Theory atomic structure NEET Notes | EduRev

NEET : Theory atomic structure NEET Notes | EduRev

 Page 1


ATOMIC STRUCTURE # 1
Atomic Structure
Introduction :
STRUCTURE OF ATOM
? ? ? ? ? ? ? ? ? ? ? ?
 Rutherford's Model Bohr's Model   Wave mechanical model
Dalton’s concept of the indivisibility of the atom was completely discredited by a series of experimental evidences
obtained by scientists. A number of new phenomena were brought to light and man’s idea about the natural
world  underwent a revolutionary change. the discovery of electricity and spectral phenomena opened the door
for radical changes in approaches to experimentation. It was concluded that atoms are made of three particles
: electrons, protons and neutrons. These particles are called the fundamental particles of matter.
Earlier efforts to reveal structure of atom :
CATHODE RAYS - DISCOVERY OF ELECTRON
Figure-1
In 1859 Julius Plucker started the study of conduction of electricity through gases at low pressure
(10
–4
atm) in a discharge tube When a high voltage of the order of 10,000 volts or more was impressed across the
electrodes, some sort of invisible rays moved from the negative electrode to the positive electrode these rays are
called as cathode rays.
PROPERTIES OF CATHODE RAYS :
 
Figure-2
Page 2


ATOMIC STRUCTURE # 1
Atomic Structure
Introduction :
STRUCTURE OF ATOM
? ? ? ? ? ? ? ? ? ? ? ?
 Rutherford's Model Bohr's Model   Wave mechanical model
Dalton’s concept of the indivisibility of the atom was completely discredited by a series of experimental evidences
obtained by scientists. A number of new phenomena were brought to light and man’s idea about the natural
world  underwent a revolutionary change. the discovery of electricity and spectral phenomena opened the door
for radical changes in approaches to experimentation. It was concluded that atoms are made of three particles
: electrons, protons and neutrons. These particles are called the fundamental particles of matter.
Earlier efforts to reveal structure of atom :
CATHODE RAYS - DISCOVERY OF ELECTRON
Figure-1
In 1859 Julius Plucker started the study of conduction of electricity through gases at low pressure
(10
–4
atm) in a discharge tube When a high voltage of the order of 10,000 volts or more was impressed across the
electrodes, some sort of invisible rays moved from the negative electrode to the positive electrode these rays are
called as cathode rays.
PROPERTIES OF CATHODE RAYS :
 
Figure-2
ATOMIC STRUCTURE # 2
Cathode rays have the following properties.
(i) Path of travelling is straight from the cathode with a very high velocity as it produces shadow of an
object placed in its path.
(ii) Cathode rays produce mechanical effects. If small light paddle wheel is placed between the electrodes,
it rotates. This indicates that the cathode rays consist of material particles.
(iii) When electric and magnetic fields are applied to the cathode rays in the discharge tube. The rays are
deflected thus establishing that they consist of charged particles. The direction of deflection showed
that cathode rays consist of negatively charged particles called electrons.
(iv) They produce a green glow when strike the glass wall beyond the anode. Light is emitted when they
strike the zinc sulphide screen.
(v) Cathode rays penetrate through thin sheets of aluminium and metals.
(vi) They affect the photographic plates
(vii) The ratio of charge(e) to mass(m) i.e. charge/mass is same for all cathode rays irrespective of the gas
used in the tube. e/m = 1.76 × 10
11
 Ckg
–1
Thus, it can be concluded that electrons are basic constituent of all the atoms.
PRODUCTION OF ANODE RAYS (DISCOVERY OF PROTON) :
Goldstein (1886) repeated the experiment with a discharge tube filled with a perforated cathode and found that
new type of rays came out through the hole in the cathode.
Figure-3
When this experiment is conducted, a faint red glow is observed on the wall behind the cathode. Since these
rays originate from the anode, they are called anode rays.
PROPERTIES OF ANODE RAYS :
? Anode rays travel along straight paths and hence they cast shadows of object placed in their path.
? They rotate a light paddle wheel placed in their path. This shows that anode rays are made up of
material particles.
? They are deflected towards the negative plate of an electric field. This shows that these rays are
positively charged.
? For different gases used in the discharge tube, the charge to mass ratio (e/m) of the positive particles
constituting the positive rays is different. When hydrogen gas is taken in the discharge tube, the e/m
value obtained for the positive rays is found to be maximum. Since the value of charge (e) on the positive
particle obtained from different gases is the same, the value of m must be minimum for the positive
particles obtained from hydrogen gas. Thus, the positive particle obtained from hydrogen gas is the
lightest among all the positive particles obtained from different gases. This particle is called the proton.
Page 3


