Atomic Structure Notes : For Class 11, JEE, NEET, AIIMS and Other Competitive Examinations

Atomic structure

This Atomic structure notes will help you prepare for Board Exam as well as competitive exams.

Atomic structure refers to the structure of atom comprising of a nucleus(center) in which the protons (positively charged) and neutrons (neutral) are present. The negatively charged particles called electrons revolve around the center of the nucleus.

The history of atomic structure and quantum mechanics dates back to the times of Democritus, the man who first proposed that matter is composed of atoms.

The study about the structure of atom gives a great insight into the entire class of chemical reactions, bonds, and their physical properties. The first scientific theory of atomic structure was proposed by John Dalton in 1800s.

The protons and neutrons make up the nucleus of the atom, which is surrounded by the electrons belonging to the atom. The atomic number of an element describes the total number of protons in its nucleus.

This Atomic structure  will help you to understand atomic mass, subatomic particles.

The mass number (symbol A, from the German word Atomgewicht (atomic weight), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. The mass number is different for each different isotope of a chemical element.

Neutral atoms have equal numbers of protons and electrons. However, atoms may gain or lose electrons in order to increase their stability, and the resulting charged entity is called an ion.
Atoms of different elements have different atomic structures because they contain different numbers of protons and electrons. This is the reason for the unique characteristics of different elements.

This Atomic structure  will help you to understand:

Atomic Models

In the 18th and 19th centuries, many scientists attempted to explain the structure of the atom with the help of atomic models. Each of these models had their own merits and demerits and were pivotal to the development of the modern atomic model.

The most notable contributions to the field were by the scientists John Dalton, J.J. Thomson, Ernest Rutherford, and Niels Bohr. Their ideas on the structure of the atom are discussed in this subsection.

Dalton’s Atomic Theory

The English chemist John Dalton suggested that all matter is made up of atoms, which were indivisible and indestructible. He also stated that all the atoms of an element were exactly the same, but the atoms of different elements differ in size and mass.
According to the postulates proposed by Dalton, the atomic structure comprised of atoms, the smallest particle responsible for the chemical reactions to occur.

The following are the postulates of Dalton’s Atomic theory:

1. Every matter is made up of atoms, Atoms are indivisible.
2. Specific elements have only one type of atoms in them.
3. Each atom has its own constant mass that varies from element to element.
4. Atoms undergo rearrangement during a chemical reaction
5. Atoms can neither be created nor be destroyed but can be transformed from one form to another.

Dalton’s atomic theory successfully explained the Laws of chemical reactions, namely,

• the Law of conservation of mass,
• Law of constant properties,
• Law of multiple proportions, and
• Law of reciprocal proportions

Demerits of Dalton’s Atomic Theory:

1. The theory was unable to explain the existence of isotopes.
2. Nothing about the structure of atom was appropriately is explain
3. The theory was unable to explain the existence of isodiphers.
4. The scientists discovered particles inside the atom that proved, the atoms are divisible.

• The discovery of particles inside atoms led to a better understanding of chemical species, these particles inside the atoms are called subatomic particles.
• Although some of these models were not able to explain the stability of atoms, two of these models, one proposed by J.J. Thomson and the other proposed by Ernest Rutherford are discussed below.

Subatomic particles

1. Electron ——– J.J THOMSHAN
2. Proton ———- Ernest Rutherford
3. Neutron ——– James Chadwick

Position of subatomic particles

Thomson Atomic Model

The English chemist Sir Joseph John Thomson put forth his model describing the atomic structure in the early 1900s.

He was later awarded the Nobel prize for the discovery of “electrons”. His work is based on an experiment called cathode ray experiment. The construction of working of the experiment is as follows:

Cathode Ray Experiment

• It has a tube made of glass which has two openings, one for the vacuum pump and the other for the inlet through which a gas is pumped in.
• The role of the vacuum pump is to maintain “partial vacuum” inside the glass chamber. A high voltage power supply is connected using electrodes i.e. cathode and Anode is fitted inside the glass tube.

