Planck's Quantum Theory and Discovery of X-rays

PLANCK’S QUANTUM THEORY,
X-RAYS & ATOMIC NUMBER
CHAPTER # 2
ATOMIC STRUCTURE
Prepared By: Sidra Javed

Max Planck
• In 1901, Max Planck
initiated Quantum
Physics by
presenting his
Quantum Theory.
• He was awarded
Nobel Prize in
Physics in 1918.

Planck’s Quantum Theory
a) Energy is not emitted or absorbed
continuously. It is emitted or absorbed in the
form of wave packets or quanta.
In case of light the quantum
of energy is often
called Photon.

b) The amount of energy associated with
quantum of radiation is directly
proportional to the frequency (ν) of
radiation i.e.
Where, h =Planck’s Constant =6.626 x 10-34 J.s
E
hE 

c) A body can emit or absorb energy only
in terms of integral multiple of a
quantum/photon.
Where n= 1, 2, 3,….
nhE 

Frequency
Definition:
“The number of waves passing
through a point per second is called
frequency.”
Unit:
s-1 or Hz (Hertz)

Wavelength
Definition:
“The distance between two
adjacent crests of troughs is called
Wavelength.”
Unit:
m (meter)

Energy & Wavelength
Since,
where, c= Velocity of Light = 3x108ms-1


1



c


According to Planck’s Quantum Theory:
Therefore,
Thus greater the Wavelength of radiation,
lower will be the energy
hE 

c
hE 

Wave Number
Definition:
“The reciprocal of Wavelength is
called Wave number.”
Unit:
oA (Angstrom) or nm (Nanometers)
1 oA = 10-10m
1 nm = 10-9m

Energy & Wave Number
As we know that,
Therefore,
Thus energy of radiation is directly
proportional to wave number.



1
hcE 

EXAMPLE 2.7
A photon of light with energy 10-19 J is
emitted by a source of light.
a) Convert this light into Wavelength, frequency
and wave number of the photon in terms of
meters, Hertz and m-1 respectively.
b) Convert this energy of photon into ergs and
calculate the wavelength in cm, frequency in Hz
and wave number in cm-1.

Solution (a)
Data:
Energy of Photon = E = 10-19 J
Wavelength = λ = ? in m
Frequency = ν = ? in Hz
Wave Number = = ? im m-1

Frequency in Hz
hE 
h
E

sJ
J
.10626.6
10
34
19



 or Hz1051.1 114 
 s

Wavelength


c

114
18
1051.1
103





s
ms
 m6
1098.1 



c


Wave Number


1

m6
1098.1
1


 15
100.5 
 m

Solution (b)
Data:
Energy = E = ? in erg
Wavelength = λ = ? in cm
Frequency = ν = ? in Hz
Wave Number = = ? in cm-1

Energy in erg
ergJ 7
101 
ergE 719
1010  
erg12
10

Value of Planck’s Constant is also converted
into erg
sergh .1010626.6 734
 
sergh .10626.6 27


Frequency in Hz
hE 
h
E

serg
erg
.10626.6
10
27
12




or Hz1051.1 114 
 s

Wavelength in cm


c

114
110
1051.1
103





s
cms
 cm4
1098.1 



c


Wave Number in cm-1


1

cm4
1098.1
1



13
100.5 
 cm

X-rays
Wilhelm Conrad Röntgen ,
a German physicist,
accidentally
discovered the X-rays
in 1895
His discovery earned
him the first Nobel
Prize in Physics in
1901.

• On 8 November 1895, while working in
his lab, Röntgen accidentally discovered
some radiations having sort wavelength
and high energy.
Cathode
(-)
Anode
(+)
???

• He observed that these rays are emitted
when cathode rays produced in a
discharge tube are pointed to fall on a
heavy metal target.
• Since these radiations were unknown at
that time so he named them the X-Rays.
They are also known as Roentgen Rays.

