JEE-AS-SM-DONE.pptx-1_compressed

Atomic Structure

Models of Atomic Structure

• J.J. Thomson’s Model

• Rutherford’s Model

• Bohr’s Model

• Planck's Quantum Theory

• de Broglie’s hypothesis

• Schrödinger's Wave Equation (SWE)

• Heisenberg’s Uncertainty principle

Discovery of Electron

• In 1891, George Johnstone Stoney named the fundamental unit of electricity as 'electron'.

• J. J. Thomson and his team identified the electron as a particle in 1897 using cathode rays.

• Discharge Tube Experiment Setup:

  • Cylindrical hard glass tube.

  • Two metallic electrodes (cathode and anode) connected to a battery.

  • Vacuum pump to maintain low pressure.

  • High voltage generator.

• Observations:

  • Readings of electric current were observed.

  • The anode end of the tube showed a greenish glow on the ZnS screen.

• Why Low Pressure?

  • At high pressure, more gas molecules are present, leading to obstructions in the paths of electrons, preventing them from reaching the anode.

• Observations and Characteristics of Cathode Rays:

  1. Move from cathode to anode.

  2. Travel in a straight line with high velocity in the absence of electric & magnetic fields.

  3. Efficiently observed with fluorescent or phosphorescent material like ZnS.

  4. Rotate a light paddle wheel placed in their path, indicating that cathode ray particles are material particles with mass and velocity.

  5. Deflected in the presence of an electric field (attracted towards the positive plate).

  6. Deflected in the presence of a magnetic field.

• Conclusions:

  • Cathode rays consist of negatively charged particles identified as electrons.

Charge to Mass Ratio

• In 1897, J.J. Thomson measured the charge (e) to mass (m) ratio of an electron.

• Electric & magnetic fields were applied perpendicular to each other and to the path of electrons.

• The charge to mass ratio is the same, irrespective of:

  • Nature of the gas.

  • Material of the cathode.

• Electrons are fundamental particles.

• e/m = 1.758820 × 10^{11} C/kg

Discovery of Anode Rays

• Discovered by Goldstein.

• Experiment involved a discharge tube with a perforated cathode.

• Existence of positively charged particles was shown using anode rays.

• A red glow is due to anode particles passing through the perforated cathode and striking the wall of the tube at the cathode side.
  *Red colour fluorescence observed due to Anode rays. Green colour fluorescence observed due to Cathode rays

Observations and Characteristics of Anode Rays

1. Anode rays possess a positive charge, as concluded by their deflections in electric & magnetic fields.

2. Anode rays travel in straight lines in the absence of both electric and magnetic fields.

3. The e/m ratio of the canal rays is different for different gases.

• Properties of anode rays depend on the nature of the gas taken in the discharge tube.

• In 1919, Rutherford discovered that the smallest and the lightest positive ions are obtained from hydrogen and called them protons.

Discovery of Neutrons

• Discovered by James Chadwick in 1932.

• A thin sheet of beryllium (Be) was bombarded with alpha particles (He^{2+}).

• Electrically neutral particles emitted were named neutrons.

• Mass of neutrons is slightly greater than that of protons.

• Nuclear reaction:
  ^{9}{4}Be + ^{4}{2}He^{2+}

  ^{12}{6}C + ^{1}{0}n

Thomson's Model

• Also known as the Plum Pudding or Watermelon model.

• An atom has a spherical shape with a radius of approximately 10^{–10} m.

• Positive charge is uniformly distributed throughout the sphere.

• Negatively charged electrons are embedded in it like raisins in a pudding.

• The mass of the atom is assumed to be uniformly distributed all over it.

• Explains the overall neutrality of an atom

Drawbacks of Thomson's Model

• Not consistent with the results of later experiments.

• Electrons are embedded in an atom in such a way that the most stable electrostatic arrangement is achieved.

Rutherford's Experiment

• Also known as the Gold Foil Experiment.

• A stream of high energy α-particles was directed at a thin gold foil (thickness ∼ 100 nm).

Process

When an α–particle strikes the screen, a glow was produced at that point on the screen

Observations:

1. Most of the α-particles passed undeflected.

2. A very small fraction was deflected by large angles.

3. Very few were deflected by 180° (∼1 in 20,000).

4. A small fraction was deflected by small angles.

Conclusions:

• Most α-particles passed through the foil without deflection, indicating the presence of large empty space in the atom.

• Few α-particles were deflected by small angles, suggesting that the positive charge is concentrated in a very small region.