Observations:

• When a high voltage power supply is switched on, there were rays emerging from the cathode towards the anode. This was confirmed by the ‘Fluorescent spots’ on the ZnS screen used. These rays were called “Cathode Rays”.
• When an external electric field is applied, the cathode rays get deflected towards the positive electrode, but in the absence of electric field, they travel in a straight line.
• When rotor Blades are placed in the path of the cathode rays, they seem to rotate. This proves that the cathode rays are made up of particles of a certain mass so that they have some energy
• When rotor Blades are placed in the path of the cathode rays, they seem to rotate. This proves that the cathode rays are made up of particles of a certain mass so that they have some energy.
• With all this evidence, Thomson concluded that cathode rays are made of negatively charged particle called “electrons”.
• On applying the electric and magnetic field upon the cathode rays (electrons),
• Thomson found the charge to mass ratio (e/m) of electrons. (e/m) for electron: 17588 × 10¹¹ e/bg.
• From this ratio, the charge of the electron was found by Mullikin through oil drop experiment. [Charge of e- = 1.6 × 10^-16 C and Mass of e- = 9.1093 × 10^-31 kg].

Conclusions:

• Based on conclusions from his cathode ray experiment, Thomson described the atomic structure as a positively charged sphere into which negatively charged electrons were embedded.
• It is commonly referred to as the “plum pudding model” because it can be visualized as a plum pudding dish where the pudding describes to the positively charged atom and the plum pieces describe the electrons
• Thomson’s atomic structure described atoms as electrically neutral, i.e. the positive and the negative charges were of equal magnitude

Limitations of Thomson’s Atomic Structure:

• Thomson’s atomic model does not clearly explain the stability of an atom.
• Also, further discoveries of other subatomic particles, couldn’t be placed inside his atomic model
• Does not explain isotopes, isobars, isotones,and isodiaphers.

This Atomic structure notes will help you to understand completly

Plum pudding model

Thomson had discovered that atoms are composite objects, made of pieces with positive and negative charge.
The negatively charged electrons within the atom were very small compared to the entire atom.

Millikan’s through oil drop experiment:

• Millikan’s oil drop experiment measured the charge of an electron. Before this experiment, existence of subatomic particles was not universally accepted
• Millikan’s apparatus contained an electric field created between a parallel pair of metal plates, which were held apart by insulating material. Electrically charged oil droplets entered the electric field and were balanced between two plates by altering the field.
• When the charged drops fell at a constant rate, the gravitational and electric forces on it were equal. Therefore, the charge on the oil drop was calculated that find the charge of a single electron was 1.6 x 10-19 C.

Rutherford Atomic Theory :

• Rutherford, a student of J. J. Thomson modified the atomic structure with the discovery of another subatomic particle called “Nucleus”.
• His atomic model is based on the Alpha ray scattering experiment.
• The nucleus is at the center of an atom, where most of the charge and mass are concentrated.
• Atomic structure is spherical.
• Electrons revolve around the nucleus in a circular orbit, similar to way Planet orbit SUN.

Alpha Ray Scattering Experiment:

Construction:

• A very thin gold foil of 1000 atoms thick is taken.
• Alpha rays (doubly charged Helium He²⁺) were made to bombard the gold foil.
• ZnS screen is placed behind the gold foil.

Observations:

• Most of the rays just went through the gold foil making scintillations (bright spots) in the ZnS screen.
• A few rays got reflected after hitting the gold foil.
• One in 1000 rays got reflected by an angle of 180° (retraced path) after hitting the gold foil.

Conclusions:

• Since most rays passed through, Rutherford concluded that most of the space inside the atom is empty.
• Few rays got reflected because of the repulsion of its positive with some other positive charge inside the atom.
• He said most of the charge and mass of the atom resides in the Nucleus.
• 1/1000th of rays got strongly deflected because of a very strong positive charge in the center of the atom he called this strong positive charge as “nucleus.

Limitations of Rutherford Atomic Model:

• If electrons have to revolve around the nucleus, they will spend energy and that too against the strong force of attraction from the nucleus, a lot of energy will be spent by the electrons and eventually, they will lose all their energy and will fall into the nucleus so the stability of atom is not explained.
• If electrons continuously revolve around the ‘nucleus, the type of spectrum expected is a continuous spectrum. But in reality, what we see is a line spectrum.
• This Atomic structure notes will help you to understand isotopes , isobars etc

Atomic Structure of Isotopes :

• Nucleons are the components of the nucleus of an atom. A nucleon can either be a proton or a neutron. Each element has a unique number of protons in it, which is described by its unique atomic number. However, several atomic structures of an element can exist, which differ in the total number of nucleons.
• These variants of elements having a different nucleon number (also known as the mass number) are called isotopes of the element. Therefore, the isotopes of an element have the same number of protons but differ in the number of neutrons.
• This Atomic structure notes will help you to understand features of
  

