NCERT Textbook - Atoms Class 12 Notes | EduRev

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Class 12 : NCERT Textbook - Atoms Class 12 Notes | EduRev

 Page 1


Physics
414
12.1  INTRODUCTION
By the nineteenth century, enough evidence had accumulated in favour of
atomic hypothesis of matter. In 1897, the experiments on electric discharge
through gases carried out by the English physicist J. J. Thomson (1856 –
1940) revealed that atoms of different elements contain negatively charged
constituents (electrons) that are identical for all atoms. However, atoms on a
whole are electrically neutral. Therefore, an atom must also contain some
positive charge to neutralise the negative charge of the electrons. But what
is the arrangement of the positive charge and the electrons inside the atom?
In other words, what is the structure of an atom?
The first model of atom was proposed by J. J. Thomson in 1898.
According to this model, the positive charge of the atom is uniformly
distributed throughout the volume of the atom and the negatively charged
electrons are embedded in it like seeds in a watermelon. This model was
picturesquely called plum pudding model of the atom. However
subsequent studies on atoms, as described in this chapter, showed that
the distribution of the electrons and positive charges are very different
from that proposed in this model.
We know that condensed matter (solids and liquids) and dense gases at
all temperatures emit electromagnetic radiation in which a continuous
distribution of several wavelengths is present, though with different
intensities. This radiation is considered to be due to oscillations of atoms
Chapter Twelve
ATOMS
Page 2


Physics
414
12.1  INTRODUCTION
By the nineteenth century, enough evidence had accumulated in favour of
atomic hypothesis of matter. In 1897, the experiments on electric discharge
through gases carried out by the English physicist J. J. Thomson (1856 –
1940) revealed that atoms of different elements contain negatively charged
constituents (electrons) that are identical for all atoms. However, atoms on a
whole are electrically neutral. Therefore, an atom must also contain some
positive charge to neutralise the negative charge of the electrons. But what
is the arrangement of the positive charge and the electrons inside the atom?
In other words, what is the structure of an atom?
The first model of atom was proposed by J. J. Thomson in 1898.
According to this model, the positive charge of the atom is uniformly
distributed throughout the volume of the atom and the negatively charged
electrons are embedded in it like seeds in a watermelon. This model was
picturesquely called plum pudding model of the atom. However
subsequent studies on atoms, as described in this chapter, showed that
the distribution of the electrons and positive charges are very different
from that proposed in this model.
We know that condensed matter (solids and liquids) and dense gases at
all temperatures emit electromagnetic radiation in which a continuous
distribution of several wavelengths is present, though with different
intensities. This radiation is considered to be due to oscillations of atoms
Chapter Twelve
ATOMS
415
Atoms
and molecules, governed by the interaction of each atom or
molecule with its neighbours. In contrast, light emitted from
rarefied gases heated in a flame, or excited electrically in a
glow tube such as the familiar neon sign or mercury vapour
light has only certain discrete wavelengths. The spectrum
appears as a series of bright lines. In such gases, the
average spacing between atoms is large. Hence, the
radiation emitted can be considered due to individual atoms
rather than because of interactions between atoms or
molecules.
In the early nineteenth century it was also established
that each element is associated with a characteristic
spectrum of radiation, for example, hydrogen always gives
a set of lines with fixed relative position between the lines.
This fact suggested an intimate relationship between the
internal structure of an atom and the spectrum of
radiation emitted by it. In 1885, Johann Jakob Balmer
(1825 – 1898) obtained a simple empirical formula which
gave the wavelengths of a group of lines emitted by atomic
hydrogen. Since hydrogen is simplest of the elements
known, we shall consider its spectrum in detail in this
chapter.
Ernst Rutherford (1871–1937), a former research
student of J. J. Thomson, was engaged in experiments on
a-particles emitted by some radioactive elements. In 1906,
he proposed a classic experiment of scattering of these
a-particles by atoms to investigate the atomic structure.
This experiment was later performed around 1911 by Hans
Geiger (1882–1945) and Ernst Marsden (1889–1970, who
was 20 year-old student and had not yet earned his
bachelor’s degree). The details are discussed in Section
12.2. The explanation of the results led to the birth of
Rutherford’s planetary model of atom (also called the
nuclear model of the atom). According to this the entire
positive charge and most of the mass of the atom is concentrated in a small
volume called the nucleus with electrons revolving around the nucleus just
as planets revolve around the sun.