• Very few α-particles (∼1 of 20,000) deflected at 180°, indicating a small positively charged core at the center (nucleus).

Nucleus

• The atom consists of a small positively charged core at the center, which carries almost the entire mass of the atom.

• It has negligible volume compared to the volume of the atom.

• Both protons and neutrons present in the nucleus are collectively called nucleons.

• Radius of the atom: ∼10^{–10} m

• Radius of the nucleus: ∼10^{–15} m

• R = R_0 A^{1/3}, where:

  • R = Radius of the nucleus of an element.

  • A = Mass number of element.

  • R_0 = 1.11

    10^{-15} m to 1.44

    10^{-15} m.

Extranuclear Part

• The nucleus is surrounded by revolving electrons.

• Electrons and the nucleus are held together by electrostatic forces of attraction.

• F{Centripetal} = F{Electrostatic}

Drawbacks of Rutherford’s Model

1. It could not explain the line spectrum of the H atom.

2. It could not explain the electronic structure of the atom.

3. It could not explain the stability of the atom stating that all atoms should collapse since electrons in orbit are constantly accelerating and radiating energy and should eventually lose all their energy and collapse into the nucleus.

R.A. Millikan’s Oil Drop Experiment

• This experiment was conducted to determine the charge on an electron.

• Charge on oil droplets measured and found to be an integral multiple of the magnitude of charge on an electron (e).

• Charge on electron: – 1.602176 × 10^{–19} C

Mass of the Electron

• From Thomson’s experiment, e/m ratio was calculated.

• From the Oil drop experiment, the charge of the electron was calculated.

• Using the data from these two experiments, the mass of the electron was determined

• mass=

  9.1

  10^{-31} kg

Subatomic Particles

Quantization of Charge

• q = n(e)

• q = n(1.6 × 10^{-19} C)

• q = n(4.8 × 10^{-10} esu)

• n = 1, 2, 3 …\The charge can’t have a continuous range of values but only take values in multiples of the charge on one electron.

• Magnitude of charge on an electron is the smallest unit and denoted as “e”. Thus charge on an electron is -e and on a proton, it is +e.

Electrostatic Force

• F_{12} = K

  q1 q2 / r^2

  • Where:

    • K = 9 × 10^9 Nm^2/C^2

    • ε_0 = Permittivity of vacuum = 8.854 × 10^{-12} C^2 V^{-1} m^{-1}

    • K = 1/(4πε_0)

Potential Energy

• P.E. = q × V

  • Where:

    • q = Charge of the particle

    • V = Potential of surface

• P.E. = K

  q1 q2 / r

Closest Distance of Approach

• R = √((4KZe^2)/(mα vα^2 ))\At a certain distance between them, the relative velocity becomes zero and after that due to repulsion, the particles starts going away from each other. This distance between the particles where velocity once becomes zero is called Closest distance of approach and can easily be calculated using conservation of the energy concept.

Electromagnetic Waves

• Electric & magnetic field oscillate perpendicular to each other.

• Electric and Magnetic fields both oscillate perpendicular to the direction of propagation of the wave.

• Do not require any medium for propagation (can travel in vacuum).

• Propagate at a constant speed, i.e., with the speed of light (c).

• c = 3 × 10^8 ms^{-1} (in vacuum)

Characteristics of Electromagnetic Waves

• Wavelength

• Frequency

• Time Period

• Wavenumber

• Velocity

• Amplitude
  *Crest and Trough
  **Frequency: Number of times a wave oscillate from crest to trough per second

• Wavelength (λ): Distance between two consecutive crests or troughs. SI unit: m

• Frequency (ν): Number of waves passing a given point in one second. SI unit: Hertz (Hz), s^{-1}. Related to time period as: ν = 1/T

• Velocity (c or v): Distance traveled by a wave in one second. SI unit: ms^{-1}. Related to frequency (ν) & wavelength (λ) as: c = νλ

• Time Period (T): Time taken to complete one oscillation. SI unit: s

• Wavenumber (\bar{ν}): Number of waves per unit length. SI unit: m^{-1}. \bar{ν} = 1/λ

• Amplitude (A): Height of the crest or the depth of the trough from the mean position. SI unit: m

• Note:

  • \bar{ν} = c \bar{ν}

  • Consists of radiations having different wavelengths or frequencies.

Electromagnetic Spectrum

• Electromagnetic radiations are arranged in the order of:

  • Increasing wavelength.