ATOMIC STRUCTURE # 1
Atomic Structure
Introduction :
STRUCTURE OF ATOM
? ? ? ? ? ? ? ? ? ? ? ?
 Rutherford's Model Bohr's Model   Wave mechanical model
Dalton’s concept of the indivisibility of the atom was completely discredited by a series of experimental evidences
obtained by scientists. A number of new phenomena were brought to light and man’s idea about the natural
world  underwent a revolutionary change. the discovery of electricity and spectral phenomena opened the door
for radical changes in approaches to experimentation. It was concluded that atoms are made of three particles
: electrons, protons and neutrons. These particles are called the fundamental particles of matter.
Earlier efforts to reveal structure of atom :
CATHODE RAYS - DISCOVERY OF ELECTRON
Figure-1
In 1859 Julius Plucker started the study of conduction of electricity through gases at low pressure
(10
–4
atm) in a discharge tube When a high voltage of the order of 10,000 volts or more was impressed across the
electrodes, some sort of invisible rays moved from the negative electrode to the positive electrode these rays are
called as cathode rays.
PROPERTIES OF CATHODE RAYS :
 
Figure-2
ATOMIC STRUCTURE # 2
Cathode rays have the following properties.
(i) Path of travelling is straight from the cathode with a very high velocity as it produces shadow of an
object placed in its path.
(ii) Cathode rays produce mechanical effects. If small light paddle wheel is placed between the electrodes,
it rotates. This indicates that the cathode rays consist of material particles.
(iii) When electric and magnetic fields are applied to the cathode rays in the discharge tube. The rays are
deflected thus establishing that they consist of charged particles. The direction of deflection showed
that cathode rays consist of negatively charged particles called electrons.
(iv) They produce a green glow when strike the glass wall beyond the anode. Light is emitted when they
strike the zinc sulphide screen.
(v) Cathode rays penetrate through thin sheets of aluminium and metals.
(vi) They affect the photographic plates
(vii) The ratio of charge(e) to mass(m) i.e. charge/mass is same for all cathode rays irrespective of the gas
used in the tube. e/m = 1.76 × 10
11
 Ckg
–1
Thus, it can be concluded that electrons are basic constituent of all the atoms.
PRODUCTION OF ANODE RAYS (DISCOVERY OF PROTON) :
Goldstein (1886) repeated the experiment with a discharge tube filled with a perforated cathode and found that
new type of rays came out through the hole in the cathode.
Figure-3
When this experiment is conducted, a faint red glow is observed on the wall behind the cathode. Since these
rays originate from the anode, they are called anode rays.
PROPERTIES OF ANODE RAYS :
? Anode rays travel along straight paths and hence they cast shadows of object placed in their path.
? They rotate a light paddle wheel placed in their path. This shows that anode rays are made up of
material particles.
? They are deflected towards the negative plate of an electric field. This shows that these rays are
positively charged.
? For different gases used in the discharge tube, the charge to mass ratio (e/m) of the positive particles
constituting the positive rays is different. When hydrogen gas is taken in the discharge tube, the e/m
value obtained for the positive rays is found to be maximum. Since the value of charge (e) on the positive
particle obtained from different gases is the same, the value of m must be minimum for the positive
particles obtained from hydrogen gas. Thus, the positive particle obtained from hydrogen gas is the
lightest among all the positive particles obtained from different gases. This particle is called the proton.
ATOMIC STRUCTURE # 3
DISCOVERY OF NEUTRON :
Later, a need was felt for the presence of electrically neutral particles as one of the constituent of atom. These
particles were discovered by Chadwick in 1932 by bombarding a thin sheet of Beryllium with ?-particles, when
electrically neutral particles having a mass slightly greater than that of the protons were emitted. He named
these particles as neutrons.
n C He Be
1
0
12
6
4
2
9
4
? ? ? ? ?
The NUCLEUS :
Electrons, protons & neutrons are the fundamental particles present in all atoms,(except hydrogen)
Table : 1
 Particles Symbol       Mass      Charge    Discoverer
 Electron
–1
e
0
 or ? 9.10939 x 10
-31 
kg  – 1.6022 x l0
–19
    J.J. Thomson
Coulombs             Stoney Lorentz 1887
0.00054 u   – 4.803 × 10
–10
 esu
 Proton
1
H
1
1.6722 x 10
–27
 kg  + 1.6022 x 10
–19
    Goldstein
     Coulombs    Rutherford1907
1.00727 u   + 4.803 x 10
–10
 esu
 Neutron
 0
n
1
1.67493 x 10
–27
 kg       neutral    James Chadwick
1.00867 u 0 1932
1 amu ? 1.66 × 10
–27
 kg
ATOMIC MODELS :
(A) Thomson’s Model of the Atom :
An atom is electrically neutral. It contains positive charges (due to the presence of protons ) as well as negative
charges (due to the presence of electrons). Hence, J.J. Thomson assumed that an atom is a uniform sphere of
positive charges with electrons embedded in it.
        Figure-4
(B) Rutherford’s Experiment :
Figure-5
Observation :
1. Most of the ?-particles passed straight through the gold foil without suffering any deflection from their
original path.
2. A few of them were deflected through small angles, while a very few were deflected to a large extent.
3. A very small percentage (1 in 20000) was deflected through angles ranging from 90° to 180°.
Page 4