  Isotopes, Isobars , Isotones & Isodiaphers :

Distinguish between Isotopes, Isobars , Isotones & Isodiaphers :

Isotopes	Isobars	Isotones	Isodiaphers
Isotopes are atom have same atomic number but different mass number or atomic mass.	Isobars are atoms of different elements which have same mass number but different atomic number.	Isotone are the atom of different element which contain same number of neutron with different mass number and atomic number.	Isodiaphers are atoms, having different atomic number and mass number but have same difference between number of neutron and number of proton proton number
hydrogen has 3 isotopes as protium dutrium and tritium having same atomic number 1 with different mass number 1,2,3.	argon and calcium have same mass number 40 but different atomic number 18,20.	silicon and phosphorous have same number of neutron 16 with different mass number 30,31 and atomic number 14,15.	in thorium proton number is 90 and neutron number is 144 144-90 = 54 in uranium proton number is 92 and neutron number is 146 146 – 92 = 54

Atomic Structures of Some Elements:The atomic structure of an isotope is described with the help of the chemical symbol of the element, the atomic number of the element, and the mass number of the isotope. For example, there exist three known naturally occurring isotopes of hydrogen, namely, protium, deuterium, and tritium. The atomic structures of these hydrogen isotopes are illustrated below.

The structure of atom of an element can be simply represented via the total number of protons, electrons, and neutrons present in it. The atomic structures of a few elements are illustrated below.

Atomic Structure of Hydrogen:

The most abundant isotope of hydrogen on the planet Earth is protium. The atomic number and the mass number of this isotope are 1 and 1 respectively.
Structure of Hydrogen atom: This implies that it contains one proton, one electron, and no neutrons

( total number of neutrons = mass number – atomic number)

Atomic Structure of Carbon

Carbon has two stable isotopes – 12C and 13C. Of these isotopes, 12C has an abundance of 98.9%. It contains 6 protons, 6 electrons, and 6 neutrons.
Structure of Carbon atom: The electrons are distributed into two shells and the outermost shell (valence shell) has four electrons. The tetravalency of carbon enables it to form a variety of chemical bonds with various elements.

Atomic Structure of Oxygen

There exist three stable isotopes of oxygen – 18O, 17O, and 16O. However, oxygen-16 is the most abundant isotope.
Structure of Oxygen atom: Since the atomic number of this isotope is 8 and the mass number is 16, it consists of 8 protons and 8 neutrons. 6 out of the 8 electrons in an oxygen atom lie in the valence shell.

• All three Oxygen isotopes have medical applications. O-16 is used in the production of radioactive N-13 which is used for PET imaging and myocardial perfusion. O-17 can be used as a tracer in the study of cerebral oxygenutilization.
• Carbon Isotopes and mainly C-13 is used extensively in many different applications. C-13 is used for instance in organic chemistry research, studies into molecular structures, metabolism, food labeling, air pollution and climate change.
• This Atomic structure notes will help you to understand all model and theory:

Bohr’s Atomic Theory :

Neils Bohr put forth his model of the atom in the year 1915. This is the most widely used atomic model to describe the atomic structure of an element which is based on Planck’s theory of quantization.

Postulates of Bohr’s Atomic Theory:

• The electrons inside atoms are placed in discrete orbits called “stationery orbits”.
• The energy levels of these shells can be represented via quantum numbers.
• Electrons can jump to higher levels by absorbing energy and move to lower energy levels by losing or emitting its energy.
• As longs as, an electron stays in its own stationery, there will be no absorption or emission of energy.
• Electrons revolve around the nucleus in these stationery orbits only.
• The energy of the stationary orbits is quantized.

Limitations of Bohr’s Atomic Theory:

• Bohr’s atomic structure works only for single electron species such as H, He⁺, Li²⁺, Be³⁺, ….
• When the emission spectrum of hydrogen was observed under a more accurate spectrometer, each line spectrum was seen to be a combination of no of smaller discrete lines.
• Both Stark and Zeeman effects couldn’t be explain using Bohr’s theory.

Electromagnetic Wave Theory ( Maxwell)

An electromagnetic wave is characterized by its intensity and the frequency ν of the time variation of the electric and magnetic fields. … In terms of the modern quantum theory, electromagnetic radiation is the flow of photons (also called light quanta) through space.

