Quick Revision: Atoms | Physics Class 12 - NEET PDF Download

 Page 1


 
 
 
     
 
  
 
  Atoms 
 
 Rutherford’s Alpha Scattering Experiment: 
Following are the observations made through this experiment: 
1. Most of  ? -particles were seen to pass through the fold foil without any appreciable 
deflection.  
2. The various ? particles, on passing through the gold foil, undergo different amounts 
of deflections. A large number of  ? particles caused fairly large deflections.  
3. A very small number of  ? -particles (about 1  8000 in ) practically retracted their paths 
or suffered deflection of nearly 
o
180 .  
4. The plot between the total number of  ? - particles ( )   N ? scattered through angle ? 
and the scattering angle ?  was found to be as shown in graph: 
 
These experimental observations led Rutherford to the following inferences: 
Page 2


 
 
 
     
 
  
 
  Atoms 
 
 Rutherford’s Alpha Scattering Experiment: 
Following are the observations made through this experiment: 
1. Most of  ? -particles were seen to pass through the fold foil without any appreciable 
deflection.  
2. The various ? particles, on passing through the gold foil, undergo different amounts 
of deflections. A large number of  ? particles caused fairly large deflections.  
3. A very small number of  ? -particles (about 1  8000 in ) practically retracted their paths 
or suffered deflection of nearly 
o
180 .  
4. The plot between the total number of  ? - particles ( )   N ? scattered through angle ? 
and the scattering angle ?  was found to be as shown in graph: 
 
These experimental observations led Rutherford to the following inferences: 
 
 
 
     
 
  
1. As most of the ? particles passed without any deviation, the atom had a lot of empty 
space in it.  
2. As fast and heavy ? particles could be deflected even through 
o
180 , the whole of the 
positive charge and practically the entire mass of the atom were confirmed to extremely 
small central cores. These were called nuclei. Because 1 in about 8000 ? particles get 
deflected through 180
?
, the size of the nucleus was assumed to be about 1/10000th of 
the size of the atom. 
 
8.1 Rutherford’s Atom Model  
On the basis of the results of ? scattering experiment, Rutherford suggested the following 
picture of an atom:  
1. Atoms can be regarded as spheres of diameters 
10
10 m but whole of the positive charge 
and almost the entire mass of these atoms are concentrated in small central cores called 
nuclei having diameters of about 
14
10 .  m 
2. The nucleus is neighbored by electrons. In other words, the electrons are distributed 
over the remaining part of the atom leaving plenty of empty space in the atom. 
  
Drawbacks of Rutherford’s Atom Model: 
I. When the electrons revolve around the nucleus, they get continuously accelerated towards 
the centre of the nucleus. According to Lorentz, an accelerated charged particle must radiate 
energy continuously. Thus, in the atom, a revolving electron must continuously emit energy 
and hence the radius of its path must go on decreasing and finally, it must fall into the nucleus. 
However, electrons revolve around the nucleus without falling into it. Clearly, Rutherford’s 
atom model couldn’t explain the stability of the atom.  
II. Suppose if Rutherford's atom model is true, the electron could revolve in orbits of all 
possible radii and thus it should emit a continuous energy spectrum. But, atoms like hydrogen 
possess a line spectrum.  
 
Page 3


 
 
 
     
 
  
 
  Atoms 
 
 Rutherford’s Alpha Scattering Experiment: 
Following are the observations made through this experiment: 
1. Most of  ? -particles were seen to pass through the fold foil without any appreciable 
deflection.  
2. The various ? particles, on passing through the gold foil, undergo different amounts 
of deflections. A large number of  ? particles caused fairly large deflections.  
3. A very small number of  ? -particles (about 1  8000 in ) practically retracted their paths 
or suffered deflection of nearly 
o
180 .  
4. The plot between the total number of  ? - particles ( )   N ? scattered through angle ? 
and the scattering angle ?  was found to be as shown in graph: 
 
These experimental observations led Rutherford to the following inferences: 
 
 
 
     
 
  
1. As most of the ? particles passed without any deviation, the atom had a lot of empty 
space in it.  
2. As fast and heavy ? particles could be deflected even through 
o
180 , the whole of the 
positive charge and practically the entire mass of the atom were confirmed to extremely 
small central cores. These were called nuclei. Because 1 in about 8000 ? particles get 
deflected through 180
?
, the size of the nucleus was assumed to be about 1/10000th of 
the size of the atom. 
 