  • Decreasing frequency.
    *Electromagnetic radiations from Gamma rays to Radio wave with Visible light in the middle.

EM Radiation: Wave or Particle?

• Wave nature of the EM radiation explains:

  • Diffraction

  • Interference

• Electromagnetic wave theory could not explain:

  • Black-body radiation

  • Photoelectric effect

  • Variation of heat capacity of solids with temperature

  • Line spectrum of Hydrogen
    Mass Continuous vs. Discontinuous: Explains that at microscopic level mass is quantized i.e., quantization is a property of matter.
    Low temperature, Low frequency, Longer wavelength
    High temperature, High frequency, Shorter wavelength

Black Body Radiation

• A black body is an idealized system that absorbs and emits all frequencies.

• It absorbs radiation regardless of the angle of incidence.
  Why the name, Black Body? vs A true black body appears black because it is not reflecting any electromagnetic radiation. However, everything you see to be black cannot ber called as blackbody because there could be radiation coming out which is not in the visible range.
  It shows quantization nature of energy and hence favors particle nature of light.

Planck’s Quantum Theory

Particle Nature of Radiation
Explains Quantisation of Energy Variation of intensity with wavelength

• The smallest packet or bundle of energy (quantum of radiation) is called a photon. This is the smallest quantity of energy that can be emitted or absorbed in the form of EM radiation.

• Energy (E) of a photon is proportional to its frequency (ν).

  • E = hν = hc/λ

    • h = Planck’s constant = 6.626 × 10^{-34} Js

  • E = nhν

    • n = number of photons = 0, 1, 2, 3, …

Important Conversions

• One electron volt (eV) = Energy gained by an electron when it is accelerated from rest through a potential difference of 1 V

• 1 eV = 1.6 × 10^{-19} J

• E (eV) = 12,400 / λ (Å)

• E (kJ/mole) = E(eV) × 96.48

Photoelectric Effect

• Phenomenon of electron ejection when a radiation of sufficient frequency falls on the metal surface.

• Electrons are ejected with the aid of light and are called photoelectrons.

Process

When radiation of sufficient energy falls on the metal plate, there starts emission of electrons called photoelectrons.

Observations

• Electrons are ejected as soon as the beam of light of sufficient frequency strikes the metal surface.

• Instant transfer of energy to the electron when a photon of sufficient frequency strikes the metal atom

• Each metal has a characteristic threshold frequency (ν_0). Minimum frequency required to eject a photoelectron from a metal surface

• Number of electrons ejected ∝ Intensity of light or Brightness of light

• No electron is ejected, regardless of the intensity of light if ν{incident} < ν0

• Even at low light intensities, electrons are ejected immediately if ν{incident} > ν0

Explanation based on Particle nature of light

• One photon is absorbed by only one electron in a single interaction. Not more than one photon can be absorbed by an electron.

• If an intense beam of light is used, a large number of photons are available and a large number of electrons are ejected. This observation shows the particle nature of light.

• When ν{incident} > ν0, Kinetic Energy of Ejected electrons ∝ ν_{Incident}

• Transfer of energy to the electron. The Kinetic Energy of the ejected electron is equivalent to the Energy possessed by the photon

• 0 ≤ K.E. ≤ Max K.E.

• K.E. is independent of the intensity of radiation

• Work function = Φ\The minimum energy required to eject an electron from the metal surface called work function.

• Striking photon’s energy hν = KE_{Max} + Φ

Calculations

From the Law of Energy Conservation
*From maximum velocity of electron
* KE{Max} = hν - hν₀ or KE{Max} = h(c/λ) - h(c/λ₀)

Plotting K.E. vs Frequency

K.E.Max = hν - hν₀
When a graph of kinetic energy vs frequency is plotted,it shows linear variation according to the equation:

Acceleration and Deceleration of Charged Particles

• Acceleration:

  • If a positive charge moves from higher to lower potential or negative charge moves from lower to higher potential.

• Deceleration:

  • Just the opposite of acceleration.
    Minimum opposing potential required to stop the photoelectron having the maximum KE = eVs where Vs = Stopping potential

Accelerating potential voltage

Voltage applied to increase the K.E. of an emitted electron
Maximum K.E.= kE_{Max} + eV
Minimum K.E.= eV

Photocurrent v/s Frequency of the Radiation and intensity

*If V> Vo The Photocurrent increases with Intensity
*Photoelectric Effect vs Collector Potential at different intensity of radiation* Intensity Increases Retarding Potential is Constant. Saturation Current- I3 > I2> I1
Photocurrent vs Collector Plate Potential at different frequencies of radiation: Retarding Potential Increase Saturation Current is Constant. ν3 > ν2 > ν_1

Bohr Atomic Model

Bohr Model Applicable only for single electron species like
H, He^+, Li^{2+}, Be^{3+}

Postulates of Bohr Model

• Stationary Orbits:

  • Electrons revolve in concentric circular orbits around the nucleus.

  • These orbits have a fixed value of energy.

  • Electrons revolve without radiating energy.

  • These orbits are also known as energy states / levels.

• Quantization of Angular Momentum:

  • The angular momentum of the electron in these orbits is always an integral multiple of \frac{h}{2π}.

  • mvr = \frac{nh}{2π}

    • n = 1, 2, 3…

    • h = Planck’s constant

    • v = Velocity of electron

    • m = Mass of electron

    • r = Radius of orbit

• Energy Transitions:

  • An electron can jump from a lower to a higher orbit by absorbing energy in the form of a photon.

    • Energy \, Absorbed = E3 - E2

  • Electrons can jump from a higher to a lower orbit by releasing energy in the form of a photon.

    • Energy \, Released = E2 - E1
      Energy change does take place in a discrete manner
      ΔE =En2 - En1

Bohr’s Frequency Rule

• Frequency (ν) of a radiation absorbed or emitted when a transition occurs:

  • ν = \frac{ΔE}{h} = \frac{E2 - E1}{h}

    • E_1 = Energy of lower energy state

    • E_2 = Energy of higher energy state

Mathematical Analysis of Bohr Model

• Calculating:

  • Radius of Bohr orbit

  • Time period of an electron in Bohr orbit

  • Velocity of an electron in Bohr orbit

  • Frequency of an electron in Bohr orbit

  • Energy of an electron in Bohr orbit

Process Described By Postulates

Electron revolves in a circular orbit
\Required centripetal force is provided by electrostatic force of attraction.
F{Centripetal}= F{Electrostatic}

Calculating the radius of Bohr orbit

equating both the forces
on re arranging mv²/r =kZe²/ r² ⇒ v²r =kZe²/ m
r = kZe²/ mv² (i)

according to Bohr's Postulates
mvr= nh/2π ⇒ v= nh/2πrm ⇒ v²= n²h²/4π²r²m² (ii)
comparing equations (i) and (ii), kZe²/ r = n²h²/4π²r²m² ⇒ r =n²h²/4π²ZmekPutting the value of constants r n= Radius of nth Bohr orbit
Radius of nth Bohr orbit⇒ rn= (0.529 × n²)/Z Å ⇒ rn n²/Z*
The Angular momentum of the electron revolving in the nth orbit = mvr= nh/2π

Calculation of velocity of an electron in Bohr orbit

v = \frac{2πKZe^2}{nh} = (2.18 × 10^6 \frac{Z}{n} )ms^{-1}

Relation between v, n and Z

v α z/n
Time period of Revolution (T)⇒
*
\T= n³/Z* × 1.5 × 10^{-16} sec^-1\

Frequency of Revolution (f )

The Frequency of revolution of an electron in its orbit = v/ 2πr ⇒ f Z²/n ×6.6 × 10^{15}
(1/T) = f = Frequency. Z²/n*

KE\ + PE= Total Energy (T.E.) of an electron revolving in a particular orbit\

Calculation of Energy of an electron

T.E. = K.E + P.E
And Centripetal force = mv²/r
Electrostatic force = kZe²/ r²
Therefore mv²/r= kZe²/ r² ⇒ mv²/2= kZe²/ 2r= k.E
And P.E = - mv²/r ⇒ P.E= - kZe²/ 2r therefore, P.E α -¹/r
Substituting the value of ‘r’ in the equation of T.E. T.E= - kZe²/ 2r\

Energy of electron is related by
En= -13.6 Z²/Atom
*
Therefore* En Z↑ and En n↓, En n↑*

Energy of an electron from nucleus

Energy ↑ as Distance of electron from the nucleus
KE = P.E= 0 At N= ∞
Energy Difference
ΔE= E2− E1 ΔE=\frac{-13.6 Z²}{N2}−{\frac{-13.6Z²}{N1}} This has the units of eV
Energy level diagram with excitation is given from n= 1 to n= ∞