These electric and magnetic waves travel perpendicular to each other and have certain characteristics, including

• amplitude, wavelength, and frequency.
• Electromagnetic radiation can travel through empty space.

The frequency is just the opposite; it’s the number of wave cycles that are completed in one second.
Amplitude and wavelength are both measures of distance.
The amplitude measures the height of the crest of the wave from the midline.
The wavelength measures the horizontal distance between cycles.

C =Vλ

Here,
C=Velocity of any electromagnetic radiation
V= frequency
λ= wavelength
Though the sciences generally classify EM waves into seven basic types, all are manifestations of the same phenomenon.
• Radio Waves: Instant Communication.
• Microwaves: Data and Heat.
• Infrared Waves: Invisible Heat.
• Visible Light Rays.
• Ultraviolet Waves: Energetic Light.
• X-rays: Penetrating Radiation.
• Gamma Rays: Nuclear Energy.

An object that absorbs all radiation falling on it, at all wavelengths, is called a black body. When a black body is at a uniform temperature, its emission has a characteristic frequency distribution that depends on the temperature. Its emission is called black-body radiation.

The photoelectric effect is the emission of electrons or other free carriers when light hits a material. Electrons emitted in this manner can be called photo electrons. This phenomenon is commonly studied in electronic physics, as well as in fields of chemistry.

• If frequency is greater than threshold frequency: Than ejection occurs and also, kinetic energy is imparted to ejected electron.
• If frequency is equal to threshold frequency, than only ejection occurs.
• If frequency is less than threshold frequency, than no ejection occurs and no kinetic energy is imparted.
  Please note hv_o is called as wave function.

Photoelectric Effect

According to the Einstein explanation of the photoelectric effect is:

The energy of photon = Energy needed to remove an electron + kinetic energy of the emitted electron
hν = W + E

Where:
• h is Planck’s constant.
• ν is the frequency of the incident photon.
• W is a work function.
• E is the maximum kinetic energy of ejected electrons: 1/2 mv².
• For this phenomenon to take place the photons should have the energy greater than or equal to the work function of the metal.

• E ≥ W
• hf ≥ W
• f ≥ Wh

In the above three equations, h is the plank’s constant, f is the frequency of the incident photon, and W is the work function of the metal used. The frequency which is equal to w/h is unique for a metal, it varies from metals to metal because the work function of each metal is different from the other.

When the photon is absorbed by metal, it transfers a part of the energy to the breaking the electron free from its orbit and rest of the energy is converted into the kinetic energy of the electron itself, therefore the equation for this could be written as,
hν = W + E

Planck’s quantum theory:

According to this theory:
1. Energy emitted or absorbed is not continuous, but is in the form of packets called quanta .In terms of light it is called as photon.
2. Each photon carries an energy which is directly proportional to the frequency of wavelength i.e. E depends upon v (nu).

• We have E=hv (where v is frequency)
• Value of h =6.634 x 10^-34J/sec
• Energy associated with no of packets is given by:
  E = nhv (where n is an integral multiple)
  This formula can also be written as:
  E = (nhc)/ (λ)
  (Because we know frequency = speed of light/wavelength)
  V = (c/ λ)
• This Atomic structure notes will give full idea about spectra

EMISSION AND ABSORBTION SPECTRA

This phenomenon gave serious blow to Rutherford model. It can be defined as: ‘splitting of light’ into various colours or colour bands is called spectra.”
When we see VIBGYOR the Violet colour merges into another and likewise other color merges into another except Violet colour.

So, in that case:

Where one-colour merges into another and there is no definite boundaries, that spectra is called continuous spectra.

• If we study it for atoms the spectra obtained is discontinuous spectra.
• The study of spectra is called spectroscopy

Atomic spectra are of two types

1. Emission spectra
2. Absorbtion spectra

Emission spectra: It is obtained when emitted light is analyzed. The light is emitted when an atom is heated or electric current is passed.These are also referred as finger prints of atoms.

Emission spectra of hydrogen

• The hydrogen gas ,at low pressure is taken in the tube.

