expression for energy levels 'Spectral frequencies can be deduced Since the ntJCIeUS can be considered to be at rest For H atom the Schrödinger wave equation can be written as (h2/2m)iö2/öe +ö2/öy2 +V]W atomic structure notes 23
  24. The potential, V between two charges is best described by a Coulomb term, ze2 V= - ql%/ 41t€or v(r) 47teor -(h2/2m ) = E It is convenient to describe the solutions to the Schrödinger equation in spherical polar coordinates (r, 0,+) rather than cartesian (x,y,z) z atomic structure notes 24
  25. The Schrödinger equation in spherical polar coordinate is 1 1 Sino r2Sin0 DO DO r2Sin20 Dp 2 2me r Dr This equation can be solved by separation of variable technique 2 41T80r qJ(r/0/+) = q.J(r/0/+) = V(r/0/+) = Radial part Angular part Angular part Solution may be a product of three functions. atomic structure notes 25
  26. where R n I(r) is called the radial part of and YI m (0/+) its angular part. The wavefunction of the electron in the hydrogenic atom is called an atomic orbital. An orbital is a one- electron wavefunction. Electron described by a particular wavefunction is said to occupy that orbital. Atomic orbitals specified by three quantum numbers n, I/ and ml.
  27. z x The wavefunction of the hydrogenic atom depends on three quantum numbers The principle quantum number : n Angular momentum quantum number: -1 Magnetic quantum number: m, = -l 2222 3211 n Orbital angular momentum = atomic structure notes 27
  28. Principal quantum numbers, n: nergy Levels Continuum d -hcR/16 -hcR/9 -hcR/4 -hcR n 2 The energy levels are En = —pe4Z2/321t2802h2n2 = -hcRZ2/n2where Where R = (pe4/321t2€02h2)/hc >Energy is —ve stabilization effect A-ligher the value of Z more stabilization >When n increases energy increases tomic structure notes 28
  29. Solution* Some-example For n=ll I -o 3 2 1 2 a 0 For ml 0 1 2 1 > Y is a constant and does not depend on 0 and For a given radial distance, same value of probability is observed at all directions from ntJCIelJS S-orbitals are spherically symmetrical x atomic structure notes 29
  30. Solution : For 1 R(n/l) = For 1=11 ml -O +11 -1 1 1 a 3 2 4 3 3 8m 2 cos0 1 2 sin O The angular variation of wavefunction depend on cos 0. The probability density is proportional to cos20. The probability density has maximum value along an arbitary axis (z-axis) on either side of the ntJCIeUS ( at o and 1800) atorn# structure notes 30
  31. Atomic Orbitals •Principal Quantum Number (n) = the energy level Of electron. •Within each energy level the complex math of Schrödingerls equation describes several shapes. are called atomic orbitals •Regions where there is a high probability of finding an electron. atomic structure notes
  32. s orbitals 01 s orbital for •Spherical every energy level 000 •Each s orbital car •Called the IS/ 2s/ etc.. orbitals. atomic structure notes
  33. p orbitals , Start at the second energy level •3 different directions '3 different shapes (dumbell) •Each can hold 2 electrons atomic s rtcture notes 33
  34. d orbitals •Start at the third energy level •5 different shapes •Each can hold 2 electrons notes 34
  35. Start at the fourth energy level Have seven different shapes; 2 electrons per shape

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related Study Notes

Upload Study Notes

If you have your own Study Notes which you think can benefit others, please upload on LearnPick. For each approved Study Note you will get 100 Credit Points and 100 Activity Score which will increase your profile visibility.

Upload Now
Home > Study Notes > Atomic Structure Notes-Chemistry