atomic structure

Definition of Physical Properties

Properties which can be studied without changing the identity of a substance

Examples of physical properties

Boiling of water, melting of ice, color, odour, density, and sublimation

Definition of Chemical Properties

Properties which cannot be studied without changing the identity of a substance

Examples of chemical properties

Neutralization reactions, decomposition reactions, and rusting

Definition of Non-Matter

That which is not matter; examples include love, emotions, feelings, thoughts, energy, sound, light, anger, and time

Relationship between Kelvin (K) and Celsius (C)

K = C + 273

Relationship between Fahrenheit (F) and Celsius (C)

C/5 = (F - 32)/9

Specific Charge

Ratio of charge to mass (Charge of particle / Mass of particle)

Specific charge of a proton

Approx 9.9 x 10^7 C/kg

Specific charge of a neutron

0

Mass number (A)

Number of neutrons + Number of protons

Identity of number of protons (p) and electrons (e) in a neutral atom

No. of p = No. of e = Z (Atomic number)

Formula for number of neutrons (n)

A - Z

Minimum real charge on any particle

1.6 x 10^-19 Coulomb

Mass of a proton in terms of mass of an electron

Mass of proton = 1837 x (Mass of electron)

Definition of a Molecule

Smallest particles of an element or compound which must have independent existence

Protons in a molecule

Sum of [(Z value of atom) x (Total no. of atoms)]

Electrons in a molecule

Sum of [(Z value of atom) x (Total no. of atoms)]

Neutrons in a molecule

Sum of [(A - Z value of atom) x (Total no. of atoms)]

Electrons in an ion

No. of protons - (Total positive charge) + (Total negative charge)

Percentage of more neutrons than electrons in an ion

[(n - e) / e] x 100%

Definition of Valency

Combining capacity of any atom

Solid state condition regarding forces

Attractive Force >> Thermal Energy

Liquid state condition regarding forces

Attractive Force < Thermal Energy

Gaseous state condition regarding forces

Attractive Force << Thermal Energy

Correct order of Thermal Energy

Gas > Liquid > Solid

Correct order of Intermolecular force

Solid > Liquid > Gas

Standard form of Scientific Notation

N x 10^n (where 1 <= N < 10)

Scientific notation decimal move towards Left

Power becomes positive

Scientific notation decimal move towards Right

Power becomes negative

Significant figure rule for non-zero digits

All non-zero digits are considered significant

Significant figure rule for leading zeros

Zeros placed to the left of non-zero digits are not considered significant

Significant figure rule for trapped zeros

Zeros placed between non-zero digits are considered significant

Significant figure rule for trailing zeros

Without decimal, they are insignificant; with a decimal point, they are significant

Significant figure rule for counting physical quantities

Considered to be infinite

Rule for addition/subtraction of Significant Figures

The result cannot have more significant figures to the right of the decimal point than any of the numbers being added or subtracted

Rule for multiplication/division of Significant Figures

The result cannot have more significant figures than the number having the minimum significant numbers in the calculation

Rule if rightmost digit is > 5

Preceding digit is increased by one (+1)

Rule if rightmost digit is < 5

Preceding digit remains the same

Rule if rightmost digit is 5 and preceding digit is Odd

Preceding digit is increased by one (+1)

Rule if rightmost digit is 5 and preceding digit is Even

Preceding digit remains the same

Definition of Isotopes

Same elements (same Z value) having different mass numbers (different A value)

Definition of Isobars

Different elements (different Z value) having the same mass number (same A value)

Definition of Isotones

Different elements having the same number of neutrons or same (A - Z) value

Definition of Isodiaphers

Different elements (different atomic number) having the same (n - p) value or (A - 2Z) value

Definition of Isoelectronic species

Different atoms, ions, or molecules having the same number of electrons

Definition of Isosters

Different molecules having the same number of total electrons and the same number of atoms

Relationship between number of alpha particles deflected (N) and thickness of foil (T)

N proportional to T

Relationship between number of alpha particles deflected (N) and Kinetic Energy (KE)

N proportional to 1 / (KE^2)

Relationship between number of alpha particles deflected (N) and Atomic Number (Z)

N proportional to Z^2

Relationship between number of alpha particles deflected (N) and Angle of Deviation (theta)

N proportional to 1 / [sin(theta/2)]^4

Formula for Centrifugal Force (Fc)