Rutherford’s nuclear model was a major step towards how we see
the atom today. However, it could not explain why atoms emit light of
only discrete wavelengths. How could an atom as simple as hydrogen,
consisting of a single electron and a single proton, emit a complex
spectrum of specific wavelengths? In the classical picture of an atom, the
electron revolves round the nucleus much like the way a planet revolves
round the sun. However, we shall see that there are some serious
difficulties in accepting such a model.
12.2 ALPHA-PARTICLE SCATTERING AND
RUTHERFORD’S NUCLEAR MODEL OF ATOM
At the suggestion of Ernst Rutherford, in 1911, H. Geiger and E. Marsden
performed some experiments. In one of their experiments, as shown in
Ernst Rutherford (1871 –
1937)  British physicist
who did pioneering work on
radioactive radiation. He
discovered alpha-rays and
beta-rays. Along with
Federick Soddy, he created
the modern theory of
radioactivity. He studied
the ‘emanation’ of thorium
and discovered a new noble
gas, an isotope of radon,
now known as thoron. By
scattering alpha-rays from
the metal foils, he
discovered the atomic
nucleus and proposed the
plenatery model of the
atom. He also estimated the
approximate size of the
nucleus.
ERNST RUTHERFORD (1871 – 1937)
Page 3


Physics
414
12.1  INTRODUCTION
By the nineteenth century, enough evidence had accumulated in favour of
atomic hypothesis of matter. In 1897, the experiments on electric discharge
through gases carried out by the English physicist J. J. Thomson (1856 –
1940) revealed that atoms of different elements contain negatively charged
constituents (electrons) that are identical for all atoms. However, atoms on a
whole are electrically neutral. Therefore, an atom must also contain some
positive charge to neutralise the negative charge of the electrons. But what
is the arrangement of the positive charge and the electrons inside the atom?
In other words, what is the structure of an atom?
The first model of atom was proposed by J. J. Thomson in 1898.
According to this model, the positive charge of the atom is uniformly
distributed throughout the volume of the atom and the negatively charged
electrons are embedded in it like seeds in a watermelon. This model was
picturesquely called plum pudding model of the atom. However
subsequent studies on atoms, as described in this chapter, showed that
the distribution of the electrons and positive charges are very different
from that proposed in this model.
We know that condensed matter (solids and liquids) and dense gases at
all temperatures emit electromagnetic radiation in which a continuous
distribution of several wavelengths is present, though with different
intensities. This radiation is considered to be due to oscillations of atoms
Chapter Twelve
ATOMS
415
Atoms
and molecules, governed by the interaction of each atom or
molecule with its neighbours. In contrast, light emitted from
rarefied gases heated in a flame, or excited electrically in a
glow tube such as the familiar neon sign or mercury vapour
light has only certain discrete wavelengths. The spectrum
appears as a series of bright lines. In such gases, the
average spacing between atoms is large. Hence, the
radiation emitted can be considered due to individual atoms
rather than because of interactions between atoms or
molecules.
In the early nineteenth century it was also established
that each element is associated with a characteristic
spectrum of radiation, for example, hydrogen always gives
a set of lines with fixed relative position between the lines.
This fact suggested an intimate relationship between the
internal structure of an atom and the spectrum of
radiation emitted by it. In 1885, Johann Jakob Balmer
(1825 – 1898) obtained a simple empirical formula which
gave the wavelengths of a group of lines emitted by atomic
hydrogen. Since hydrogen is simplest of the elements
known, we shall consider its spectrum in detail in this
chapter.
Ernst Rutherford (1871–1937), a former research
student of J. J. Thomson, was engaged in experiments on
a-particles emitted by some radioactive elements. In 1906,
he proposed a classic experiment of scattering of these
a-particles by atoms to investigate the atomic structure.
This experiment was later performed around 1911 by Hans
Geiger (1882–1945) and Ernst Marsden (1889–1970, who
was 20 year-old student and had not yet earned his
bachelor’s degree). The details are discussed in Section
12.2. The explanation of the results led to the birth of
Rutherford’s planetary model of atom (also called the
nuclear model of the atom). According to this the entire
positive charge and most of the mass of the atom is concentrated in a small
volume called the nucleus with electrons revolving around the nucleus just
as planets revolve around the sun.