8.1 Rutherford’s Atom Model  
On the basis of the results of ? scattering experiment, Rutherford suggested the following 
picture of an atom:  
1. Atoms can be regarded as spheres of diameters 
10
10 m but whole of the positive charge 
and almost the entire mass of these atoms are concentrated in small central cores called 
nuclei having diameters of about 
14
10 .  m 
2. The nucleus is neighbored by electrons. In other words, the electrons are distributed 
over the remaining part of the atom leaving plenty of empty space in the atom. 
  
Drawbacks of Rutherford’s Atom Model: 
I. When the electrons revolve around the nucleus, they get continuously accelerated towards 
the centre of the nucleus. According to Lorentz, an accelerated charged particle must radiate 
energy continuously. Thus, in the atom, a revolving electron must continuously emit energy 
and hence the radius of its path must go on decreasing and finally, it must fall into the nucleus. 
However, electrons revolve around the nucleus without falling into it. Clearly, Rutherford’s 
atom model couldn’t explain the stability of the atom.  
II. Suppose if Rutherford's atom model is true, the electron could revolve in orbits of all 
possible radii and thus it should emit a continuous energy spectrum. But, atoms like hydrogen 
possess a line spectrum.  
 
 
 
 
     
 
  
Alpha-particle Trajectory: 
• The path of an a-particle depends on the impact parameter, which is the distance from 
the particle’s starting point to the centre of the nucleus. 
• In a beam of a-particles, each particle has a different impact parameter, causing them 
to scatter in various directions. They all have nearly the same energy. 
• An a-particle that comes very close to the nucleus (small impact parameter) scatters a 
lot. If it hits the nucleus head-on (very small impact parameter), it bounces back (? ˜ 
180°). 
• If the impact parameter is large, the a-particle barely changes direction (? ˜ 0°). 
• The fact that few a-particles bounce back means that head-on collisions are rare, 
showing that most of the atom's mass and positive charge is concentrated in a small 
area. This helps determine the size of the nucleus. 
 
 
Electron Orbits (Rutherford Model): 
1. Rutherford’s Nuclear Model: 
The atom is modelled as a small, dense, positively charged nucleus with electrons revolving 
around it in fixed orbits. 
Page 4


 
 
 
     
 
  
 
  Atoms 
 
 Rutherford’s Alpha Scattering Experiment: 
Following are the observations made through this experiment: 
1. Most of  ? -particles were seen to pass through the fold foil without any appreciable 
deflection.  
2. The various ? particles, on passing through the gold foil, undergo different amounts 
of deflections. A large number of  ? particles caused fairly large deflections.  
3. A very small number of  ? -particles (about 1  8000 in ) practically retracted their paths 
or suffered deflection of nearly 
o
180 .  
4. The plot between the total number of  ? - particles ( )   N ? scattered through angle ? 
and the scattering angle ?  was found to be as shown in graph: 
 
These experimental observations led Rutherford to the following inferences: 
 
 
 
     
 
  
1. As most of the ? particles passed without any deviation, the atom had a lot of empty 
space in it.  
2. As fast and heavy ? particles could be deflected even through 
o
180 , the whole of the 
positive charge and practically the entire mass of the atom were confirmed to extremely 
small central cores. These were called nuclei. Because 1 in about 8000 ? particles get 
deflected through 180
?
, the size of the nucleus was assumed to be about 1/10000th of 
the size of the atom. 
 
8.1 Rutherford’s Atom Model  
On the basis of the results of ? scattering experiment, Rutherford suggested the following 
picture of an atom:  
1. Atoms can be regarded as spheres of diameters 
10
10 m but whole of the positive charge 
and almost the entire mass of these atoms are concentrated in small central cores called 
nuclei having diameters of about 
14
10 .  m 
2. The nucleus is neighbored by electrons. In other words, the electrons are distributed 
over the remaining part of the atom leaving plenty of empty space in the atom. 
  