• Then light emitted by it was examined

• It was noticed that spectra obtained consist of large number of closely spaced lines which falls in different regions as shown:

• Rydberg gave the formula as below:

\(\bar{v} = \frac{1}{\bar{v}}\) = \(R[\frac{1}{{1^n}^2} – \frac{1}{{2^n}^2}]\)

where R = Rydberg constant = \(1.097*{10}^7 {m}^{-1}\)

For Lyman n₁ = 1 & n₂ = 2,3,4

For Balmer n₁ = 2 & n₂ = 3,4,5

For Paschen n₁ = 3 & n₂ = 4,5

For Bracket n₁ = 4 & n₂ = 5,6,7

For Pfund n₁ = 5 & n₂ = 6,7,8

This was Rydberg formula

Limiting line: the limiting line in H spectrum was when n₂ = infinity

BOHR’S THEORY OF ATOMIC STRUCTURE

According to Bohr:

• Atom is electrically neutral i.e. number of Protons = number of Electrons.
• In center of an atom, a dense body called Nucleus is present.
• In Nucleus, Protons and Neutrons are present.
• Proton(P) = +ve

1. N = no charge.
2. Outside nucleus, shells or energy levels designated as K, L, M, N —-so on are present.
3. In shells Electrons revolve
4. E = -vely charged
5. Each shell has fixed amount of energy therefore they are called as stationary states or energy levels.

• i. Velocity of electron in nth Bohr orbit
  • V_n= 2.165*10⁶ Z/N m/s
• ii. Radius of nth Bohr orbit
  • r_n=0.53*10^-10 n²/Z m = 0.53 n²/Z Å
• iii. E_n =-2.178*10^-18 Z²/n² J/atom
  • E_n = -1312 Z²/n²KJ/mol
  • E_n = -13.6 Z²/n² eV/atom
• iv. ΔE= -2.178*10^-18(1/n₁²-1/n₂²)Z² J/atom
• The energy of electron is quantized.
• Only those orbits are permitted in which angular momentum of electron is integral multiple of h/2π.
• The electron in its ground state neither absorb or emit energy that is it keeps on revolving in orbit without losing any energy.
• Energy is emitted or absorbed only when electron jumps from its lower state to higher state called as excited state .
• The excited state being unstable, electron returns to its ground state and in doing so it emit the absorbed energy equal to E=E₂-E₁

Usefulness of Bohr model:

• It explained stability of an atom.
• It explained the spectrum of hydrogen.

Limitations of Bohr’s Atomic Theory:

• Bohr’s atomic structure works only for single electron species such as H, He+, Li2+, Be3+, ….
• When the emission spectrum of hydrogen was observed under a more accurate spectrometer, each line spectrum was seen to be a combination of no of smaller discrete lines.
  Both Stark and Zeeman effects couldn’t be explain using Bohr’s theory.

EXPLANATION OF HYDROGEN SPECTRA

• According to Bohr,
  When energy is supplied to atoms of hydrogen, the electron from lower energy gets excited to higher energy level.
  The excited state being unstable, it jumps back to its original state that is ground state.
• Some electrons move to their ground state in one jump, some in multiple jumps. Each jump corresponds to line in a spectrum.
• As we know the gas in tube consists of many hydrogen atoms.
• Therefore, each electron on getting energy gets excited.
• On returning to the ground state, they either move in single jump or multiple jump.

This is the reason that we get so many lines in different regions in hydrogen spectrum.

The wavelength emitted by them can be calculated as:
We know that

E = E₂-E₁

or hv = E₂-E₁
or v = E₂-E₁/h
We also know v = c/ λ
λ = hc/E2-E1

\(\lambda = \frac{hc}{{E}_{2}-{E}_{1}}\)

Limitations of Bohr model of an atom:

1. Bohr model failed to explain the line spectra of multi-electron atoms.
2. He couldn’t explain splitting of line in the magnetic field (Zeeman effect) and in electric field (stark effect).
3. He failed to explain three-dimensional model of an atom.
4. He was unable to explain the shapes of molecule.
5. He couldn’t explain the dual nature of matter and Heisenberg uncertainty principle.

This led to the discovery of Quantum mechanics..

This Atomic structure notes will give full idea about debroglie

DUAL NATURE OF PARTICLE: DEBROGLIE AND HEISENBERG UNCERTAINTY PRINCIPLE in ATOMIC STRUCTURE

As we have studied that light has dual character .That is particle as well as wave character. In the same way, it was proved that all material particles too have wave like character.
It was explained by De-Broglie: According to him when any particle is in motion it emits wave.”
The wavelength associated with it is given by:
E=hv
E =mc²
From both we can write,
mc² = hv
λ= h/mc
in case c is repalaced

Derivation of Bohr postulate of angular momentum from de Broglie relation

According to Bohr model, the electron move around the nucleus in circular orbit. According to De Broglie, the wave can be in phase or can be out of phase. For the wave to be in phase the circumference should be integral multiple of wavelength

\(λ = \frac{h}{mv}\)

Significance of De- Broglie relation:

In real life, it does not have any significance. This is because in real life we come across only macroscopic objects which have significant mass. So, the wavelength emitted by them is almost nil. The wavelength is significant only for microscopic bodies, but in real life we do not come across microscopic objects.

