## FSc Notes Chemistry Part 1 Chapter 5 Atomic Structure Lecture 5

### Origins of Hydrogen Spectrum on the Basis of Bohr's Model:

According to Bohr's Model, the electron in hydrogen atom may
revolve in any shell ( K,L,M,N,O,P or Q ) depending upon its energy. When
hydrogen gas is provided energy either by heating or by an electric discharge
its electron absorbs energy and moves from lower shall to a high shell. The
electron comes back to the lower energy orbit, releasing the same amount of
energy which had been absorbed by it during its jumping from lower or higher
energy level. When electron jumps back from higher to lower energy level, it
emits energy which appears in the form of light having particular wavelength.
Lyman, Balmer, Paschen, Brackett and Pfund Series of lines are produced as a
result of electron transitions from higher orbits to lower orbits.

**Lyman Series:**

In this series, electron was jumped down from

2nd, 3rd, 4th,
5th, 6th, 7th orbits to 1st orbit i.e. for lyman series n1 = 1 & N2 = 2, 3, 4,5,6,7.

The wavelengths of all these radiations, emitted, were in
the range of UV region.

**Balmer Series:**

In this series, electron of hydrogen atom was jumped down
from

3rd, 4th, 5th, 6th & 7th orbits to and orbit. i.e. for Balmer series n1= 2 & n2 3,4,5,6 & 7.

The wavelengths of all these radiation, emitted, were in the
range of visible region.

**Paschen Series:**

In this series, electron of hydrogen atom, was jumped down
from

4th, 5th, 6th & 7th orbit to 3rd orbit i.e. N1= 3 & N2= 4, 5, 6,
7.

The wavelength of all these radiations, were in the range of
infrared region.

**Brackett Series:**

In this series, the electron of hydrogen atom was jumped
down from

5th, C orbit to 4th orbit i.e. n1=4 & N2 = 5, 6, 7.

The wavelengths of all these radiations were in the range of
infrared (IR) region.

**Pfund Series:**

In this series, electron of hydrogen atom was jumped down
from 5th, 6th, 7th orbit to 5th orbit. i.e. n1 = 5 & n2 = 6,7.

The wavelengths of these radiations were in the range of
infrared (IR) region.

### Defects in Bohr's Atomic Model:

Although Bohr's Atom Model can successfully explain the
stability of atom, ionization energy and the spectra of hydrogen like ions (e.g
He+, Li++ etc ) but it fails to explain the following.

- The energy states of more complicated atoms.
- The fine structure obtained in the high resolving spectrometer in the line spectrum of hydrogen atom is taken in the “magnetic field “some new lines are created ( Zee man effect ). In this way when this hydrogen spectrum is passed through “electric field “again some new lines are produced (stark effect).

### Both these effects cannot be explained by Bohr's theory.

#### Dual Nature of Electron:

Electron behaves as “wave” as well as “particle ". This
is known as dual nature of electron. According to "Mechanical Theory”
electron is a particle as explained by Bohr. In 1905, Plank and Einstein gave
an ideal, that the energy radiations consist of minute discrete particles (packet
of energy). Each discrete particle is known as a quantum (plural is quanta). In
case of light energy a quantum is called as photon.

**Plank's Equation is: E = hv h= 6.62x10(-34)**

**Einstein's Equation is: E= mc (2) C= 3x10(8)m/sec**

This concept is against the wave nature of energy. On the
other hand according to “wave theory " energy behaves as waves which more
in a continuous manner. This theory gives anti—particle concept of energy.
Based on “wave theory ", Louis De-Broglie ", explained the wave
nature of electron. The wave nature (anti-particle ), of electron was confirmed
in 1927 by " Clifton Davision " and " Germer" by
discovering electron diffraction. Diffraction is a wave phenomenon. From the
above explanations, dual nature of electron is confirmed.

#### Louis DR. Broglie's Equation:

In 1923, De—Broglie derived an equation which explains wave
like properties of a body of mass "m" moving with velocity
"r". Through this equation we can calculate the wavelength of any
material object of mass "m" moving with velocity "V". As is
the characteristic of waves, so material objects like electron can behave as
waves.

De—Broglie wave equation is here h (Plank’s constant) =
6.62x10-34 J sec

m = Mass of body

c = Velocity

v = wavelength associated with the body.

This equation can be derived as:

According to plank's equation:

E = hv--------------I

According to Einstein's equation.

E= mc(2)-----------II

Comparing eq I & II

hv = mc(2)

**Or**

hv = m.c.c

**Or**

mc = hv/c ------III

But v/c = 1/wavelength

Putting value of in eq III

mc = h/wavelength

**Or**

**Wavelength = h/mc**

From the above equation ( de—Broglie ) wave equation it is
clear that wavelength and mass(m) of a body are inversely proportional. So we
can say that every material object possesses a particle wavelength. But as the
mass increases, the wavelength decreases and hence for bodies of larger mass,
the wavelength is so smaller that it can be neglected and thus wave nature of
such bodies cannot be explained. On the other hand, particles like electron,
have very smaller mass and hence their wavelength will behavior of material
bodies with very small mass can be explained by de—Broglie wave equation.

Heisenberg Uncertainty Principle:

In 1927, Warner Heisenberg, presented the uncertainty
principle. This principle can be defined as:

Both the position and momentum of electron cannot be determined
simultaneously with accurate values. One of them will be accurate then the
other one will be more uncertain.

This can be explained as:

According to De—Broglie equation, the momentum (mc) and
wavelength are inversely proportional. To locate the position of an electron in
an atom, we use waves whose wavelength is shorter than the size of electron.
Thus the momentum of the wave will be maximum. So when this radiation (wave)
hit electron, due to high momentum of radiation, electron is displaced from its
original position. Thus the position of electron is uncertain. Thus the Bohr's
assumption, that electron travel in definite orbit with definite momentum is no
more satisfactory. Thus we can only find the probable position of electron in
an atom. The problem of determining the probable position of electron around
the nucleus of atom is solved be Schrodinger, a German chemist. He told that
electrons are moving with wavelike motion in three dimensional spaces around
the nucleus and not in fixed path. Thus Schrodinger rejected the idea of shell
and orbit and introduced the idea of “Orbital ". An orbital may be defined
as the space or region around the nucleus in which electron is most probably
located is known as atomic orbital.

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