Atom:

• An atom is the smallest particle of an element that can participate in a chemical reaction.
• The radius of an atom is measured in nanometers.
• The hydrogen atom is the tiniest of all atoms.

Structure of an Atom:

• By 1900, it had been discovered that the atom is not a simple, indivisible particle, but rather a collection of sub-atomic particles.
• J.J. Thomson discovered the 'electron,' a subatomic particle.
• J.J. Thomson was the first to propose a model for atom structure.
• E. Goldstein discovered new radiations in a gas discharge in 1886 and named them canal rays.
• Another positively charged subatomic particle was discovered using canal ray experiments and named proton.

Constituent of Atom:

• Several phenomena, such as radioactivity, demonstrate that atoms are divisible and consist of three fundamental particles: electron, proton, and neutron.

Electron: 

• J.J. Thomson discovered the electron in $1897$.
• When a high-voltage electric charge is passed through a low-pressure gas, a stream of rays is emitted from the cathode surface. These are referred to as cathode rays. 

• The magnitude of charge on electron is $1.6\times 10^{-19}C$.

• The mass of electron is  $9.109\times 10^{-31}kg$.

Properties of Cathode Rays:

• Cathode rays always travel away from the cathode in a straight line, casting shadows on metallic objects in their path.
• Cathode rays cause mechanical motion in the path of a spin wheel. As a result, they have kinetic energy and must be material particles.
• Because the cathode ray beam is deflected towards the positively charged plate, the particles in the cathode rays have a negative charge.
• Cathode rays can be deflected by both an electric and a magnetic field.
• Cathode rays have the ability to penetrate through thin layers of matter.
• Cathode rays emit X-rays when they strike a metallic target with a high melting point, such as tungsten. 
• Cathode rays glow when they strike glass or certain other materials.

The nature of cathode rays is unaffected by :

1. The cathode's nature and 
2. 2. The gas in the discharge tube. 

Charge/Mass Ratio (e/m)

• J.J. Thomson determined the charge-to-mass ratio of the electron by measuring the deflection under the influence of both electric and magnetic fields at the same time.

• For electrons, the value of the ratio $e/m$ was found to $-1.7588\times 10^{11}Ck{g}^{-1}$.

• R.A. Millikan measured the charge on the electron.

Proton ${(}_1^{1}por{}_1^{1}H)$:

• E. Goldstein demonstrated the existence of positively charged particles in an atom.
• When a high voltage is applied across the electrodes, a new type of ray is produced that passes through the perforated cathode and causes a glow on the opposite wall to the anode.
• Anode rays and canal rays are other names for these rays.

• The magnitude of charge on proton is $1.6\times 10^{-19}C$.

• The mass of proton is  $1.673\times 10^{-27}kg$.

Properties of Anode Rays 

• Anode rays travel in a straight line and cast shadows.
• Anode rays are bent in the opposite direction as cathode rays by the magnetic and electric fields.
• The anode rays can also rotate the wheel in their path and cause heating.
• The charge to mass ratio $(e/m)$ of positive rays is less than $e/m$ of electrons and depends on the nature of the gas used in the tube.

$\frac{e}{m}=9.579\times 10^{7}Ck{g}^{-1}$

• When electrons are removed from neutral atoms or molecules of gas, positively charged ions are formed. Positively charged ions move towards the perforated cathode, forming a beam of positive rays.

Neutron ${(}_0^{1}n)$:

• The neutrons were discovered by James Chadwick.
• These particles are neutral having charge equals zero.
• Their mass is approximate same as that of a hydrogen atom, i.e. $1.675\times 10^{-27}kg$.

Atomic Models:

-Various atomic models were proposed to show the arrangement and distribution of particles (electrons, protons and neutrons) within an atom. 

1) Thomson’s Atomic Model :

• The first simple model of an atom was proposed by J.J. Thomson.
• According to Thomson, an atom is a positively charged uniform sphere of radius $10^{-8}cm$ in which electrons are embedded in such a way that negative charge equals to positive charge.
• This model is also called plum-pudding model and watermelon model.
• This model was unable to explain the stability of an atom. 