For Single Electron Systems
ground state is the Lowest energy state of any atom or ion , where n=1
Excited State: States of atom or ion other than the ground state such that n > 1
*Ionisation energy (I.E.): It is the Minimum energy required to remove an electron from n = 1 to n = ∞. Which equals ΔE = 13.6 Z^2
*Ionisation potential (I.P.)Potential difference through which a free electron must be accelerated from rest such that its K.E. = I.E*
Excitation Energy: The energy required to move an electron from n = 1 to any other state

Excitation potential (V) -

Potential difference through which an electron must be accelerated from rest such that its K.E. = Excitation energy*
Binding or Separation energy: It is the Energy required to move an electron from any state to n = ∞ , which is ground state From any state to n = ∞
Summary- Energy Required in Electronic Transitions is B. E = IE*From n= 1 to any other state Excited Energy

Spectroscopy

Is the branch of science that deals with the study of spectra
Spectrograph/ Spectroscope Instrument used to separate radiation of different wavelengths
Spectrogram Spectrum of the given radiation

Classification of Spectra:

Based on Origin Emission Spectra and Absorption
Based on Nature- Emission Spectrum can be either Discrete or Continuous

Emission Spectrum

Continuous Spectrum Distribution of colours (VIBGYOR) such that each colour merges into the next one*
Continuous Spectrum is the output of a Prism and Screen
Discrete is further divided into Line and Band

Line Spectrum

It is Ordered arrangement of lines of a particular wavelength separated by dark space. Also called atomic spectra
Emission spectra is Gas in Excited state in Discharge tube at low Pressure Prism Screen and can identify of unknown atoms

Band Spectrum

It is Continuous bands separated by some dark space or Molecular spectrum
Absorption Spectrum Gas in Ground State Prism Screen.The gas in the ground state absorbs radiation of particular wavelengths and rediations of remaing wavelength passes.

Absorption Spectrum contains

Some dark lines in the continuous spectrum Represent absorbed radiations
Emission Spectral Lines/ De-Excitation Series Line Spectrum of Hydrogen Due to de-excitation of electron from higher to lower orbit
Energy Level Diagram for H atom Given are n= 1,n=2, n=3,n=4, n=5, n= ∞ with values -13.6 eV to 0 eV
Rydberg’s Formula- Electron makes transition from n2 to n1 and λ-1= 1.09678 x 107 x Z2 [1/ n12 _ 1/ n22]
For any atom 1/λ = RH Z2 x [1/n12 - 1/ n22] - where RH is Rydberg constant H which 1.09678 x 107 m-1 ≈ 1.1 x 107 m-1

Spectral series of H atom: Lyman, and beyond that Balmer, Paschen, Brackett, Pfund ending with Humphrey in the far infrared region.

• Lyman Series

  • Lyman series n_1 = 1 (Final state). Spectral series are in UV region

• The range is 10.2 ≤ (ΔE)Lyman ≤ 13.6 eV
  And 12400/13.6 Å ≤λ ≤ 12400/10.2 Å

• Balmer Series is second spectral series for H atom and Found in visible region by Balmer with (Initial states, n_2 > 2),n1 = 2

Paschen Series (Initial states, n2 > 3). Third spectral series and Found in IR region
Brackett Series(Initial states, n2 > 4). fourth spectral series and Found in IR region by Brackett =RH x 1/λ
Pfund and Humphrey Series both have n =5 & 6 respectively and are Found in IR region
Maximum Number of Spectral Lines - For transition upto n = 1 or n = nSeries = Higher - n = Series Maximum Number of spectral lines given by formula = \[(nH - nL+ 1) (nH - nL)]/ 2\
In Lyman series (nHigher - 1) In Balmer series (nHigher - 2) In Paschen series (nHigher - 3) ≡ Number of spectral lines

• Example Number of spectral lines in Lyman series from 4th shell (nH - 1) = 4 - 1 = 3

Pathway to Quantum Mechanical Model

Dual Nature of Matter Heisenberg’s Uncertainty Principle
Dual Nature of Matter-Louis de Broglie de Broglie proposed that particle has dual nature i.e., Wave and Particle nature *

de Broglie Hypothesis

The Wave is associated with moving particles
To Find Formula
Planck's equation E= hc/λ and Einstein's Mass Energy relationship E = mc²
hc/λ = mc² ⇒ λ= h/mc By the same analogy, de Broglie proposed for matter λ= h/mv
De Broglie Wavelength (λ) = h/p = h/mv- Where Momentum (p ) = mass (m )x velocity (v) and h is Planck’s constant.
If Velocity approaches c then Relativistic Mass m = mO (1-v²/c²)-¹/²
Davisson and Germer’s Experiment- Confirmed de Broglie’s predictions and an electron beam undergoes diffraction, thus verifying equation.
Wavelength of a ball & an electron!
Ball: λ ~ insignificant
Electron, λ ~ significant λ α 1/m Wave nature can’t be detected for macroscopic object
de Broglie’s Equation λ = h/(2 K.E. × m)