Heisenberg’s uncertainty principle:

According to Heisenberg, it is impossible to measure both the position and momentum of moving particle with accuracy.
• If value of position is small ,it can be measured accurately but not momentum.
• If value of momentum is small it is measured accurately but not the position.

Mathematically that means:
\(Δx * Δp ≥ \frac{h}{4pi})
Δx = uncertainty in position
Δp = uncertainty in momentum

Explanation:

• Suppose we need to measure position accurately, than we need to use light.
• So, that the photon of light must strike the electron and reflected photon is seen with microscope.
• Due to hitting, the position and velocity of electron is changed.
• But to pin point position, the light of shorter wavelength should be used.
• The shorter wavelength means high frequency and high energy.
• So, this high energy photon may change the speed and direction of particle.

QUANTUM MECHANICS

It was given by Schrodinger. He said if we take both the characters in account that is particle character and wave character, we have to define a property that is a wave function.

Schrodinger wave equation

On the basis of it Schrodinger simplified equation as:

Physical significance of wave function:

• wave function gives the amplitude associated with it. But if we do square of it, than it gives the probability of finding the electron in particular region.

Orbital: It is three-dimensional space, where probability of finding an electron is maximum.

There are four types of orbital:

• s-orbital: Spherical in shape, non-directional. It has only 1 orbital therefore, can accommodate only 2 electrons.
• P-orbital: dumb-bell shaped and directional. It has 3 orbital (p_x, p_y, p_z). It can accommodate maximum of 6 electrons.
• d-orbital: It has double dumbbell, directional. It has 5 orbital (d_xy,d_yz,d_zx,d_x²-y²,d_z²).It can accommodate maximum of 10 electrons
• F-orbital: It has diffused shape. It has 7 orbital therefore, can accommodate maximum of 14 electrons.

Quantum numbers

Quantum numbers are set of 4 numbers, which gives complete information about the address of electron.

There are 4 types of quantum numbers:
• Principal quantum number.
• Azimuthal quantum number.
• Magnetic quantum number.
• Spin quantum number.

Principal quantum number:

• It is represented as ‘n’.
• It was given by Bohr.
• It represents the orbit where electron is going to be present.

Uses of Quantum numbers:
1. It gives number of electron in orbit by formula 2n².
2. It gives angular momentum of electron.
3. It gives energy of electron.
4. It gives radius of orbit.

Azimuthal quantum number:

• It gives information about sub shell of an atom.
• It is represented as ‘l’.
• It was introduced by Somerfield.
• It always has value (n-1).

Example: if n=1, l=0
If n=2, l=0, 1
If n=3, l=0, 1, 2

Magnetic quantum number:

• It describes the behavior of electron in magnetic field.
• It is represented as ‘m’.
• It was given by land.
• Its value is equal to –l,0, +l

For example:

if n=1, l=0, m=0 that is only one orbital
If n=2, l=0,1, m=-1,0, +1 that is three orbitals

Spin quantum number:

• It gives the info about spinning of electron about its axis i.e. clockwise or anticlockwise
• It is denoted by ‘s’.
• Its value is either =+1/2, -1/2

Pauli’s Exclusion Principle

According to this principle: “no two electrons can have the same set of all four quantum numbers.”

Or,

it states that an orbital can have maximum of two electrons and that must be of opposite spin. Due to this, it was concluded that an orbital can have maximum of two electrons which can have all 3-quantum number same but the spin will be definitely different.

Shapes of atomic orbitals:

• s –orbital

Its shape is spherical. For 1s the probability of finding electron is maximum near nucleus and it decreases as we move away from nucleus.

For 2s: Again, probability of finding electron is maximum near nucleus and decrease as the distance increase. But it has one ring in it, where probability of finding electron is zero that is a nodal plane or a node.
The shape of 2s differs from 1s as it has one node and 1s has no node. Similarly, in 3s there are two nodes.
The different s orbitals differ from each other in number of nodes, size and energy.