ATOMIC STRUCTURE # 1
Atomic Structure
Introduction :
STRUCTURE OF ATOM
? ? ? ? ? ? ? ? ? ? ? ?
 Rutherford's Model Bohr's Model   Wave mechanical model
Dalton’s concept of the indivisibility of the atom was completely discredited by a series of experimental evidences
obtained by scientists. A number of new phenomena were brought to light and man’s idea about the natural
world  underwent a revolutionary change. the discovery of electricity and spectral phenomena opened the door
for radical changes in approaches to experimentation. It was concluded that atoms are made of three particles
: electrons, protons and neutrons. These particles are called the fundamental particles of matter.
Earlier efforts to reveal structure of atom :
CATHODE RAYS - DISCOVERY OF ELECTRON
Figure-1
In 1859 Julius Plucker started the study of conduction of electricity through gases at low pressure
(10
–4
atm) in a discharge tube When a high voltage of the order of 10,000 volts or more was impressed across the
electrodes, some sort of invisible rays moved from the negative electrode to the positive electrode these rays are
called as cathode rays.
PROPERTIES OF CATHODE RAYS :
 
Figure-2
ATOMIC STRUCTURE # 2
Cathode rays have the following properties.
(i) Path of travelling is straight from the cathode with a very high velocity as it produces shadow of an
object placed in its path.
(ii) Cathode rays produce mechanical effects. If small light paddle wheel is placed between the electrodes,
it rotates. This indicates that the cathode rays consist of material particles.
(iii) When electric and magnetic fields are applied to the cathode rays in the discharge tube. The rays are
deflected thus establishing that they consist of charged particles. The direction of deflection showed
that cathode rays consist of negatively charged particles called electrons.
(iv) They produce a green glow when strike the glass wall beyond the anode. Light is emitted when they
strike the zinc sulphide screen.
(v) Cathode rays penetrate through thin sheets of aluminium and metals.
(vi) They affect the photographic plates
(vii) The ratio of charge(e) to mass(m) i.e. charge/mass is same for all cathode rays irrespective of the gas
used in the tube. e/m = 1.76 × 10
11
 Ckg
–1
Thus, it can be concluded that electrons are basic constituent of all the atoms.
PRODUCTION OF ANODE RAYS (DISCOVERY OF PROTON) :
Goldstein (1886) repeated the experiment with a discharge tube filled with a perforated cathode and found that
new type of rays came out through the hole in the cathode.
Figure-3
When this experiment is conducted, a faint red glow is observed on the wall behind the cathode. Since these
rays originate from the anode, they are called anode rays.
PROPERTIES OF ANODE RAYS :
? Anode rays travel along straight paths and hence they cast shadows of object placed in their path.
? They rotate a light paddle wheel placed in their path. This shows that anode rays are made up of
material particles.
? They are deflected towards the negative plate of an electric field. This shows that these rays are
positively charged.
? For different gases used in the discharge tube, the charge to mass ratio (e/m) of the positive particles
constituting the positive rays is different. When hydrogen gas is taken in the discharge tube, the e/m
value obtained for the positive rays is found to be maximum. Since the value of charge (e) on the positive
particle obtained from different gases is the same, the value of m must be minimum for the positive
particles obtained from hydrogen gas. Thus, the positive particle obtained from hydrogen gas is the