2) Rutherford’s Atomic Model :

• The $\alpha -$particle scattering experiment served as the foundation for this model.
• Rutherford's $\alpha -$particle scattering experiments are concerned with the discovery of the nucleus.
• These experiments resulted in the following conclusions:

1. The atom has a very small rigid, positively charged body called the nucleus, and the $\alpha -$particles are repelled from the metal foil due to this positively charged nucleus. 
2. The entire mass of the atom is concentrated in the nucleus, so it is very heavy and rigid.

The following are the model's main postulates:

1. An atom is mostly made up of empty space. At its core, each atom has a heavy positively charged body known as the nucleus.
2. Planetary electrons are negatively charged electrons that revolve around the nucleus.
3. The nucleus is very small in comparison to the atom.
4. A strong interaction force holds all protons and neutrons together in the nucleus.
5. Rutherford's atomic model failed because he was unable to explain the atom's electronic structure. In other words, it does not provide information about the distribution of electrons around the nucleus.

Note: During $\alpha -$particle scattering experiment, $\alpha -$particles were bombarded by a thin sheet of heavy metals such as gold and platinum because their nuclei are large, resulting in good results.

Electromagnetic Radiations:

• These radiations have particle like and wave like properties.
• These radiations do not require a medium to move and can exist in a vacuum.
• The following is a list of the different types of electromagnetic radiations in increasing wavelength order.

$Cosmicrays<\gamma -rays<X-rays<UVrays<visiblelight<infraredrays<microwaves<FMradiowaves<longradiowaves.$

• The small portion around frequency $1015Hz$ is known as visible light.

• The relation between frequency, wavelength and velocity of light is  $c=\nu \lambda$
• Wave number: $\bar{\nu }=\frac{1}{\lambda }$
• Its unit is $m^{-1}$.

Note: X-rays are effectively produced when electrons strike the dense metal anode and have a very high penetrating power through matter, which is why these rays are used to study the interiors of objects.

• By increasing the potential difference between the anode and cathode, the penetration power of X-rays can be increased.

Electromagnetic Waves:

• Atomic spectrum of hydrogen atom:

$\frac{1}{\lambda }=\bar{\nu }=R_H=(\frac{1}{n_1^2}-\frac{1}{n_2^2})$where, $R_H$is the Rydberg constant and its value is $108978c{m}^{-1}$

$n_1$and $n_2$have integral values as follows:

Spectral Series:

1. Lyman Series - U.V region - $n_1=1$
2. Balmer Series - Visible region - $n_1=2$
3. Pascher Series - IR - $n_1=3$
4. Brackett Series - IR - $n_1=4$
5. Pfund Series - IR - $n_1=5$

Photoelectric Effect:

• When a metal surface is illuminated with light of a sufficient frequency, electrons are ejected.
• The threshold frequency is the minimum frequency required for electron ejection $(v_0)$.

• The frequency of radiation is directly related to the energy of the ejected electrons.
• The number of electrons ejected each second is determined by the radiation intensity.
• It can be expressed as: $h_v-h_{v_0}=\frac{1}{2}{m}_e{v}^2$

Plank’s Quantum Theory:

• Max Planck proposed this theory.
• The following are the main postulates of this theory:

1. The energy emitted or absorbed by atoms and molecules will be in the form of discrete packets of energy called quanta.
2. The energy of quanta $(E)$ is directly proportional to its frequency shown below:

$E\propto v$

$E=hv$

Here, $h$ is the Planck’s constant $(6.626\times 10^{-34}Js)$.