Rutherford’s nuclear model was a major step towards how we see
the atom today. However, it could not explain why atoms emit light of
only discrete wavelengths. How could an atom as simple as hydrogen,
consisting of a single electron and a single proton, emit a complex
spectrum of specific wavelengths? In the classical picture of an atom, the
electron revolves round the nucleus much like the way a planet revolves
round the sun. However, we shall see that there are some serious
difficulties in accepting such a model.
12.2 ALPHA-PARTICLE SCATTERING AND
RUTHERFORD’S NUCLEAR MODEL OF ATOM
At the suggestion of Ernst Rutherford, in 1911, H. Geiger and E. Marsden
performed some experiments. In one of their experiments, as shown in
Ernst Rutherford (1871 –
1937)  British physicist
who did pioneering work on
radioactive radiation. He
discovered alpha-rays and
beta-rays. Along with
Federick Soddy, he created
the modern theory of
radioactivity. He studied
the ‘emanation’ of thorium
and discovered a new noble
gas, an isotope of radon,
now known as thoron. By
scattering alpha-rays from
the metal foils, he
discovered the atomic
nucleus and proposed the
plenatery model of the
atom. He also estimated the
approximate size of the
nucleus.
ERNST RUTHERFORD (1871 – 1937)
Physics
416
Fig. 12.1, they directed a beam of
5.5 MeV a-particles emitted from a
214
83
Bi radioactive source at a thin metal
foil made of gold. Figure 12.2 shows a
schematic diagram of this experiment.
Alpha-particles emitted by a 
214
83
Bi
radioactive source were collimated into
a narrow beam by their passage
through lead bricks. The beam was
allowed to fall on a thin foil of gold of
thickness 2.1 × 10
–7
 m. The scattered
alpha-particles were observed through
a rotatable detector consisting of zinc
sulphide screen and a microscope. The
scattered alpha-particles on striking
the screen produced brief light flashes
or scintillations. These flashes may be
viewed through a microscope and the
distribution of the number of scattered
particles may be studied as a function
of angle of scattering.
FIGURE 12.2 Schematic arrangement of the Geiger-Marsden experiment.
A typical graph of the total number of a-particles scattered at different
angles, in a given interval of time, is shown in Fig. 12.3. The dots in this
figure represent the data points and the solid curve is the theoretical
prediction based on the assumption that the target atom has a small,
dense, positively charged nucleus. Many of the a-particles pass through
the foil. It means that they do not suffer any collisions. Only about 0.14%
of the incident a-particles scatter by more than 1º; and about 1 in 8000
deflect by more than 90º. Rutherford argued that, to deflect the a-particle
backwards, it must experience a large repulsive force. This force could
FIGURE 12.1 Geiger-Marsden scattering experiment.
The entire apparatus is placed in a vacuum chamber
(not shown in this figure).
Page 4


Physics
414
12.1  INTRODUCTION
By the nineteenth century, enough evidence had accumulated in favour of
atomic hypothesis of matter. In 1897, the experiments on electric discharge
through gases carried out by the English physicist J. J. Thomson (1856 –
1940) revealed that atoms of different elements contain negatively charged
constituents (electrons) that are identical for all atoms. However, atoms on a
whole are electrically neutral. Therefore, an atom must also contain some
positive charge to neutralise the negative charge of the electrons. But what
is the arrangement of the positive charge and the electrons inside the atom?
In other words, what is the structure of an atom?
The first model of atom was proposed by J. J. Thomson in 1898.
According to this model, the positive charge of the atom is uniformly
distributed throughout the volume of the atom and the negatively charged
electrons are embedded in it like seeds in a watermelon. This model was
picturesquely called plum pudding model of the atom. However
subsequent studies on atoms, as described in this chapter, showed that
the distribution of the electrons and positive charges are very different
from that proposed in this model.
We know that condensed matter (solids and liquids) and dense gases at
all temperatures emit electromagnetic radiation in which a continuous
distribution of several wavelengths is present, though with different
intensities. This radiation is considered to be due to oscillations of atoms
Chapter Twelve
ATOMS
415
Atoms
and molecules, governed by the interaction of each atom or
molecule with its neighbours. In contrast, light emitted from
rarefied gases heated in a flame, or excited electrically in a
glow tube such as the familiar neon sign or mercury vapour
light has only certain discrete wavelengths. The spectrum
appears as a series of bright lines. In such gases, the
average spacing between atoms is large. Hence, the
radiation emitted can be considered due to individual atoms
rather than because of interactions between atoms or
molecules.