lightest among all the positive particles obtained from different gases. This particle is called the proton.
ATOMIC STRUCTURE # 3
DISCOVERY OF NEUTRON :
Later, a need was felt for the presence of electrically neutral particles as one of the constituent of atom. These
particles were discovered by Chadwick in 1932 by bombarding a thin sheet of Beryllium with ?-particles, when
electrically neutral particles having a mass slightly greater than that of the protons were emitted. He named
these particles as neutrons.
n C He Be
1
0
12
6
4
2
9
4
? ? ? ? ?
The NUCLEUS :
Electrons, protons & neutrons are the fundamental particles present in all atoms,(except hydrogen)
Table : 1
 Particles Symbol       Mass      Charge    Discoverer
 Electron
–1
e
0
 or ? 9.10939 x 10
-31 
kg  – 1.6022 x l0
–19
    J.J. Thomson
Coulombs             Stoney Lorentz 1887
0.00054 u   – 4.803 × 10
–10
 esu
 Proton
1
H
1
1.6722 x 10
–27
 kg  + 1.6022 x 10
–19
    Goldstein
     Coulombs    Rutherford1907
1.00727 u   + 4.803 x 10
–10
 esu
 Neutron
 0
n
1
1.67493 x 10
–27
 kg       neutral    James Chadwick
1.00867 u 0 1932
1 amu ? 1.66 × 10
–27
 kg
ATOMIC MODELS :
(A) Thomson’s Model of the Atom :
An atom is electrically neutral. It contains positive charges (due to the presence of protons ) as well as negative
charges (due to the presence of electrons). Hence, J.J. Thomson assumed that an atom is a uniform sphere of
positive charges with electrons embedded in it.
        Figure-4
(B) Rutherford’s Experiment :
Figure-5
Observation :
1. Most of the ?-particles passed straight through the gold foil without suffering any deflection from their
original path.
2. A few of them were deflected through small angles, while a very few were deflected to a large extent.
3. A very small percentage (1 in 20000) was deflected through angles ranging from 90° to 180°.
ATOMIC STRUCTURE # 4
Rutherford’s nuclear concept of the atom.
(i) The atom of an element consists of a small positively charged ‘nucleus’ which is situated at the centre
of the atom and which carries almost the entire mass of the atom.
(ii) The electrons are distributed in the empty space of the atom around the nucleus in different concentric
circular paths, called orbits.
(iii) The number of electrons in orbits is equal to the number of positive charges (protons) in the nucleus.
Hence, the atom is electrically neutral.
(iv) The volume of the nucleus is negligibly small as compared to the volume of the atom.
(v) Most of the space in the atom is empty.
DRAWBACKS OF RUTHERFORD’S MODEL :
1. This was not according to the classical theory of electromagnetism proposed by maxwell. According to
this theory, every accelerated charged particle must emit radiations in the form of electromagnetic
waves and loses it total energy.
Since energy of electrons keep on decreasing, so radius of the circular orbits should also decrease and
ultimately the electron should fall in nucleus.
2. It could not explain the line spectrum of H-atom.
PROPERTIES OF CHARGE :
1. Q = ne ( charge is quantized)
2. Charge are of two types :
(i) positive charge (ii) Negative Charge
e = –1.6 x 10
–19
p = + 1.6 x 10
–19
C
This does not mean that a proton has a greater charge but it implies that the charge is equal and opposite.
Same charge repel each other and opposite charges attract each other.
3. Charge is a SCALAR Qty. and the force between the charges always acts along the line joining the charges.
The magnitude of the force between the two charge placed at a distance ‘r’ is given by
F
E
=      
0
4
1
? ?
 