Drawbacks of Rutherford’s Atom Model: 
I. When the electrons revolve around the nucleus, they get continuously accelerated towards 
the centre of the nucleus. According to Lorentz, an accelerated charged particle must radiate 
energy continuously. Thus, in the atom, a revolving electron must continuously emit energy 
and hence the radius of its path must go on decreasing and finally, it must fall into the nucleus. 
However, electrons revolve around the nucleus without falling into it. Clearly, Rutherford’s 
atom model couldn’t explain the stability of the atom.  
II. Suppose if Rutherford's atom model is true, the electron could revolve in orbits of all 
possible radii and thus it should emit a continuous energy spectrum. But, atoms like hydrogen 
possess a line spectrum.  
 
 
 
 
     
 
  
Alpha-particle Trajectory: 
• The path of an a-particle depends on the impact parameter, which is the distance from 
the particle’s starting point to the centre of the nucleus. 
• In a beam of a-particles, each particle has a different impact parameter, causing them 
to scatter in various directions. They all have nearly the same energy. 
• An a-particle that comes very close to the nucleus (small impact parameter) scatters a 
lot. If it hits the nucleus head-on (very small impact parameter), it bounces back (? ˜ 
180°). 
• If the impact parameter is large, the a-particle barely changes direction (? ˜ 0°). 
• The fact that few a-particles bounce back means that head-on collisions are rare, 
showing that most of the atom's mass and positive charge is concentrated in a small 
area. This helps determine the size of the nucleus. 
 
 
Electron Orbits (Rutherford Model): 
1. Rutherford’s Nuclear Model: 
The atom is modelled as a small, dense, positively charged nucleus with electrons revolving 
around it in fixed orbits. 
 
 
 
     
 
  
The force of attraction between the nucleus and the electrons provides the necessary centripetal 
force to keep the electrons in stable orbits. 
2. Centripetal Force: 
The electrostatic force ( 
e
F ) between the electron and the nucleus equals the centripetal force 
(
c
F ): 
22
2
0
1
4
 
ec
e mv
FF
rr ?
= = = 
where: 
0
 = permittivity of free space 
e = electron charge 
r = orbit radius 
m = electron mass 
 v = velocity of the electron 
3. Relation between Orbit Radius and Electron Velocity: 
The radius r of the electron's orbit is related to its velocity v by the formula: 
 
2
2
0
 
4
e
r
mv ?
= 
4. Kinetic Energy (K): 
The kinetic energy K of the electron is given by: 
2
2
0
8
 
1
2
e
K mv
r ?
== 
5. Electrostatic Potential Energy (U): 
Page 5


 
 
 
     
 
  
 
  Atoms 
 
 Rutherford’s Alpha Scattering Experiment: 
Following are the observations made through this experiment: 
1. Most of  ? -particles were seen to pass through the fold foil without any appreciable 
deflection.  
2. The various ? particles, on passing through the gold foil, undergo different amounts 
of deflections. A large number of  ? particles caused fairly large deflections.  
3. A very small number of  ? -particles (about 1  8000 in ) practically retracted their paths 
or suffered deflection of nearly 
o
180 .  
4. The plot between the total number of  ? - particles ( )   N ? scattered through angle ? 
and the scattering angle ?  was found to be as shown in graph: 
 
These experimental observations led Rutherford to the following inferences: 
 
 
 
     
 
  
1. As most of the ? particles passed without any deviation, the atom had a lot of empty 
space in it.  
2. As fast and heavy ? particles could be deflected even through 
o
180 , the whole of the 
positive charge and practically the entire mass of the atom were confirmed to extremely 
small central cores. These were called nuclei. Because 1 in about 8000 ? particles get 
deflected through 180
?
, the size of the nucleus was assumed to be about 1/10000th of 
the size of the atom. 
 