In the early nineteenth century it was also established
that each element is associated with a characteristic
spectrum of radiation, for example, hydrogen always gives
a set of lines with fixed relative position between the lines.
This fact suggested an intimate relationship between the
internal structure of an atom and the spectrum of
radiation emitted by it. In 1885, Johann Jakob Balmer
(1825 – 1898) obtained a simple empirical formula which
gave the wavelengths of a group of lines emitted by atomic
hydrogen. Since hydrogen is simplest of the elements
known, we shall consider its spectrum in detail in this
chapter.
Ernst Rutherford (1871–1937), a former research
student of J. J. Thomson, was engaged in experiments on
a-particles emitted by some radioactive elements. In 1906,
he proposed a classic experiment of scattering of these
a-particles by atoms to investigate the atomic structure.
This experiment was later performed around 1911 by Hans
Geiger (1882–1945) and Ernst Marsden (1889–1970, who
was 20 year-old student and had not yet earned his
bachelor’s degree). The details are discussed in Section
12.2. The explanation of the results led to the birth of
Rutherford’s planetary model of atom (also called the
nuclear model of the atom). According to this the entire
positive charge and most of the mass of the atom is concentrated in a small
volume called the nucleus with electrons revolving around the nucleus just
as planets revolve around the sun.
Rutherford’s nuclear model was a major step towards how we see
the atom today. However, it could not explain why atoms emit light of
only discrete wavelengths. How could an atom as simple as hydrogen,
consisting of a single electron and a single proton, emit a complex
spectrum of specific wavelengths? In the classical picture of an atom, the
electron revolves round the nucleus much like the way a planet revolves
round the sun. However, we shall see that there are some serious
difficulties in accepting such a model.
12.2 ALPHA-PARTICLE SCATTERING AND
RUTHERFORD’S NUCLEAR MODEL OF ATOM
At the suggestion of Ernst Rutherford, in 1911, H. Geiger and E. Marsden
performed some experiments. In one of their experiments, as shown in
Ernst Rutherford (1871 –
1937)  British physicist
who did pioneering work on
radioactive radiation. He
discovered alpha-rays and
beta-rays. Along with
Federick Soddy, he created
the modern theory of
radioactivity. He studied
the ‘emanation’ of thorium
and discovered a new noble
gas, an isotope of radon,
now known as thoron. By
scattering alpha-rays from
the metal foils, he
discovered the atomic
nucleus and proposed the
plenatery model of the
atom. He also estimated the
approximate size of the
nucleus.
ERNST RUTHERFORD (1871 – 1937)
Physics
416
Fig. 12.1, they directed a beam of
5.5 MeV a-particles emitted from a
214
83
Bi radioactive source at a thin metal
foil made of gold. Figure 12.2 shows a
schematic diagram of this experiment.
Alpha-particles emitted by a 
214
83
Bi
radioactive source were collimated into
a narrow beam by their passage
through lead bricks. The beam was
allowed to fall on a thin foil of gold of
thickness 2.1 × 10
–7
 m. The scattered
alpha-particles were observed through
a rotatable detector consisting of zinc
sulphide screen and a microscope. The
scattered alpha-particles on striking
the screen produced brief light flashes
or scintillations. These flashes may be
viewed through a microscope and the
distribution of the number of scattered
particles may be studied as a function
of angle of scattering.
FIGURE 12.2 Schematic arrangement of the Geiger-Marsden experiment.
A typical graph of the total number of a-particles scattered at different
angles, in a given interval of time, is shown in Fig. 12.3. The dots in this
figure represent the data points and the solid curve is the theoretical
prediction based on the assumption that the target atom has a small,
dense, positively charged nucleus. Many of the a-particles pass through
the foil. It means that they do not suffer any collisions. Only about 0.14%
of the incident a-particles scatter by more than 1º; and about 1 in 8000
deflect by more than 90º. Rutherford argued that, to deflect the a-particle
backwards, it must experience a large repulsive force. This force could
FIGURE 12.1 Geiger-Marsden scattering experiment.
The entire apparatus is placed in a vacuum chamber
(not shown in this figure).
417
Atoms
be provided if the greater part of the
mass of the atom and its positive charge
were concentrated tightly at its centre.
Then the incoming a-particle could get
very close to the positive charge without
penetrating it, and such a close
encounter would result in a large
deflection. This agreement supported
the hypothesis of the nuclear atom. This
is why Rutherford is credited with the
discovery of the nucleus.