Electron as a Wave: circumference 2πr = nλ when Electrons are in phase and in sync with orbital
mvr= nh/2π = Bohr’s Postulate verified when electrons are in phase

Heisenberg’s Uncertainty Principle

Exact position & momentum of a microscopic particle cannot be determined simultaneously
Δx . Δp h /4𝜋- Δx . m . Δv h /4𝜋Where Δx =Uncertainty in position and Δp =Uncertainty in momentum of Mass is m
There is Always A minimum error in the position measurement Δx = +λ/-, For accurate momentum Δx=1
For accurate position 0 , λ .For a photon λ=0 and E= hc/λ = ∞

**Heisenberg's Uncertainty Principle: High energy photon/λ
Δx . Δv = ±10^{-4} m^2s^{-1}
Velocity High accuracy Δv is small Position Uncertain
*Meaningless for larger particles*
Analysing Energy -
Significance of the Uncertainty Principle Replaced of an electron Precise statements of position& momentum with probability
It Forms the basis of Quantum Mechanical Model of atomRules out the existence of definite paths of electrons
Introduced concept of probability of finding the electrons and Not an instrumental error, rather a conceptual error

Limitations of Bohr Model

• Could not explain the line spectra of atoms containing more than one electron

• Could not explain the presence of doublet i.e. two closely spaced lines

• Unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) and electric field (Stark effect)

• No conclusion was given for the principle of quantization of angular momentum.

• Unable to explain de Broglie’s concept & Heisenberg’s Uncertainty Principle

Quantum Mechanical Model
Schrodinger Wave Equation (SWE)
∂2𝚿/∂x2 + ∂2𝚿/∂y2 + ∂2𝚿/∂z2 + 8𝝅2m/ h2 ( E - V ) 𝚿 = 0 Where 𝚿 = Amplitude of the electron wave or Wave function x, y, z = Cartesian coordinates V.Potential energy of the electron E = Total energy of the electro

About Wave Function

SWE is solved to get values of 𝚿 and their corresponding energies- A function that contains all the dynamical information about a system
𝚿 SWE can be solved for H like species more easily in Spherical polar coordinates ( r , 𝛳 , ɸ )

Spherical Coordinate System where

x= r sin𝜃 cosɸ
y =r sin𝜃 sinɸ
z = r cos*𝜃

And r is the Radial part with angles 𝜃 and ɸ givenAngular part of wave function
Where 𝚿 =n and l and 𝜃, ɸ = l, ml
H like species requires a set of quantum numbers (n, l, m s)
Quantum numbers (n, l, m) were derived from Schrodinger equation-
# What is an Orbital- It is a 3D region around the nucleus Probability of finding an electron is maximum but Does not define a definite path of electrons.

Quantum Numbers

Set of four numbers required to define an electron in an atom completely Principal Quantum Number ( n ) =The Designates the energy shell for electron (n = 1, 2, 3…) Represented as K, L, M, N,….
Orbital angular momentum in any shell = nh/ 2π
Azimuthal Quantum number (l ) = Designates the subshell to which the electron and Describes the 3-D shape of the orbital or the electron cloud
( l = 0 to (n - 1))
Boundary Surface Diagram-Encloses the 3D region where probability of finding electrons is maximum
Collection of similar shaped orbitals of same n. l 0 Subshell s 1 p 2 d 3 f number of subshells in the nth shell
(Magnetic Quantum Number (ml =Designates the orbital to which the electron Maximum number of orbitals in a subshell = (2l + 1)Can have values from - l to + l including zero s =Non-directional in nature & P= Directional in nature
Remember
spin of an electron s = +1/2
The Spin Quantum Number determines Spin angular momentum (S) which is the Maximum Spin n/2* and can calculate Spin multiplicity (S.M.) = 2 [S] + 1=\Rules for Filling Electrons in Orbitals Rules Aufbau Principle Hund’s Rule of Maximum Multiplicity Pauli’s Exclusion