2
2 1
r
q q
   (electrical force)
4. If two charge q
1
 and q
2
 are sepreated by distance r then the potential energy of the two charge system is given
by.
P.E. =      
0
4
1
? ?
 
r
q q
2 1
5. If a charged particle q is placed on a surface of potential V then the potential energy of the charge is
q x V.
Estimation of closest distance of approach (derivation)
Ex.1 An ?-particle is projected from infinity with the velocity V
0
 towards the nucleus of an atom having atomic number
equal to Z then find out (i) closest distance of approach (R) (ii) what is the velocity of the ?-particle at the
distance R
1
 (R
1
 > R) from the nucleus.
Sol.
+
m
?
V
?
1 2 3
R 
R
1
Page 5


ATOMIC STRUCTURE # 1
Atomic Structure
Introduction :
STRUCTURE OF ATOM
? ? ? ? ? ? ? ? ? ? ? ?
 Rutherford's Model Bohr's Model   Wave mechanical model
Dalton’s concept of the indivisibility of the atom was completely discredited by a series of experimental evidences
obtained by scientists. A number of new phenomena were brought to light and man’s idea about the natural
world  underwent a revolutionary change. the discovery of electricity and spectral phenomena opened the door
for radical changes in approaches to experimentation. It was concluded that atoms are made of three particles
: electrons, protons and neutrons. These particles are called the fundamental particles of matter.
Earlier efforts to reveal structure of atom :
CATHODE RAYS - DISCOVERY OF ELECTRON
Figure-1
In 1859 Julius Plucker started the study of conduction of electricity through gases at low pressure
(10
–4
atm) in a discharge tube When a high voltage of the order of 10,000 volts or more was impressed across the
electrodes, some sort of invisible rays moved from the negative electrode to the positive electrode these rays are
called as cathode rays.
PROPERTIES OF CATHODE RAYS :
 