In Rutherford’s nuclear model of
the atom, the entire positive charge and
most of the mass of the atom are
concentrated in the nucleus with the
electrons some distance away. The
electrons would be moving in orbits
about the nucleus just as the planets
do around the sun. Rutherford’s
experiments suggested the size of
the nucleus to be about 10
–15
 m to
10
–14
 m. From kinetic theory, the size
of an atom was known to be 10
–10
 m,
about 10,000 to 100,000 times larger
than the size of the nucleus (see Chapter 11, Section 11.6 in Class XI
Physics textbook). Thus, the electrons would seem to be at a distance
from the nucleus of about 10,000 to 100,000 times the size of the nucleus
itself. Thus, most of an atom is empty space. With the atom being largely
empty space, it is easy to see why most a-particles go right through a
thin metal foil. However, when a-particle happens to come near a nucleus,
the intense electric field there scatters it through a large angle. The atomic
electrons, being so light, do not appreciably affect the a-particles.
The scattering data shown in Fig. 12.3 can be analysed by employing
Rutherford’s nuclear model of the atom. As the gold foil is very thin, it
can be assumed that a-particles will suffer not more than one scattering
during their passage through it. Therefore, computation of the trajectory
of an alpha-particle scattered by a single nucleus is enough. Alpha-
particles are nuclei of helium atoms and, therefore, carry two units, 2e,
of positive charge and have the mass of the helium atom. The charge of
the gold nucleus is Ze, where Z is the atomic number of the atom; for
gold Z = 79. Since the nucleus of gold is about 50 times heavier than an
a-particle, it is reasonable to assume that it remains stationary
throughout the scattering process. Under these assumptions, the
trajectory of an alpha-particle can be computed employing Newton’s
second law of motion and the Coulomb’s law for electrostatic
force of repulsion between the alpha-particle and the positively
charged nucleus.
FIGURE 12.3 Experimental data points (shown by
dots) on scattering of a-particles by a thin foil at
different angles obtained by Geiger and Marsden
using the setup shown in Figs. 12.1 and
12.2. Rutherford’s nuclear model predicts the solid
curve which is seen to be in good agreement with
experiment.
Page 5


Physics
414
12.1  INTRODUCTION
By the nineteenth century, enough evidence had accumulated in favour of
atomic hypothesis of matter. In 1897, the experiments on electric discharge
through gases carried out by the English physicist J. J. Thomson (1856 –
1940) revealed that atoms of different elements contain negatively charged
constituents (electrons) that are identical for all atoms. However, atoms on a
whole are electrically neutral. Therefore, an atom must also contain some
positive charge to neutralise the negative charge of the electrons. But what
is the arrangement of the positive charge and the electrons inside the atom?
In other words, what is the structure of an atom?
The first model of atom was proposed by J. J. Thomson in 1898.
According to this model, the positive charge of the atom is uniformly
distributed throughout the volume of the atom and the negatively charged
electrons are embedded in it like seeds in a watermelon. This model was
picturesquely called plum pudding model of the atom. However
subsequent studies on atoms, as described in this chapter, showed that
the distribution of the electrons and positive charges are very different
from that proposed in this model.
We know that condensed matter (solids and liquids) and dense gases at
all temperatures emit electromagnetic radiation in which a continuous
distribution of several wavelengths is present, though with different
intensities. This radiation is considered to be due to oscillations of atoms
Chapter Twelve
ATOMS
415
Atoms
and molecules, governed by the interaction of each atom or
molecule with its neighbours. In contrast, light emitted from
rarefied gases heated in a flame, or excited electrically in a
glow tube such as the familiar neon sign or mercury vapour
light has only certain discrete wavelengths. The spectrum
appears as a series of bright lines. In such gases, the
average spacing between atoms is large. Hence, the
radiation emitted can be considered due to individual atoms
rather than because of interactions between atoms or
molecules.
In the early nineteenth century it was also established
that each element is associated with a characteristic
spectrum of radiation, for example, hydrogen always gives
a set of lines with fixed relative position between the lines.
This fact suggested an intimate relationship between the
internal structure of an atom and the spectrum of
radiation emitted by it. In 1885, Johann Jakob Balmer
(1825 – 1898) obtained a simple empirical formula which
gave the wavelengths of a group of lines emitted by atomic
hydrogen. Since hydrogen is simplest of the elements
known, we shall consider its spectrum in detail in this
chapter.
