PHYSICS
UNIT - 4
Chapter 7 : X-RAYS
Origin of X-rays
X-rays are produced when fast moving electrons strike a suitable target.
Characteristic and Continuous X-ray Spectra
When fast moving electrons strike a suitable target and lose their K.E. to the target atoms. This
loss of K.E. is converted into x-rays.
The loss of K.E. may take place by two different processes giving rise to two different types of x-
ray spectra:
i) Characteristic x-ray spectra
Few of the fast moving electrons coming from the filament penetrate deep inside the target
atom and knock out tightly bound electrons from the innermost shells (K or L shell) of the atom.
The vacancy so created is filled up by electrons from the upper shells jumping into the lower
vacant shell. The energy difference between the two levels is radiated in the form of X-rays
photon as shown in the figure. The wavelength of the x-rays emitted is characteristic of the
target element and is independent of the accelerating potential. Hence these x-rays are called
characteristic x-rays. The x-rays emitted consist of a series of distinct lines called as the Lynman,
Balmer series as shown in the figure.
ii) Continuous x-ray spectra
Few of the fast moving electrons coming
from the filament do not strike any orbital
electrons of the atoms of the target
material. But they penetrate deep into the
interior of the atoms and are deflected and
slowed down due to the attractive force of
the nucleus. This gives rise to loss of K.E.
which is given out continuously in the form
of x-rays of continuously varying
wavelengths. This is called continuous x-ray
spectra. The wavelength does not depend
on the target material but depends only on
the accelerating potential. The continuous
x-ray spectra consists of x-rays having
X-Rays Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, continuously varying wavelength ranging from a large value to a certain minimum value called
cut-off wavelength (λmin).
Expression for cut-off wavelength (λmin)
Let the velocity of electron change from to .
Then, loss of K.E. of the electron
This loss of K.E. is given out in the form of x-ray photons of frequency, say .
Thus we can write,
The energy of the photons will be maximum when the final velocity
Thus, we have,
………….eqn. 1
K.E. of an electron accelerated by a potential V is,
Substituting this in eqn. 1 we get,
Substituting for and we get
Moseley’s Law
It states that the frequency of a spectral line in characteristic x-ray spectra is directly
proportional to the square of the atomic number of the target element emitting it.
i.e. ( )
where is the frequency
is the atomic number of the target element
is a constant called nuclear screening constant ( for K-series lines)
The exact form of equation of Moseley’s Law is
( ) [ ]
where and is the quantum number of the final and initial shells involved in
the transition.
is the Rydberg’s constant,
For the line, ,
( )
Importance (or significance) of Moseley’s Law
1) According to Moseley’s Law, it is the atomic number of an element and not its atomic weight
which determines the physical and chemical properties of the element. This provided the
guideline that elements must be arranged according to their atomic number and not atomic
weight in the periodic table. The led to the correction of the Mendeleev’s periodic table to the
Modern periodic table.
X-Rays Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
UNIT - 4
Chapter 7 : X-RAYS
Origin of X-rays
X-rays are produced when fast moving electrons strike a suitable target.
Characteristic and Continuous X-ray Spectra
When fast moving electrons strike a suitable target and lose their K.E. to the target atoms. This
loss of K.E. is converted into x-rays.
The loss of K.E. may take place by two different processes giving rise to two different types of x-
ray spectra:
i) Characteristic x-ray spectra
Few of the fast moving electrons coming from the filament penetrate deep inside the target
atom and knock out tightly bound electrons from the innermost shells (K or L shell) of the atom.
The vacancy so created is filled up by electrons from the upper shells jumping into the lower
vacant shell. The energy difference between the two levels is radiated in the form of X-rays
photon as shown in the figure. The wavelength of the x-rays emitted is characteristic of the
target element and is independent of the accelerating potential. Hence these x-rays are called
characteristic x-rays. The x-rays emitted consist of a series of distinct lines called as the Lynman,
Balmer series as shown in the figure.
ii) Continuous x-ray spectra
Few of the fast moving electrons coming
from the filament do not strike any orbital
electrons of the atoms of the target
material. But they penetrate deep into the
interior of the atoms and are deflected and
slowed down due to the attractive force of
the nucleus. This gives rise to loss of K.E.
which is given out continuously in the form
of x-rays of continuously varying
wavelengths. This is called continuous x-ray
spectra. The wavelength does not depend
on the target material but depends only on
the accelerating potential. The continuous
x-ray spectra consists of x-rays having
X-Rays Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, continuously varying wavelength ranging from a large value to a certain minimum value called
cut-off wavelength (λmin).
Expression for cut-off wavelength (λmin)
Let the velocity of electron change from to .
Then, loss of K.E. of the electron
This loss of K.E. is given out in the form of x-ray photons of frequency, say .
Thus we can write,
The energy of the photons will be maximum when the final velocity
Thus, we have,
………….eqn. 1
K.E. of an electron accelerated by a potential V is,
Substituting this in eqn. 1 we get,
Substituting for and we get
Moseley’s Law
It states that the frequency of a spectral line in characteristic x-ray spectra is directly
proportional to the square of the atomic number of the target element emitting it.
i.e. ( )
where is the frequency
is the atomic number of the target element
is a constant called nuclear screening constant ( for K-series lines)
The exact form of equation of Moseley’s Law is
( ) [ ]
where and is the quantum number of the final and initial shells involved in
the transition.
is the Rydberg’s constant,
For the line, ,
( )
Importance (or significance) of Moseley’s Law
1) According to Moseley’s Law, it is the atomic number of an element and not its atomic weight
which determines the physical and chemical properties of the element. This provided the
guideline that elements must be arranged according to their atomic number and not atomic
weight in the periodic table. The led to the correction of the Mendeleev’s periodic table to the
Modern periodic table.
X-Rays Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
