NCERT Chemistry Class XI: Structure of an Atom

Atom

an ultimate particle which cannot be furthur subdivided

Dalton’s Atomic Theory

Atomic theory which regarded the atoms as the ultimate particle of matter, defined the law of conservation of mass, law of constant composition and multiple proportion; however, failed to explain the results of many experiments

Thomson’s Model of Atom

The model of the atoms which consits of a uniform sphere of positive charges which the electrons of distributed more or less uniformly; also known as the “Plum Pudding Model”

Drawbacks of Thomson’s Model of Atom

The drawbacks of the atomic model include that the mass of the atoms is considered to be evenly spread over the atom and it does not reflect the movement of the electrons

Rutherford’s Scattering Experiment

experiment which concluded that there is a very large empty space inside the atom and that there is a nucleus at the center of the atom repulsing ⍺-particles.

Rutherford’s Atomic Model

atomic model which proposed that the atom consists of a heavy positively charged nucleus where all the protons and neutrons are present, the volume of the nucleus is very small and only minute fraction of the total volume, and that there is an empty space around the nucleus called the extra nuclear part.

diameter of atom

The … of an atom is 10^5 times the diameter of the nucleus

volume of the atom

the … of an atom is 10^15 times the volume of the nucleus

Drawbacks of the Rutherford Model

this atomic model could not explain the stability of the atom and inferred that the electrons lose energy at every turn thereby falling into the nucleus and making the atom unstable.

Atomic Number

number of protons in the nucleus

Mass Number

the sum of the number neutrons and protons of an element

Mass of a Proton

1.672 × 10^-27 kg

Mass of a Neutron

1.675 × 10^-27kg

Mass of a Electron

9.1 × 10^-31kg

Isotopes

Atoms of a given element which have the same atomic number but differ in their mass numbers

Atomic Weight

the average of mass of all the isotopes of that element

Atomic Weight Formula

[(Relative Abundance of Isotope A%)(Mass of Isotope A) + (Relative Abundance of Isotope B%)(Mass of Isotope B)]

Isobars

atoms of different elements which have the same mass number but different atomic numbers

Isodiaphers

atoms of different elements which have the same difference of the number of neutrons & protons.

Isotones

atoms of different elements which have the same number of neutrons

Isosters

molecules which have the same number of electrons

Electromagnetic Waves

the transfer of energy from one body to another body at the speed of light in the form of waves with or without a medium

Wavelength (ƛ)

the distance between two nearest crests or troughs

Wave number (ṽ)

the reciprocal of the wavelength

Frequency (ν)

the number of waves which pass through a point in 1 second which is measured in Hertz(Hz) or s^-1.

Time period (T)

time taken by a wave to pass through one point

Formula for time period

T=1/v second

Velocity( c )

distance covered by a wave in 1 second

Formula for the velocity of a wave

c = ƛ/T = ƛv

Speed of Light

3.0 × 10⁸ m/s

Amplitude (a)

the height of the crest or depth of trough

Velocity of a wave is…

…inversely proportional to the wavelength

Planck’s Quantum Theory

the theory which states that the energy emitted/absorbed by the object is discontinuous in the form of small packets of energy called quanta and, in the case of light, the quanta are photons. It also states that the energy of each quantum is directly proportional to the frequency of the radiation and the total amount of energy transferred from one body to another will be some integral multiple of the energy of a quantum

Quanta

small discrete packets of energy

Photons

quanta but in the case of light and have no mass

Plank’s Energy Equation

E = hv = hc/ƛ = hcṽ

Plank’s Energy Equation

E = nhv = nhc/ƛ = nhcṽ, where n = number of quanta

Bohr’s Atomic Model

atomic model based on quantum theory of radiation, classical laws of physics and the particle nature of the electron. ONLY applicable for single electron species like H,He+, Li2+, etc.

Coulombic force formula

F = (kq₁q₂)/r²

Coulomb’s Constant

8.99 × 10 9 Nm²/C²

Centrifugal Force formula

F=mv²/r

Angular momentum formula

L=mvr

1st Postulate of Bohr’s Atomic Model

postulate which states that an atom has a heavy, positively charged region called the nucleus where all the protons and neutrons are located present at the center of the atom

2nd Postulate of Bohr’s Atomic Model

postulate which states that electrons revolve around the nucleus in orbits and the electrons are attracted to the nucleus while also being affected by centrifugal force, cancelling both forces out.

Attraction force of electrons towards nucleus =

= centrifugal force of electrons in orbit

3rd Postulate of Bohr’s Atomic Model

postulate which states that electrons can revolve only in orbits where that angular momentum of the electron is an integral multiple of nh/2π where n=the number of orbits and h=Plank’s constant. CANNOT have fractional values

4th Postulate of Bohr’s Atomic Model

the postulate which states that the orbits in which electrons can revolve are known as stationary objects because the energy of electrons is always constant in these orbits

5th Postulate of Bohr’s Atomic Model

the postulate which states that each stationary orbit is associated with definite amounts of energy, therefore these orbits are also called as energy levels and are numbered as 1,2,3,4,5…or K,L,M,N,O,… from the nucleus outwards.