Fc = (m * v^2) / r

Force of Attraction (Fa) in orbit derivation

Fa = (K * Z * e^2) / r^2

Orbital Kinetic Energy (KE)

KE = 1/2 * m * v^2 = (Z * e^2 * K) / 2r

Orbital Potential Energy (PE)

PE = -(Z * e^2 * K) / r

Orbital Total Energy (TE)

TE = -(Z * e^2 * K) / 2r

Energy Relationship between PE and KE

PE = -2 * KE

Energy Relationship between TE and KE

TE = -KE

Ratio of PE to KE

-2

Radius of Nucleus (R)

R = [1.33 x A^(1/3)] x 10^-13 cm (where A is mass number)

Distance of Closest Approach (r)

r = (4 * Z * e^2 * K) / (malpha * valpha^2)

Density of a nucleus

A constant quantity and very large

Definition of Wave Number (v-bar)

Reciprocal of Wavelength (1/lambda)

Speed of light/radiation (C)

C = frequency * wavelength

Definition of Quantum/Photon

Discrete and indivisible packets of energy

Energy of a single photon (Eph)

Eph = h * frequency = (h * c) / wavelength

Total Energy of N quanta (ETotal)

ETotal = N * h * frequency OR N * (h * c / wavelength)

Planck constant (h) value

6.626 x 10^-34 Js

Avogadro number (NA)

6.022 x 10^23

Conversion of 1 eV to Joules

1.6 x 10^-19 J

Shortcut formula for Energy in eV

E(eV) = 1240 / wavelength(nm)

Additive properties of wavelength when energy is conserved

1/lambda = 1/lambda1 + 1/lambda2

Definition of Power

Power = Energy / Time

Definition of Stationary State

A fixed orbit where an electron revolves and its energy remains constant

Bohr Postulate for Quantization of Angular Momentum (L)

L = mvr = nh / 2pi

General formula for Radius of nth orbit

r = (n^2 * h^2) / (4 * pi^2 * m * Z * e^2 * K)

Numerical formula for Radius (r)

r = (0.529 Angstrom) * (n^2 / Z)

Numerical formula for Velocity of electron (V)

V = 2.18 x 10^6 * (Z / n) m/s

Velocity acquired by electron accelerated from rest

v = sqrt(2eV / m)

Relationship between Time period (T) and n, Z

T proportional to n^3 / Z^2

Relationship between Frequency (f) and n, Z

f proportional to Z^2 / n^3

Energy of an electron in nth orbit (TE in eV)

TE = -13.6 * (Z^2 / n^2) eV

Definition of Ground State

The state of electron where its energy is minimum (n=1)

Definition of nth Excited State

Orbit No. = n + 1

Ionization Energy (IE) of Uni-electronic system

IE = +13.6 * (Z^2 / 1^2) eV

Definition of Separation Energy (SE)

Energy required to send an electron from its excited state to infinite energy state; SEnth = -E(n+1)

Rydberg Equation for Wavelength

1/lambda = RH * Z^2 * (1/n1^2 - 1/n2^2)

Rydberg Constant (RH)

109677 cm^-1 or 10967700 m^-1

Rydberg Calculation trick for wavelength

1/R = 912 Angstrom

Rydberg Equation for Energy Change (delta E)

delta E = R-primeH * Z^2 * (1/n1^2 - 1/n2^2) where R-primeH approx 2.18 x 10^-18 J

Total number of spectral lines for transition from n to 1

n(n-1)/2

Total number of spectral lines for transition from n2 to n1

(n2 - n1)(n2 - n1 + 1) / 2

Einstein Photoelectric Equation

Energy of photon (Eph) = Work-function (phi) + KE_max

Definition of Work-function (phi)

Minimum energy needed to overcome in order to take an electron out of a metal surface

Formula for Work-function (phi)

phi = h * frequency0 = (h * c) / wavelength0

Conditions for Photoelectric Effect

Eph >= phi, frequency >= frequency0, and wavelength

De-Broglie Wavelength Equation

lambda = h / p = h / (m * v)

De-Broglie relationship between wavelength and Kinetic Energy (KE)

lambda = h / sqrt(2 * m * KE)

De-Broglie relationship between wavelength and Voltage (V)

lambda = h / sqrt(2 * m * q * V)

Shortcut formula for electron wavelength (lambda_e)

lambda_e = sqrt(150 / V) Angstrom or 12.3 / sqrt(V) Angstrom