4Atomic structure

📚
ATOMIC STRUCTURE
▢ Dalton's Atomic Theory:

Table 1: Basic Idea

Point
Description
Matter
Composed of tiny individual particles called atoms
Atom
Basic unit of matter taking part in chemical reaction
▢ Subatomic Particles:

Table 1: Electron, Proton & Neutron

Particle
Charge
Mass
Discovered by
Special point
Electron
\(-1.6 \times 10^{-19}\ C\)
\(9.1 \times 10^{-31}\ kg\) = \(\frac{1}{1837}\) mass of H atom
J. J. Thomson
\(\frac{e}{m} = 1.8 \times 10^{11}\ C/kg\)
Proton
\(+1.6 \times 10^{-19}\ C\)
\(1.67 \times 10^{-27}\ kg\)
Goldstein
Positive particle
Neutron
0
\(1.67 \times 10^{-27}\ kg\)
Chadwick
Neutral particle
▢ Atomic Species:

Table 1: Different Types of Atomic Species

Species
Meaning
Key point
Isotopes
Same atomic number
Same \(Z\)
Isobars
Same mass number
Same \(A\)
Isotones
Same number of neutrons
Same \(N\)
Isodiaphers
Same isotopic number
\(N - Z\) same
Isosters
Same number of atoms and electrons
Molecular similarity
Isoelectronic species
Same number of electrons
Electronic similarity
Nuclear isomers
Same element with different radioactivity / nuclear energy state
Radioactive forms
Isomorphs
Compounds with identical crystal structure + similar formula
\(K_2SO_4\), \(K_2CrO_4\)
Isobels
Atoms / species having same geometry and hybridization
\(SO_2\), \(SnCl_2\)
Isochores
Graph line showing temperature-pressure variation at constant volume
Constant volume
❖ Isomorph Examples:
  • •
    \(K_2SO_4\), \(K_2CrO_4\)
  • •
    \(MgSO_4 \cdot 7H_2O\), \(ZnSO_4 \cdot 7H_2O\), \(FeSO_4 \cdot 7H_2O\)
▢ Atomic Models:
❖ Thomson Atomic Model:
◉ Other Names:
  • •
    Watermelon model
  • •
    Plum pudding model

Table 1: Thomson Model

Part
Represents
Plum / watermelon pulp
Positive charge
Seeds
Negative electrons
❖ Rutherford Scattering Experiment:
◉ Experiment: Alpha particle scattering experiment using helium nuclei / \(\alpha\)-particles
◉ Observations:

Table 1: Rutherford Observations

Observation
Conclusion
Most \(\alpha\)-particles passed undeflected
Most of atom is empty space
Few \(\alpha\)-particles showed small / large deflection
Positive charge concentrated in small region
Very few \(\alpha\)-particles returned back
Dense central nucleus present
◉ Conclusions:
  • •
    Atom has a small dense positively charged nucleus
  • •
    Electrons revolve around nucleus
  • •
    Most of atom is empty space
  • •
    Nucleus discovered; neutron not discovered by Rutherford
  • •
    Used helium nucleus / \(\alpha\)-particle, not helium atom
◉ Rutherford Atomic Model:
◈ Other Name: Planetary electron model
◈ Nuclear Radius: \(r_n = r_0 A^{1/3}\)
▢ Electromagnetic Spectrum:
❖ Order: Radio waves < Microwaves < Infrared < Visible light < Ultraviolet rays < X-rays < \(\gamma\)-rays < Cosmic rays
▢ Hydrogen Spectrum:
❖ Rydberg Formula: \(\frac{1}{\lambda} = \bar{\nu} = R\left[\frac{1}{n_1^2} - \frac{1}{n_2^2}\right]\)
❖ Rydberg Constant: \(R = 1.09 \times 10^7\ m^{-1}\)
❖ For Hydrogen-like Species: \(R = Z^2 \times 1.09 \times 10^7\ m^{-1}\)

Table 1: Hydrogen Spectral Series

Series
Region
\(n_1\)
\(n_2\)
Lyman series
UV region
1
2, 3, 4...
Balmer series
Visible region
2
3, 4, 5...
Paschen series
IR region
3
4, 5, 6...
Brackett series
IR region
4
5, 6, 7...
Pfund series
IR region
5
6, 7, 8...
Humphreys series
Far IR region
6
7, 8, 9...
▢ Bohr's Atomic Model:
❖ Postulates / Theory:

Table 1: Bohr Model Equations

Concept
Equation
Centripetal force = electrostatic force
\(\frac{mv^2}{r} = \frac{1}{4\pi\epsilon_0}\frac{e^2}{r^2}\)
Angular momentum quantization
\(mvr = \frac{nh}{2\pi}\)
Energy change
\(E_2 - E_1 = \Delta E = h\nu\)
❖ Energy of Electron:
◉ General Formula: \(E_n = -\frac{2\pi^2 Z^2me^4}{n^2h^2}\)
◉ For Calculation: \(E_n \propto \frac{Z^2}{n^2}\)
◉ For Hydrogen Atom: \(E_n = -\frac{13.6}{n^2}\ eV\ per\ atom\)
◉ Energy Difference: \(E*{2-1}=13.6\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]\)
◉ Note: \(E_2 - E_1 > E_n - E_2\)
❖ Radius of Electron:
◉ General Formula: \(r_n = \frac{n^2h^2}{4\pi^2Zme^2}\)
◉ For Hydrogen-like Atom: \(r_n = \frac{0.53\times n^2}{Z}\ \mathring{A}\)
❖ Velocity of Electron:
◉ Formula: \(v_n = \frac{2\pi Ze^2}{nh}\)
◉ Value: \(v_n = 2.88 \times 10^6 \times \frac{Z}{n}\ ms^{-1}\)
▢ De-Broglie Wavelength:
❖ Formulae:
  • •
    \(\lambda = \frac{h}{p}\)
  • •
    \(\lambda = \frac{h}{mv}\)
  • •
    \(\lambda = \frac{h}{\sqrt{2mE_k}}\)
❖ Planck Constant: \(h = 6.6 \times 10^{-34}\ Js\)
▢ Heisenberg Uncertainty Principle:

Table 1: Uncertainty Relations

Relation
Meaning
\(\Delta x \cdot \Delta p \geq \frac{h}{4\pi}\)
\(\Delta x\) = uncertainty in position; \(\Delta p\) = uncertainty in momentum
\(\Delta E \cdot \Delta t \geq \frac{h}{4\pi}\)
\(\Delta E\) = uncertainty in energy; \(\Delta t\) = uncertainty in time
▢ Quantum Numbers / Wave Mechanical Model:
❖ Given By: Schrödinger

Table 1: Quantum Numbers

Quantum number
Symbol
Range
Significance
Given by
Principal quantum number
\(n\)
1 to \(\infty\)
Shell / energy level / size of orbital / distance of electron from nucleus
Bohr
Azimuthal quantum number
\(l\)
0 to \(n-1\)
Subshell + shape of orbital
Sommerfeld
Magnetic quantum number
\(m_l\)
\(-l\) to \(+l\)
Orbital orientation; explains Stark + Zeeman effect
Lande
Spin quantum number
\(s\)
\(+\frac{1}{2}\), \(-\frac{1}{2}\)
Spin of electron
—
❖ Principal Quantum Number:

Table 1: Shells

\(n\)
Shell
1
K
2
L
3
M
4
N
❖ Azimuthal Quantum Number:

Table 1: Subshells & Shapes

\(l\)
Subshell
Shape
0
s
Spherical
1
p
Dumb-bell
2
d
Double dumb-bell
3
f
Complex
❖ Magnetic Quantum Number:

Table 1: Orbitals

Subshell
\(m_l\) values
Number of orbitals
s
0
1
p
-1, 0, +1
3
d
-2, -1, 0, +1, +2
5
f
-3, -2, -1, 0, +1, +2, +3
7
▢ Electronic Configuration Rules:
❖ Bohr-Bury Scheme:
  • •
    Maximum electrons in outermost orbit = 8
  • •
    Maximum electrons in penultimate shell = 18
  • •
    New orbit starts filling when outermost orbit gets 8 electrons
❖ Aufbau Rule:
  • •
    Orbital of lowest energy fills first
  • •
    Energy order depends on \(n + l\)
  • •
    Lower \(n+l\) → lower energy
  • •
    If \(n+l\) same, lower \(n\) fills first
❖ Hund's Rule of Maximum Multiplicity:
  • •
    No pairing in degenerate orbitals until each orbital has one electron
  • •
    Single electrons in same energy level have parallel spin
❖ Pauli's Exclusion Principle:
  • •
    No two electrons in an atom can have same set of 4 quantum numbers
  • •
    One orbital can contain maximum 2 electrons with opposite spins
▢ High-Yield Recall:

Table 1: Atomic Structure One-Liners

Fact
Answer
Matter composed of atoms
Dalton
Electron discovered by
J. J. Thomson
Proton discovered by
Goldstein
Neutron discovered by
Chadwick
Electron charge
\(-1.6 \times 10^{-19}\ C\)
Proton charge
\(+1.6 \times 10^{-19}\ C\)
Neutron charge
0
Same atomic number
Isotopes
Same mass number
Isobars
Same neutrons
Isotones
Same \(N-Z\)
Isodiaphers
Same electrons
Isoelectronic species
Same crystal structure
Isomorphs
Watermelon model
Thomson model
Nucleus discovered by
Rutherford alpha scattering experiment
Rutherford used
\(\alpha\)-particles / helium nuclei
Most atom is
Empty space
Nuclear radius
\(r_n = r_0A^{1/3}\)
Visible hydrogen series
Balmer series
UV hydrogen series
Lyman series
IR hydrogen series
Paschen, Brackett, Pfund
Far IR hydrogen series
Humphreys
Rydberg constant
\(1.09 \times 10^7\ m^{-1}\)
Bohr angular momentum
\(mvr = \frac{nh}{2\pi}\)
Energy of H atom
\(E_n = -\frac{13.6}{n^2}\ eV\)
Bohr radius formula
\(r_n = \frac{0.53n^2}{Z}\ \mathring{A}\)
De-Broglie equation
\(\lambda = \frac{h}{mv}\)
Uncertainty principle
\(\Delta x\Delta p \geq \frac{h}{4\pi}\)
Wave mechanical model
Schrödinger
Principal quantum number
Shell / energy level
Azimuthal quantum number
Subshell shape
Magnetic quantum number
Orbital orientation
Spin quantum number
Electron spin
Lowest energy orbital fills first
Aufbau rule
No pairing before single occupancy
Hund's rule
No same 4 quantum numbers
Pauli's exclusion principle
Q1.
How many protons, electrons and neutrons are present in the element 4321X? [IOM 2008]
📅IOM 2008
Q2.
Atomic no. of Arsenic is 33. What will be the electronic configuration of outermost shell? [MOE 2064]
📅MOE 2064
Q3.
The electron in an atom [MOE 2062]
📅MOE 2062
Q4.
Which of the following does not belong to 3d series? [MOE 2003]
📅MOE 2003
Q5.
Which is correct? [MOE 2002]
📅MOE 2002
Q6.
Iron has atomic number 26. What is the electronic configuration of iron cation which can form the complex [Fe(CN)6]4-? Ar = 1s2 2s2 2p6 3s2 3p6 [MOE 2058]
📅MOE 2058
Q7.
Which one of the following statements is not correct? [MOE 2000]
📅MOE 2000
Q8.
Magnetic quantum no. of an atom gives [MOE 2055]
📅MOE 2055
Q9.
Which of the following sequence is correct if given elements are arranged according to ascending atomic no.? [IOM 2008]
📅IOM 2008
Q10.
Which of the following electron denoted by the following quantum no. has the highest energy? [I.E. 2009]
📅I.E. 2009
Q11.
If 75% of substance decay in 32 minutes then, find how much time it will take to decay 50% of same substance. [IOM 2009]
📅IOM 2009
Q12.
The half life of a radioactive substance is 2 months, then the amount of substance left in 1 year [IOM 2009]
📅IOM 2009
Q13.
Concept of quantization of energy was introduced by [MOE 2009]
📅MOE 2009
Q14.
Atomic orbitals are filled up in the ground state in order of the increasing energy level. This is the statement of ........ [MOE 2009]
📅MOE 2009
Q15.
In any given orbit electron fill up in increasing order of energy, it is known as [BPKIHS 2006]
📅BPKIHS 2006
Q16.
Equal volume of all gases at same temperature and pressure has equal number of molecules is the statement of [Bangladesh 2008]
📅Bangladesh 2008
Q17.
An orbital have azimuthal quantum no l = 1. The Shape of orbital is [Bangladesh 2008]
📅Bangladesh 2008
Q18.
DDT on exposure to water decomposes. It's half life is 10 years. How much time will it take for its 90% decomposition? [BPKIHS 2007]
📅BPKIHS 2007
Q19.
The configuration 1s1, 2s1 2p6 shows [BPKIHS 2006]
📅BPKIHS 2006
Q20.
The half life of a radioactive isotope is 10 hours, how much of its reactivity will remain after 30 hours? [BPKIHS 2005]
📅BPKIHS 2005
Q21.
The splitting of spectral lines under the effect of magnetic field is [BPKIHS 2004]
📅BPKIHS 2004
Q22.
Shape of orbital is given by the ........ Quantum number [BPKIHS]
📅BPKIHS
Q23.
The increasing order for the values of e/m for electron, proton, neutron and α-particle is [I.E.]
📅I.E.
Q24.
Maximum no. of orbitals in a shell is given by [BPKIHS]
📅BPKIHS
Q25.
Which of the following shows highest magnetic moment? [BPKIHS 1994, I.E. 2011]
📅BPKIHS 1994•I.E. 2011
Q26.
An electron jumps from higher orbit to lower orbit. Then energy of electron. [I.E. 2005]
📅I.E. 2005
Q27.
Half life of a radioactive substance is 1060 years, what is its average life? [I.E.]
📅I.E.
Q28.
The silicon atom has unpaired electrons which is due to [I.E.]
📅I.E.
Q29.
In sun the source of energy is [I.E./BPKIHS]
📅I.E.•BPKIHS