Figure-2
ATOMIC STRUCTURE # 2
Cathode rays have the following properties.
(i) Path of travelling is straight from the cathode with a very high velocity as it produces shadow of an
object placed in its path.
(ii) Cathode rays produce mechanical effects. If small light paddle wheel is placed between the electrodes,
it rotates. This indicates that the cathode rays consist of material particles.
(iii) When electric and magnetic fields are applied to the cathode rays in the discharge tube. The rays are
deflected thus establishing that they consist of charged particles. The direction of deflection showed
that cathode rays consist of negatively charged particles called electrons.
(iv) They produce a green glow when strike the glass wall beyond the anode. Light is emitted when they
strike the zinc sulphide screen.
(v) Cathode rays penetrate through thin sheets of aluminium and metals.
(vi) They affect the photographic plates
(vii) The ratio of charge(e) to mass(m) i.e. charge/mass is same for all cathode rays irrespective of the gas
used in the tube. e/m = 1.76 × 10
11
 Ckg
–1
Thus, it can be concluded that electrons are basic constituent of all the atoms.
PRODUCTION OF ANODE RAYS (DISCOVERY OF PROTON) :
Goldstein (1886) repeated the experiment with a discharge tube filled with a perforated cathode and found that
new type of rays came out through the hole in the cathode.
Figure-3
When this experiment is conducted, a faint red glow is observed on the wall behind the cathode. Since these
rays originate from the anode, they are called anode rays.
PROPERTIES OF ANODE RAYS :
? Anode rays travel along straight paths and hence they cast shadows of object placed in their path.
? They rotate a light paddle wheel placed in their path. This shows that anode rays are made up of
material particles.
? They are deflected towards the negative plate of an electric field. This shows that these rays are
positively charged.
? For different gases used in the discharge tube, the charge to mass ratio (e/m) of the positive particles
constituting the positive rays is different. When hydrogen gas is taken in the discharge tube, the e/m
value obtained for the positive rays is found to be maximum. Since the value of charge (e) on the positive
particle obtained from different gases is the same, the value of m must be minimum for the positive
particles obtained from hydrogen gas. Thus, the positive particle obtained from hydrogen gas is the
lightest among all the positive particles obtained from different gases. This particle is called the proton.
ATOMIC STRUCTURE # 3
DISCOVERY OF NEUTRON :
Later, a need was felt for the presence of electrically neutral particles as one of the constituent of atom. These
particles were discovered by Chadwick in 1932 by bombarding a thin sheet of Beryllium with ?-particles, when
electrically neutral particles having a mass slightly greater than that of the protons were emitted. He named
these particles as neutrons.
n C He Be
1
0
12
6
4
2
9
4
? ? ? ? ?
The NUCLEUS :
Electrons, protons & neutrons are the fundamental particles present in all atoms,(except hydrogen)
Table : 1
 Particles Symbol       Mass      Charge    Discoverer
 Electron
–1
e
0
 or ? 9.10939 x 10
-31 
kg  – 1.6022 x l0
–19
    J.J. Thomson
Coulombs             Stoney Lorentz 1887
0.00054 u   – 4.803 × 10
–10
 esu
 Proton
1
H
1
1.6722 x 10
–27
 kg  + 1.6022 x 10
–19
    Goldstein
     Coulombs    Rutherford1907
1.00727 u   + 4.803 x 10
–10
 esu
 Neutron
 0
n
1
1.67493 x 10
–27
 kg       neutral    James Chadwick
1.00867 u 0 1932
1 amu ? 1.66 × 10
–27
 kg
ATOMIC MODELS :
(A) Thomson’s Model of the Atom :
An atom is electrically neutral. It contains positive charges (due to the presence of protons ) as well as negative
charges (due to the presence of electrons). Hence, J.J. Thomson assumed that an atom is a uniform sphere of
positive charges with electrons embedded in it.
        Figure-4
(B) Rutherford’s Experiment :
Figure-5
Observation :
1. Most of the ?-particles passed straight through the gold foil without suffering any deflection from their
original path.
2. A few of them were deflected through small angles, while a very few were deflected to a large extent.
3. A very small percentage (1 in 20000) was deflected through angles ranging from 90° to 180°.
ATOMIC STRUCTURE # 4
Rutherford’s nuclear concept of the atom.
(i) The atom of an element consists of a small positively charged ‘nucleus’ which is situated at the centre
of the atom and which carries almost the entire mass of the atom.
(ii) The electrons are distributed in the empty space of the atom around the nucleus in different concentric
circular paths, called orbits.
(iii) The number of electrons in orbits is equal to the number of positive charges (protons) in the nucleus.
Hence, the atom is electrically neutral.
(iv) The volume of the nucleus is negligibly small as compared to the volume of the atom.
(v) Most of the space in the atom is empty.
DRAWBACKS OF RUTHERFORD’S MODEL :
1. This was not according to the classical theory of electromagnetism proposed by maxwell. According to
this theory, every accelerated charged particle must emit radiations in the form of electromagnetic
waves and loses it total energy.
Since energy of electrons keep on decreasing, so radius of the circular orbits should also decrease and
ultimately the electron should fall in nucleus.
2. It could not explain the line spectrum of H-atom.
PROPERTIES OF CHARGE :
1. Q = ne ( charge is quantized)
2. Charge are of two types :
(i) positive charge (ii) Negative Charge
e = –1.6 x 10
–19
p = + 1.6 x 10
–19
C
This does not mean that a proton has a greater charge but it implies that the charge is equal and opposite.
Same charge repel each other and opposite charges attract each other.
3. Charge is a SCALAR Qty. and the force between the charges always acts along the line joining the charges.
The magnitude of the force between the two charge placed at a distance ‘r’ is given by
F
E
=      
0
4
1
? ?
 