6th Postulate of Bohr’s Atomic Model

The postulate which states that the energy is absorbed when an electron jumps from the inner orbit to the outer orbit and emitted when an electron jumps from the outer orbit to the inner orbit.

Equation for the radius of various orbits

r = n²h²/4π²mKZe² = 0.529 x n²/Z Å

Equation for the velocity of an electron

v = 2πKZe²/nh = 2.188 × 10⁶ m/s

Equation for time period (T_n)

T_n = circumference/velocity with a proportionality of n³/z²

Equation for the frequency of revolution(v_n)

v_n = velocity/circumference with a proportionality of z²/n³

Equation for the energy of an electron

E_n= (2π²mK²Z²e⁴)/n²h² = -13.6 x Z²/n² eV/atom

Ionization energy

the minimum amount of energy required to eject an electron from the ground state of an isolated atom

Seperation energy

the minimum amount of energy required to escape out electrons from its excited energy

Excitation energy

The amount of energy required to shift an electron from the ground state to any excited state

Atomic spectrum

when radiation is passed through a spectroscope for the dispersion of the radiation, a pattern is obtained on the photographic plate

Spectrum

where a ray of white light is spread out into a series of colored bands

Continuous spectrum

spectrum where all the colors blend into each other

absorption spectrum

spectrum where a white light is passed through a sample which absorbs radiation at certain wavelengths leaving dark bands on the photographic plate

line emission spectrum

spectrum were a white light is passed through a sample which emits radiation at very specific wavelengths

Rydberg Formula

ṽ = 1/ƛ = RZ²(1/n₁² - 1/n₂²)

Rydberg constant

R = 109678 cm^-1

1st Limitation of the Bohr Model

Bohr’s theory is only applicable to single electron species

2nd Limitation of the Bohr Model

Bohr’s theory does not explain why the angular momentum of the revolving electron is equal to nh/2π.

3rd Limitation of the Bohr Model

Bohr’s theory does not explain the fine structure of the spectral lines obtained by a spectroscope

4th Limitation of the Bohr Model

Bohr inter related quantum theory of radiation with the classical laws of physics without any explanation

5th Limitation of the Bohr Model

Bohr’s theory does not explain the splitting of spectral lines in the presence of a magnetic field or electric field.

Heisenburg’s Uncertainty Principle

“It is impossible to measure simultaneously the exact position and exact momentum of a body as small as an electron

Schrodinger’s Equation

Hψ = Eψ

Wave function

Represents the electron in an atom by a set of 3 quantum numbers found by the Schrodinger equation

Atomic orbital

the 3D space around the nucleus where the probability of finding the electron is about 90%

Probability Density

the probability of pinpointing the location of an electron is proportional to the square of the wave function.

Probability density formula

|ψ|²= electron finding probability/density

Principal Quantum Number (n)

the quantum number which represents the name and energy of the shell to which the electron belongs to

Greater the value of n,…

greater the value of _, greater is the distance from the nucleus

Greater the value of n, …

greater the value of _, greater is the energy of the shell

Velocity of an electron

v = 2.18 ×10⁶ Z/n m/s

Number of electrons in a particular shell is equal to…

2n²

Azimuthal/Secondary/Angular/Subsidiary Quantum Number

the quantum number which represents the name of the subshell, shape of the orbital, and the orbital angular momentum denoted by “l”

“s” subshell

spherical orbital when l=0

“p” subshell

dumb-bell shaped orbital when l=1

“d” orbital

double dumb-bell shaped orbital when l=2

“f” orbital

complex shaped orbital when l=3

Equation for Number of Electrons per Subshell

2(2l + 1)

Orbital Angular Momentum formula

√l(l+1) x h/2π

Magnetic (Orientation) Quantum Number (m or m_l

the quantum number which represents the orientation of the electron cloud (orbital) and describe the distributions of the orbital

Value of m equals …

all integers between -l to +l including zero

Values of m

number of orbitals in a subshell is represented by the

Spin Quantum Number (s)

the quantum number which represents the direction of electron spin around its own axis and can be +½ or -½ depending on clockwise or anti-clockwise. Not derived from Schrodinger’s equation

Spin Angular Momentum equation

√s(s+1) x h/2π where s always equals to ½

Spin of 2 electrons is always …

spin of electrons is always antiparallel

Formula for number of orbitals in a shell

n²

Node:

The point/line/plane/surface where the probability of finding an electron is 0.

Total Node =

__ node = n - 1

Radial node formula

n - l - 1

Angular node formula

l

Radial Node

the node which is found on the radius of the atom

Aufbau Principle

the principle which states that the subshell with the minimum energy is filled up first until the maximum quota of electrons to go to next higher energy is reached