Ernst Rutherford (1871–1937), a former research
student of J. J. Thomson, was engaged in experiments on
a-particles emitted by some radioactive elements. In 1906,
he proposed a classic experiment of scattering of these
a-particles by atoms to investigate the atomic structure.
This experiment was later performed around 1911 by Hans
Geiger (1882–1945) and Ernst Marsden (1889–1970, who
was 20 year-old student and had not yet earned his
bachelor’s degree). The details are discussed in Section
12.2. The explanation of the results led to the birth of
Rutherford’s planetary model of atom (also called the
nuclear model of the atom). According to this the entire
positive charge and most of the mass of the atom is concentrated in a small
volume called the nucleus with electrons revolving around the nucleus just
as planets revolve around the sun.
Rutherford’s nuclear model was a major step towards how we see
the atom today. However, it could not explain why atoms emit light of
only discrete wavelengths. How could an atom as simple as hydrogen,
consisting of a single electron and a single proton, emit a complex
spectrum of specific wavelengths? In the classical picture of an atom, the
electron revolves round the nucleus much like the way a planet revolves
round the sun. However, we shall see that there are some serious
difficulties in accepting such a model.
12.2 ALPHA-PARTICLE SCATTERING AND
RUTHERFORD’S NUCLEAR MODEL OF ATOM
At the suggestion of Ernst Rutherford, in 1911, H. Geiger and E. Marsden
performed some experiments. In one of their experiments, as shown in
Ernst Rutherford (1871 –
1937)  British physicist
who did pioneering work on
radioactive radiation. He
discovered alpha-rays and
beta-rays. Along with
Federick Soddy, he created
the modern theory of
radioactivity. He studied
the ‘emanation’ of thorium
and discovered a new noble
gas, an isotope of radon,
now known as thoron. By
scattering alpha-rays from
the metal foils, he
discovered the atomic
nucleus and proposed the
plenatery model of the
atom. He also estimated the
approximate size of the
nucleus.
ERNST RUTHERFORD (1871 – 1937)
Physics
416
Fig. 12.1, they directed a beam of
5.5 MeV a-particles emitted from a
214
83
Bi radioactive source at a thin metal
foil made of gold. Figure 12.2 shows a
schematic diagram of this experiment.
Alpha-particles emitted by a 
214
83
Bi
radioactive source were collimated into
a narrow beam by their passage
through lead bricks. The beam was
allowed to fall on a thin foil of gold of
thickness 2.1 × 10
–7
 m. The scattered
alpha-particles were observed through
a rotatable detector consisting of zinc
sulphide screen and a microscope. The
scattered alpha-particles on striking
the screen produced brief light flashes
or scintillations. These flashes may be
viewed through a microscope and the
distribution of the number of scattered
particles may be studied as a function
of angle of scattering.
FIGURE 12.2 Schematic arrangement of the Geiger-Marsden experiment.
A typical graph of the total number of a-particles scattered at different
angles, in a given interval of time, is shown in Fig. 12.3. The dots in this
figure represent the data points and the solid curve is the theoretical
prediction based on the assumption that the target atom has a small,
dense, positively charged nucleus. Many of the a-particles pass through
the foil. It means that they do not suffer any collisions. Only about 0.14%
of the incident a-particles scatter by more than 1º; and about 1 in 8000
deflect by more than 90º. Rutherford argued that, to deflect the a-particle
backwards, it must experience a large repulsive force. This force could
FIGURE 12.1 Geiger-Marsden scattering experiment.
The entire apparatus is placed in a vacuum chamber
(not shown in this figure).
417
Atoms
be provided if the greater part of the
mass of the atom and its positive charge
were concentrated tightly at its centre.
Then the incoming a-particle could get
very close to the positive charge without
penetrating it, and such a close
encounter would result in a large
deflection. This agreement supported
the hypothesis of the nuclear atom. This
is why Rutherford is credited with the
discovery of the nucleus.