• Shape of p orbital

Its shape is dumb-bell. It is found that probability of finding electron is maximum in both the lobes. There is a plane passing through nucleus where probability of finding the electron is almost zero. That is nodal plane.
There are 3 sub-shells: p_x, p_y and p_z.

It is directional in nature. All the 3p orbitals are degenerate that is have same energy.

• Shape of d orbital:

It has 5 subshells: d_xy, d_yz, d_zx, d_x²-y² and d_z²

There shapes are given as shown:

The shape of d_z² is called as doughnut shape or baby soother type shape.

Number of nodes in any orbital can be calculated by: (n-l-1).
Number of spherical or radial nodes = (n-l-1)
Number of planar or angular nodes = l
Number of nodes of any type in orbial = n-1

Electronic Configuration of an Atom

The electrons have to be filled in the s, p, d, f in accordance with the following rule.
Aufbau’s principle: The filling of electrons should take place in accordance with the ascending order of energy of orbitals:
• Lower energy orbital should be filled first and higher energy levels.
• The energy of orbital α(p + l) value it two orbitals have same (n + l) value, E α n
• Ascending order of energy 1s, 2s, 2p, 3s, 3p, 4s, 3d, . . .

Pauli’s exclusion principle: No two electrons can have all the four quantum numbers to be the same or, if two electrons have to placed in an energy state they should be placed with opposite spies.
Hund’s rule of maximum multiplicity: In case of filling degenerate (same energy) orbitals, all the degenerate orbitals have to be singly filled first and then only pairing has to happen.

Important Questions & Answers Of Atomic Struture

1. The Vividh Bharati station of All India Radio, Delhi, broadcasts on a frequency of 1,368 kHz (kilo hertz). Calculate the wavelength of the electromagnetic radiation emitted by transmitter. Which part of the electromagnetic spectrum does it belong to?
   1. 219.3 m
   2. 415.3 m
   3. 95.2 m
   4. 212.4 m

Ans:

The wavelength, λ, is equal to c/ν, where c is the speed of electromagnetic radiation in vacuum and ν is the frequency. Substituting the given values, we have

λ = c/v

=3*10⁸ m s^-1/1368khz

=3.00*10⁸ m s^-1/1368*10³ s^-1

=219.3 m

This is a characteristic radiowave wavelength.

2. Calculate (a) wavenumber and (b)frequency of yellow radiation having wavelength 5800 Å.
   2. 234*10⁴ cm¹
   3. 342*10² m¹
   4. 724*10⁴ cm^-1, 5.172*10¹⁴s^-1
   5. 724*10² cm^-1, 5.23*10¹³s^-1

Ans :

Calculation of wave number   \(\bar{v}\) =

a) λ=5800Å = 5800 × 10^–8 cm

= 5800 × 10^–10 m

\(\bar{v}\) = Wave number = 1/ λ=1/5800*10^-10

\(\bar{v}\) = 1.724*10⁶m^-1

\(\bar{v}\) = 1.724*10¹⁴cm^-1

b) Calculation of the frequency (ν)

\(\bar{v}\) = c/ λ = 3*10⁸ms^-1/5800*10^-10

\(\bar{v}\)  = 5.172*10¹⁴s^-1

3  Calculate the energy associated with the first orbit of He⁺. What is the radius of this orbit?

1. 0.026 nm
2. 0.0264 nm
3. 0.164 nm
4. 0.02645 nm

Ans:

E_n = (2.18*10^-18 J)Z²/n²    atom^-1

For He⁺, n = 1,  Z = 2

E₁=  -(2.18*10^-18 J) Z²

     = -8.72*10^-18 J

The radius of the orbit is given by equation :

Since n= 1, Z=  2

rn= (0.0529nm) 12/2

    =  0.02645nm

4  Which of the following are isoelectronic species i.e., those having the same number of electrons?

 Na⁺, K⁺, Mg^2+, Ca^2+, S^2–, Ar.

1. Na⁺, K⁺ & S^2–, Ar
2. K⁺, Mg²⁺& Na⁺, K⁺
3. Na⁺, Mg²⁺& K⁺, Ca²⁺, S^2–, Ar.
4. Ca²⁺, S^2–, Ar.& Na⁺, K⁺

Ans: Na⁺, Mg²⁺ both have 10 electrons

K⁺, Ca²⁺, S^2–, Ar have 18 electrons