2
2 1
r
q q
   (electrical force)
4. If two charge q
1
 and q
2
 are sepreated by distance r then the potential energy of the two charge system is given
by.
P.E. =      
0
4
1
? ?
 
r
q q
2 1
5. If a charged particle q is placed on a surface of potential V then the potential energy of the charge is
q x V.
Estimation of closest distance of approach (derivation)
Ex.1 An ?-particle is projected from infinity with the velocity V
0
 towards the nucleus of an atom having atomic number
equal to Z then find out (i) closest distance of approach (R) (ii) what is the velocity of the ?-particle at the
distance R
1
 (R
1
 > R) from the nucleus.
Sol.
+
m
?
V
?
1 2 3
R 
R
1
ATOMIC STRUCTURE # 5
From energy conservation P.E
1
 + KE
1
 = P.E
2
 + KE
2
? 0 + 
2
1
 m
?
 V
?
2
?= 
R
) e 2 )( Ze ( K
 + 0
R = 
2
2
V m
KZe 4
? ?
(closest distance of approch)
Let velocity at R
1
 is V
1
.
From energy conservation P.E
1
 + KE
1
 = P.E
3
 + KE
3
? 0 + 
2
1
 m
?
 V
?
2
?= 
1
R
) e 2 )( Ze ( K
 + 
2
1
 m
?
 V
1
2
Size of the nucleus :
The volume of the nucleus is very small and is only a minute fraction of the total volume of the atom. Nucleus has
a diameter of the order of 10
–12
 to 10
–13
 cm and the atom has a diameter of the order of 10
–8
 cm.
Thus, diameter (size) of the atom is 100,000 times the diameter of the nucleus.
The radius of a nucleus is proportional to the cube root of the number of nucleons within it.
R = R
0
 (A)
1/3
 cm
where R
0
 can be 1.1 × 10
–13
  to 1.44 × 10
–13
 cm ; A = mass number ; R = Radius of the nucleus.
Nucleus contains protons & neutrons except hydrogen atoms which does not contain neutron in the nucleus.
ATOMIC NUMBER (Z) AND MASS NUMBER (A) :
? Atomic number (Z) of an element
= Total number of protons present in the nucleus
= Total number of electrons present in the atom
? Atomic number is also known as proton number because the charge on the nucleus depends upon the
number of protons.
? Since the electrons have negligible mass, the entire mass of the atom is mainly due to protons and
neutrons only. Since these particles are present in the nucleus, therefore they are collectively called
nucleons.
? As each of these particles has one unit mass on the atomic mass scale, therefore the sum of the
number of protons and neutrons will be nearly equal to the mass of the atom.
? Mass number of an element = No. of protons (Z) + No. of neutrons (n).
? The mass number of an element is nearly equal to the atomic mass of that element. However, the main
difference between the two is that mass number is always a whole number whereas atomic mass is
usually not a whole number.
? The atomic number (Z) and mass number (A) of an element ‘X’ are usually represented alongwith the
symbol of the element as
e.g. Cl , Na
35
17
23
11
 and so on.
1. ?sotopes : Such atoms of the same element having same atomic number but different mass numbers
are called isotopes.
D , H
2
1
1
1
 and T
3
1
and named as protium, deuterium (D) and tritium (T) respectively. Ordinary hydrogen is
protium.
2. Isobars : Such atoms of different elements which have same mass numbers (and of course different
atomic numbers) are called isobars
e.g. . Ca , K , Ar
40
20
40
19
40
18
3. Isotones : Such atoms of different elements which contain the same number of neutrons are called
isotones
e.g. . O , N , C
16
8
15
7
14
6
4. Isoelectronic : The species (atoms or ions) containing the same number of electrons are called
isoelectronic.
For example, O
2–
, F
–
, Na
+
, Mg
2+
, Al
3+
, Ne all contain 10 electrons each and hence they are isoelectronic.
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