In Rutherford’s nuclear model of
the atom, the entire positive charge and
most of the mass of the atom are
concentrated in the nucleus with the
electrons some distance away. The
electrons would be moving in orbits
about the nucleus just as the planets
do around the sun. Rutherford’s
experiments suggested the size of
the nucleus to be about 10
–15
 m to
10
–14
 m. From kinetic theory, the size
of an atom was known to be 10
–10
 m,
about 10,000 to 100,000 times larger
than the size of the nucleus (see Chapter 11, Section 11.6 in Class XI
Physics textbook). Thus, the electrons would seem to be at a distance
from the nucleus of about 10,000 to 100,000 times the size of the nucleus
itself. Thus, most of an atom is empty space. With the atom being largely
empty space, it is easy to see why most a-particles go right through a
thin metal foil. However, when a-particle happens to come near a nucleus,
the intense electric field there scatters it through a large angle. The atomic
electrons, being so light, do not appreciably affect the a-particles.
The scattering data shown in Fig. 12.3 can be analysed by employing
Rutherford’s nuclear model of the atom. As the gold foil is very thin, it
can be assumed that a-particles will suffer not more than one scattering
during their passage through it. Therefore, computation of the trajectory
of an alpha-particle scattered by a single nucleus is enough. Alpha-
particles are nuclei of helium atoms and, therefore, carry two units, 2e,
of positive charge and have the mass of the helium atom. The charge of
the gold nucleus is Ze, where Z is the atomic number of the atom; for
gold Z = 79. Since the nucleus of gold is about 50 times heavier than an
a-particle, it is reasonable to assume that it remains stationary
throughout the scattering process. Under these assumptions, the
trajectory of an alpha-particle can be computed employing Newton’s
second law of motion and the Coulomb’s law for electrostatic
force of repulsion between the alpha-particle and the positively
charged nucleus.
FIGURE 12.3 Experimental data points (shown by
dots) on scattering of a-particles by a thin foil at
different angles obtained by Geiger and Marsden
using the setup shown in Figs. 12.1 and
12.2. Rutherford’s nuclear model predicts the solid
curve which is seen to be in good agreement with
experiment.
Physics
418 EXAMPLE 12.1
The magnitude of this force is
2
0
(2 )( ) 1
4
eZe
F
r 
 
 
(12.1)
where r is the distance between the a-particle and the nucleus. The force
is directed along the line joining the a-particle and the nucleus. The
magnitude and direction of the force on an a-particle continuously
changes as it approaches the nucleus and recedes away from it.
12.2.1  Alpha-particle trajectory
The trajectory traced by an a-particle depends on the impact parameter,
b of collision. The impact parameter is the perpendicular distance of the
initial velocity vector of the a-particle from the centre of the nucleus (Fig.
12.4). A given beam of a-particles has a
distribution of impact parameters b, so that
the beam is scattered in various directions
with different probabilities (Fig. 12.4). (In
a beam, all particles have nearly same
kinetic energy.) It is seen that an a-particle
close to the nucleus (small impact
parameter) suffers large scattering. In case
of head-on collision, the impact parameter
is minimum and the a-particle rebounds
back (?  ? p). For a large impact parameter,
the a-particle goes nearly undeviated and
has a small deflection (?  ? 0).
The fact that only a small fraction of the
number of incident particles rebound back
indicates that the number of a-particles
undergoing head on collision is small. This,
in turn, implies that the mass of the atom is concentrated in a small
volume. Rutherford scattering therefore, is a powerful way to determine
an upper limit to the size of the nucleus.
Example 12.1 In the Rutherford’s nuclear model of the atom, the
nucleus (radius about 10
–15
 m) is analogous to the sun about which
the electron move in orbit (radius ˜ 10
–10
 m) like the earth orbits
around the sun. If the dimensions of the solar system had the same
proportions as those of the atom, would the earth be closer to or
farther away from the sun than actually it is? The radius of earth’s
orbit is about 1.5 × 10
11
 m. The radius of sun is taken as 7 × 10
8
 m.
Solution The ratio of the radius of electron’s orbit to the radius of
nucleus is (10
–10
 m)/(10
–15
 m) = 10
5
, that is, the radius of the electron’s
orbit is 10
5
 times larger than the radius of nucleus. If the radius of
the earth’s orbit around the sun were 10
5
 times larger than the radius
of the sun, the radius of the earth’s orbit would be 10
5
 × 7 × 10
8
 m =
7 × 10
13
 m. This is more than 100 times greater than the actual orbital
radius of earth. Thus, the earth would be much farther away from
the sun.
It implies that an atom contains a much greater fraction of empty
space than our solar system does.
FIGURE 12.4 Trajectory of a-particles in the
coulomb field of a target nucleus. The impact
parameter, b and scattering angle ?
are also depicted.
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