HOW X-RAYS ARE PRODUCED?
• When an electron in cathode ray hits a
metal atom in the target, it can (if it has
sufficient energy) knock out an electron
from an inner shell of the atom.
+-
-
-
-
--
--
--
Cathode
(-)
-
-
-
-
-
-
-
--
-

• This produces a metal ion with an
electron missing from an inner orbital.
• The electronic configuration of target
metal becomes unstable
+
-
-
-
--
--
--

• An electron from an orbital of higher
energy drops in to the half-filled orbital
and a photon (hν) is emitted.
• The photon corresponds to
electromagnetic radiations in the X-ray
region.
+
-
-
-
--
--
--
hν

PROPERTIES OF X-RAYS
1. The X-rays are electromagnetic
radiations of very high frequency and
energy.
2. Energy and λ of X-rays depends upon
the nature of anode.
3. Every metal has its own characteristic X-
rays.
4. X-Rays are emitted from the target in all
directions.

X-RAYS & THE DISCOVERY OF
ATOMIC NUMBER (Z)
Henry G. J. Moseley was an
English physicist and
student of Rutherford.
In 1913 Moseley did systematic
and comprehensive study of
X-rays.
Moseley studied a range of
Wavelengths (0.04 to 0.08 oA)

MOSELEY’S RESEARCH
• Moseley used the
technique of “X-ray
spectroscopy” for his
experiments
• X-ray spectroscopy
was a latest technique
discovered by Max
Von Laue, a German
scientist.

DETERMINATION OF ATOMIC
NUMBER
• Moseley determined the atomic numbers
of the elements using X-rays which
produced in a cathode ray tube when the
electron beam (cathode ray) falls on a
metal target.
• He analyzed the spectral lines obtained
from 38 different metals (From Al to Au)
used as targets.

• Moseley proved that the Frequencies of
X-Rays are directly proportional to the
number of protons in the nucleus.
• He defined the number of protons in the
Nucleus as Atomic Number (Z).

CONCLUSIONS OF MOSELEY’S
ANALYSIS
• The spectral lines
could be classified
into two distinct
groups.
– Lines of shorter
wavelengths : K-series
– Lines of Longer
wavelengths : L-series

• If the target metal is of higher atomic
number, the frequency of X-rays becomes
higher.
• He formulated a relationship between
Frequency (ν) and atomic number (Z) of
the elements which is called Moseley’s
Law.

Moseley’s law
“The square root of Frequency (ν) of a
spectral line in X-Ray spectrum varies as
the Atomic Number (Z) of an element
emitting it.”
Where “a” and “b” are constant quantities.
Z
 bZa 

• This discovery changed the methods of
classification of elements. The Modern
Periodic table we now use is also based on
Moseley’s findings.

• This was the time when World War I broke out
in Western Europe. Moseley volunteered for
the Royal engineers of British Army.
• In a tragic loss to science, Moseley was shot
and killed during the Battle of Gallipoli on
August 10, 1915, at the age of just 27.
• A number of prominent authors, have
speculated that Moseley would have been
deserving of the Nobel Prize in Physics in 1916
which was awarded to nobody that year.

PRACTICAL APPLICATIONS OF
X-RAYS
• After the discovery of X-Rays by
Roentgen in December 1895, scientists
started experimenting with X-rays in
order to fine their practical applications.
• Since X-rays have different penetrating
powers for different types of matter so
they can be used to photograph interior
of an object.

Surgical Assistance
• Since X-rays have
different penetrating
powers for different types
of matter so they can be
used to photograph
interior of an object.
• In January 1986, scientists
successfully used X-rays
to assist in setting a
person’s broken arm.

Crystal Structures
• The layers of the closely packed particles in
a crystal constitute planes.
• In 1912 Max Von Laue suggested that the
particles in a crystals might be separated by
specific distances like a grating. Therefore a
beam of X-Rays should be diffracted by a
crystal.

• This was quickly verified experimentally
and a diffraction pattern of crystals was
obtained on a photographic film proving
that particles and planes of the crystals
are symmetrically arranged. The pattern
is known as “Laue Pattern” of the
substance.

X-ray Diffraction
• In 1913 William Bragg and Lawrence Bragg
devised a simpler apparatus to determine
the internal structure of a crystal, which is
called X-ray Diffraction Technique.

THE END

Planck's Quantum Theory and Discovery of X-rays

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