1. The energy of quanta is quantized or fixed, thus, $E=nhv$

Bohr’s Atomic Model:

• This atomic model, proposed by Neils Bohr, is based on Planck's quantum theory of radiations. 
• Electrons in an atom only revolve around the nucleus in specific circular paths known as orbits. Each orbit contains a fixed amount of energy.
• Only those orbits are permitted in which the electron's angular momentum $(mvr)$ is a whole number multiple of $\frac{h}{2\pi }$(${}^{\prime }{h}^{\prime }$is a Planck's constant, i.e. $mvr=nh2\pi$ where $n=1,2,\mathrm{3.....}$)

• When an electron jumps from a higher energy level to a lower energy level, energy is emitted, and energy is absorbed when an electron jumps from a lower energy level to a higher energy level.
• When a transition between two different energy levels or states occurs, the frequency of radiation absorbed or emitted is given by $v=\frac{\Delta }{E}h=\frac{E2-E1}{h}$where, $E_{1}and{E}_2$are the energies of lower and higher energy states. 

• The energy of an electron in a specific energy level $(n)$ is given by:

$E_n=-21.8\times 10^{-12}\times \frac{Z^2}{n^2}ergato{m}^{-1}$

$=-21.8\times 10^{-19}\times \frac{Z^2}{n^2}Jato{m}^{-1}$

$=-13.6\times \frac{Z^2}{n^2}eVatom$

$n=\frac{hc}{{\lambda }_n}=-R_H(\frac{1}{n_2^2}-\frac{1}{n_1^2})\times Z_2$

• The radius of nth orbit is shown below:

$r_n=\frac{0.53n^2}{Z}{A}^o$

• The velocity of electron in nth orbit is $v=\frac{218\times 10^{8}Z}{n}cm/s$

Failures of Bohr’s Atomic Theory: 

• He was unable to explain the splitting of spectral lines in the presence of a magnetic field (Zeeman effect) and an electric field (Stark effect).
• He was unable to explain the line spectra of multi-electron atoms, which contain more than one electron.
• He was unable to explain the atom's three-dimensional existence.
• Because of the dual nature of matter and the uncertainty principle, Bohr's theory failed.

Atomic Number (Z):

• Moseley introduced the concept of atomic number.
• Atomic number denotes the number of protons in the nucleus.
• The number of protons in a neutral atom equals the number of electrons.

Mass Number (A) :

• The mass number is the sum of the number of protons and neutrons in the nucleus.
• An atom with an atomic number and a mass number is denoted by ${}_z^{A}X$.

• Protons and neutrons are referred to collectively as nucleons.

Different Atomic Species: 

There are different types of atomic species. 

• Isotopes:

-Isotopes share the same atomic number but have different mass numbers.

-Isotopes share the same chemical properties but have different physical properties. 

-For example: ${}_1^{1}H$(protium), ${}_1^{2}H$(deuterium), ${}_1^{3}H$(tritium).

• Isobars: 

-Isobars are atoms that share the same mass number but have different atomic numbers.

-Isobars are atoms of different elements with distinct physical and chemical properties.

-For example: ${}_1^{3}H$ and ${}_2^{4}He$,${}_{18}^{40}Ar$${,}_{19}^{40}Kand{}_{20}^{40}Ca,{}_{52}^{130}Te,{}_{56}^{130}Baand{}_{54}^{130}Xe$

• Isotones:

-Isotones are atoms of different elements that have the same number of neutrons but different mass numbers.

-For example: ${}_1^{3}H,{}_2^{4}He,{}_{15}^{31}P,{}_{16}^{32}S,{}_{19}^{39}Kand{}_{20}^{40}Ca$

• Isoelectronic:

-Isoelectronic species contain the same number of electrons.

-For example $Ne,N{a}^{+},M{g}^{+2}$ all contain 10 number of electrons.

Quantum Mechanical Model of the Atom 

The formulation of a quantum mechanical model of an atom is based on two key concepts.

1) Dual Nature of Material Objects (de-Broglie Concept):

• In 1924 de-Broglie proposed that matter such as radiation acts as both particle and wave. 
• According to de-Broglie, the wavelength associated with a particle of mass, moving with velocity is given by 

$\lambda =\frac{h}{mv}=\frac{h}{p}$ where, $h$= Planck’s constant, $p$ momentum 

• This equation is known as de-Broglie equation.

2) Heisenberg’s Uncertainty Principle: 

• Heisenberg pointed out that measuring the position and momentum (or velocity) of a microscopic particle at the same time is impossible with absolute precision.

Mathematically, $\Delta x\times \Delta p=\frac{h}{4\pi }$

Here,$△$= uncertainty in position 

$△x$= uncertainty in momentum 

Now, $p=mv$

Hence, $△p=m△v$

On putting the value of $△p$ in the above expression, 

$m\Delta v\times \Delta x>\frac{h}{4\pi }$

or,

$\Delta x\times \Delta v=\frac{h}{4\pi \times m}$

Quantum Numbers

-Four sets of quantum numbers completely describe the position and nature of an electron.

1. Principal Quantum Number $(n)$: (Bohr)

• It determines the size of an electron's orbits and its energy.
• It can be represented by n, where $n=1,2,3,\dots ,\infty$(only positive integers).
• The various shells are denoted as $K,L,M,\dots etc.$
• The maximum numbers of electrons in any orbit can be calculated as $2n^2$where n is principal quantum number.

2. Azimuthal Quantum Number $(l)$: (Sommerfeld) 

• Also referred to as the angular momentum quantum number or the secondary quantum number.
• It determines the shape of an electron's orbit and its orbital angular momentum.
• It can be represented by $l$. It has the values from zero to $(n-1)$.${}^{\prime }{l}^{\prime }$ is equal to $0,1,2,3$ for $s,p,dandf$ orbitals respectively.

3. Magnetic Quantum Number $(m)$: (Lande) :

• Because it gives the orientation or distribution of the electron cloud, it determines the direction of orientation of electrons in suborbit (subshell). 
• It has all values from $-l$ through zero to $+l$, with total of $(2l+1)$values.
• It describes the splitting of spectral lines caused by a magnetic field (Zeeman effect).

4. Spin Quantum Number $(s)$: (Uhlenbech and Goldschmidt)

• It determines the orientation of the electron's spin.
• It has two values for electron spinning about its own axis.
• The spin quantum number either equal to $-\frac{1}{2}$(anti-clockwise) and $+\frac{1}{2}$(clockwise) totally depending on the spin of electron.
• For example: Assume the $5^{th}$electron of an atom

$n=2,l=1(p-orbit)$

$m=-1,s=-\frac{1}{2}or+\frac{1}{2}$

Electronic Configuration of Elements 

• The electronic configuration of an element is the arrangement of electrons in various shells, subshells, or orbitals of an atom.
• The following rule governs the filling of electrons in different orbitals: 

Aufbau’s Principle :

-"Sub-shells are filled with electrons in increasing order of their energies," according to this principle.

-This implies that lower energy sub-shells will be filled first, followed by higher energy sub-shells.

• The lower the value of $(n+l)$for an orbital, the lower is the energy. This is in according with $(n+l)$ rule. For e.g. between $3d$ and $4s$, the 4s $(4+0=4)$ will be filled before $3d(3+2=5)$.
• If two orbitals have the same $(n+l)$ value, the orbital with the lower n value will be filled first. For example: between $2pand3s,2p(2+1=3)$ will be filled first than $3s(3+0=3)$.
• The order of increasing energies can be written as :

$1s,2s,2p,3s,3p,4s,4p,3d,5s,5p,4d,6s,4f,5d,6p,7s,5f,6d,7p$

Note: Only Chromium and Copper do not obey this principle.

Their configurations are shown below.

${}_{24}Cr=1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}4s^1$

${}_{29}Cu=1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^1$

• Because completely filled and completely half-filled subshells have less energy, they are more stable than any other arrangement. Therefore, $3d^{5}4s^{1}and3d^{10}4s^1$ arrangements are more stable than that of $3d^{4}4s^{2}and3d^{9}4s^2$ respectively.

Hund’s Rule of Maximum Multiplicity: 

• "Pairing of electrons in a sub-shell begins after all available atomic orbitals or the sub-shell are singly filled (half-filled)," according to this rule.

Pauli’s Exclusion Principle :

• It says that, “No two electrons would have the same number of all the four quantum numbers.”