The Rutherford Model

Drawback of Rutherford Model

Bohr's Model

Quantum Model

At ordinary pressure, gases do not conduct electricity. Though gases conduct electricity at very

The rays produced by the discharge of electricity through gases are called

The presence of electrons in an atom was proved by

Anode rays, consisting of positively charged particles known as

In 1911, Ernst Rutherford and his co-workers carried out a series of experiments
using **alpha-particles** . A beam of alpha-particles was directed against a thin
foil of about **0.0004 cm** thickness of gold, platinum, silver or copper respectively.
The foil was surrounded by circular fluorescent zinc.

**1.** Most of the alpha-particles (nearly 99%) went straight without suffering any deflection.

**2.** A few of them got deflected through **small angles** .

**3.** A very few (about one in 20,000) did not pass through the foil at all but suffered **large
deflections** (more than 90°) or even came back in more or less the direction from which
they have come, i.e., a **deflection of 180°** .

The following observations were made:

Emission or absorption processes in hydrogen give rise to series, which are sequences of lines corresponding to atomic transitions, each ending or beginning with the same atomic state in hydrogen. Thus, for example, the Balmer Series involves transitions starting (for absorption) or ending (for emission) with the first excited state of hydrogen, while the Lyman Series involves transitions that start or end with the ground state of hydrogen.

According to the classical

Bohr made calculations and find out that an atom would collapse in

Niels Bohr suggested that the problem about hydrogen spectrum can be solved if we can make some assumptions.
According to classical theory, the frequency of the electromagnetic waves emitted by a revolving electron
is equal to the frequency of revolution.

##
Postulates

(i) Every atom consists of**nucleus and suitable number of electrons** revolved around the nucleus in circular orbits.
(ii) Electrons revolved only in certain non-radiating orbits called **stationery orbits** for which the total
angular momentum is an integral multiple of **h/2p** where **h** is plank's constant.

**L** is the Angular momentum of the revolving electrons.

(iii) Radiation occurs when an electron jumps from one orbit to another. It is emitted when electron jumps from higher orbit to a lower orbit i.e., E_{2} - E_{1} = hf, where f is frequency of radiation.

Bohr’s model helps to calculate the energies of various**stationary states** in hydrogen atom.
The energy (E_{n}) associated with each stationary state is called its **energy level** .
It is given by the expression,

Where**n** is the quantum number and has integral values 1, 2, 3 ......

For hydrogen
## De Broglie Wavelength

##
The Quantum Model

##
Shapes of Atomic Orbitals

**(i)** **s-orbital** :The shape of the cloud is the shape of the s-orbital. The cloud is not uniform
but **denser** in the region where the **probability of finding the electron is maximum** .

The size of an orbital**increases** as the principal quantum number increases, thus a 2s-orbital is **larger** than
1s-orbital. A 2s-orbital differs from 1s-orbital in having a nodal surface. A **nodal surface** is the region
in space where the probability of finding electron is zero.

**(ii)** **p-orbital** :There are three p-orbitals **p**_{x}, p_{y} and p_{z} .
They are **dumb-bell** shaped , the two levels being seperated by a **nodal plane** , i.e., a plane where there is no likely
hood of finding the electron. The p-oritals have a marked directional character, depending on whether the
p_{x}, p_{y} and p_{z} orbital is considered.

The p-orbitals consist of**two lobes**
with the atomic nucleus lying between them. The axis of each p-orbital is **perpendicular** to other two.

**(ii)** **d-orbital** : There are five d-orbitals which are directional and of **same energy**.
The shapes of four d-orbitals resemble four **leaf cloves** . The fifth d-orbital loops differently.

These d-orbitals are shown below.
##
The Aufbau Principle

(i) Every atom consists of

(iii) Radiation occurs when an electron jumps from one orbit to another. It is emitted when electron jumps from higher orbit to a lower orbit i.e., E

Bohr’s model helps to calculate the energies of various

Where

For hydrogen

In 1924, the French physicist de Broglie suggested that the electron has a **dual nature** .
In other words, electron have a dual character; they behave as **particles** as well as **waves** .
The wavelength associated with a particle of mass **'m'** , moving with velocity **'v'** is given
by de Broglie's relation as

## Heisenberg's Uncertainity Principle

According to Heisenberg’s uncertainty principle, it is not possible to measure, **simultaneously**,
the **position** and the **momentum** of a particle with unlimited precision. Mathematically this may be expressed

Improving on the Bohr Model, Sommerfeld, in order to account for the additional lines present in the
spectra of atoms, assumed that each principal energy level contains a number of ** sub-levels** , each of which
possesses slightly different energy. The subsidiary orbits are designated s, p, d and f.
The increasing energy levels of these sub-levels are:
** s < p < d < f **
There are four quantum numbers. These are **principal quantum number** , **azimuthal quantum number** ,
**magnetic quantum number** and **spin quantum number** .

Permissible values of the quantum numbers for various orbitals are mentioned in the table given below:

Permissible values of the quantum numbers for various orbitals are mentioned in the table given below:

The size of an orbital

The p-orbitals consist of

These d-orbitals are shown below.

Aufbau principle states that the orbitals get filled up in an **increasing order of their energies** .
It means that the last added electron will occupy the available orbital with the least energy.

There is a simpler method to get the order.

**(i)** Write a column of 's' orbitals from 1 to 8.

**(ii)** Write a second column for the 'p' orbitals starting at n=2. (1p is not an orbital combination allowed by quantum mechanics)

**(iii)** Write a column for the 'd' orbitals starting at n=3.

**(iv)** Write a final column for 4f and 5f. There are no elements that will need a 6f or 7f
shell to fill.

**(v)** Read the chart by running the diagonals starting from 1s.

Now the order of orbitals are known to fill, one thing remaining is memorizing how large each orbital is:

There is a simpler method to get the order.

Now the order of orbitals are known to fill, one thing remaining is memorizing how large each orbital is:

s orbitals have 1 possible value of m to hold 2 electrons

p orbitals have 3 possible value of m to hold 6 electrons

d orbitals have 5 possible value of m to hold 10 electrons

f orbitals have 7 possible value of m to hold 14 electrons