8.1 Rutherford’s Atom Model  
On the basis of the results of ? scattering experiment, Rutherford suggested the following 
picture of an atom:  
1. Atoms can be regarded as spheres of diameters 
10
10 m but whole of the positive charge 
and almost the entire mass of these atoms are concentrated in small central cores called 
nuclei having diameters of about 
14
10 .  m 
2. The nucleus is neighbored by electrons. In other words, the electrons are distributed 
over the remaining part of the atom leaving plenty of empty space in the atom. 
  
Drawbacks of Rutherford’s Atom Model: 
I. When the electrons revolve around the nucleus, they get continuously accelerated towards 
the centre of the nucleus. According to Lorentz, an accelerated charged particle must radiate 
energy continuously. Thus, in the atom, a revolving electron must continuously emit energy 
and hence the radius of its path must go on decreasing and finally, it must fall into the nucleus. 
However, electrons revolve around the nucleus without falling into it. Clearly, Rutherford’s 
atom model couldn’t explain the stability of the atom.  
II. Suppose if Rutherford's atom model is true, the electron could revolve in orbits of all 
possible radii and thus it should emit a continuous energy spectrum. But, atoms like hydrogen 
possess a line spectrum.  
 
 
 
 
     
 
  
Alpha-particle Trajectory: 
• The path of an a-particle depends on the impact parameter, which is the distance from 
the particle’s starting point to the centre of the nucleus. 
• In a beam of a-particles, each particle has a different impact parameter, causing them 
to scatter in various directions. They all have nearly the same energy. 
• An a-particle that comes very close to the nucleus (small impact parameter) scatters a 
lot. If it hits the nucleus head-on (very small impact parameter), it bounces back (? ˜ 
180°). 
• If the impact parameter is large, the a-particle barely changes direction (? ˜ 0°). 
• The fact that few a-particles bounce back means that head-on collisions are rare, 
showing that most of the atom's mass and positive charge is concentrated in a small 
area. This helps determine the size of the nucleus. 
 
 
Electron Orbits (Rutherford Model): 
1. Rutherford’s Nuclear Model: 
The atom is modelled as a small, dense, positively charged nucleus with electrons revolving 
around it in fixed orbits. 
 
 
 
     
 
  
The force of attraction between the nucleus and the electrons provides the necessary centripetal 
force to keep the electrons in stable orbits. 
2. Centripetal Force: 
The electrostatic force ( 
e
F ) between the electron and the nucleus equals the centripetal force 
(
c
F ): 
22
2
0
1
4
 
ec
e mv
FF
rr ?
= = = 
where: 
0
 = permittivity of free space 
e = electron charge 
r = orbit radius 
m = electron mass 
 v = velocity of the electron 
3. Relation between Orbit Radius and Electron Velocity: 
The radius r of the electron's orbit is related to its velocity v by the formula: 
 
2
2
0
 
4
e
r
mv ?
= 
4. Kinetic Energy (K): 
The kinetic energy K of the electron is given by: 
2
2
0
8
 
1
2
e
K mv
r ?
== 
5. Electrostatic Potential Energy (U): 
 
 
 
     
 
  
The potential energy U of the electron due to the nucleus is: 
 
2
0
4
e
U
r ?
=- 
The negative sign indicates that the force is attractive. 
6. Total Energy (E): 
The total energy E of the electron in the hydrogen atom is the sum of its kinetic and potential 
energy: 
   
22
00
84
ee
E K U
rr ??
= + = - 
2
0
 
8
e
E
r ?
=- 
The total energy is negative, meaning the electron is bound to the nucleus. 
 
Atomic Spectra: 
1. Characteristic Spectrum of Elements: 
Each element has its own unique spectrum of radiation, which it emits. 
2. Emission Line Spectrum: 
• When a gas or vapour is excited at low pressure (often by an electric current), it emits 
radiation with specific wavelengths. 
• This is called the emission line spectrum, where bright lines appear on a dark 
background. 
• The spectrum of atomic hydrogen is an example. 
3. Identification through Emission Line Spectra: