Ernest Rutherford's alpha ray scattering experiment led him to propose the nuclear model of the atom. The key findings were: 1) Most alpha particles passed through the thin gold foil with little deflection, but a small percentage were deflected by large angles, including backwards. 2) This could only be explained if the positive charge of the atom was concentrated into a very small, dense nucleus. 3) Rutherford concluded atoms have a small, dense nucleus containing its positive charge and mass, with electrons orbiting the nucleus. This nuclear model replaced the plum pudding model, but had its own limitations that were later addressed by Niels Bohr's model of electron orbits and quantization

1. Ernest Rutherford
Lect. Lovedeep Singh

2. INTRODUCTION
 The structure of matter that shapes the world
around us has been a subject of study since long
time.
 The first contribution in this regard came from
Dalton who postulated that matter is made of
atoms, which are indidvisible. The word atom
comes from a Greek word Atomos which means
‘no cut’. J.J. Thomson proposed a sturcture for
the atom, which was modified by Rutherford
and later by Neils Bohr.

3.  Dalton’s Atomic Theory
All elements are consists of very small invisible particles,
called atoms. Atoms of same element are exactly same
and atoms of different element are different.
 Thomson’s Atomic Model
Every atom is uniformly positive
charged sphere of radius of the
order of 10-10 m, in which entire
mass is uniformly distributed and
negative charged electrons are
embedded randomly. The atom as
a whole is neutral. This was
also known as plum-pudding model
of an atom.

4. Limitations of Thomson’s Atomic Model
1. It could not explain the origin of spectral series of
hydrogen and other atoms.
2. It could not explain large angle scattering of α –
particles.
Rutherford’s α – Ray Scattering Experiment
An α – particle is helium nucleus containing 2 protons and 2
neutrons. Therefore , an alpha particle has 4 units of mass.
This experiment was done by Rutherford and his
collaborators , Geiger and Marsden and is shown in fig.

5. ZnS

6. Conclusion
 A typical graph of the total
number of α-particles
scattered at different
angles, in a given interval of
time, is shown in Fig. The dots
in this figure represent the
data points.
 Many of the α-particles pass through the foil. It means that they do not
suffer any collisions. Only about 0.14% of the incident α-particles
scatter by more than 1º; and about 1 in 8000 deflect by more than 90º.

7. Conclusion
 Rutherford argued that, to deflect the α-particle
backwards, it must experience a large repulsive force. This
force could be provided if the greater part of the mass of
the atom and its positive charge were concentrated tightly
at its centre.
This led Rutherford to postulate that entire positive charge
of the atom must be concentrated in a tiny central core of
the atom. This tiny central core of each atom was called
atomic nucleus.

9. Distance of Closest Approach
 Distance of closest approach is the minimum distance between α-
particle and centre of nucleus just before it reflects back by 180o
 When the distance between α-particle and the nucleus is equal to the
distance of the closest approach ( ), the α-particle comes to rest. At
this point or distance, the kinetic energy of α-particle is completely
converted into electric potential energy of the system.
 Obviously, the radius of nucleus must be smaller than above value.

10. Impact Parameter
 The trajectory traced by an α-particle depends on the impact
parameter, b of collision. The impact parameter is the perpendicular
distance of the initial velocity vector of the α-particle from the central
line of the nucleus.
 For large impact parameters,
force experienced by α-particle
is weak as F varies inversely as
square of distance and α-particle
will deviate much smaller
and vice-versa.
Rutherford calculated-

11. Rutherford’s Model of an Atom
 An atom is composed of positively charged particles. Majority of the
mass of an atom was concentrated in a very small region. This region of
the atom was called as the nucleus of an atom. It was found out later
that the very small and dense nucleus of an atom is composed of
neutrons and protons.
 Atoms nucleus is surrounded by negatively charged particles
called electrons. The electrons revolve around the nucleus in a fixed
circular path at very high speed. These fixed circular paths were termed
as “orbits.”
 An atom has no net charge or they are electrically neutral because
electrons are negatively charged and the densely concentrated nucleus
is positively charged. A strong electrostatic force of attractions holds
together the nucleus and electrons.
 The size of the nucleus of an atom is very small in comparison to the
total size of an atom.

12. Electron Orbits
 The electrostatic force of attraction, Fe between the revolving electrons
and the nucleus provides the requisite centripetal force (Fc) to keep
them in their orbits. Thus, for a dynamically stable orbit in a hydrogen
atom, Fe = Fc
For hydrogen atom, Z= 1
The total energy of the electron is negative. This implies the fact that
the electron is bound to the nucleus.

13. ATOMIC SPECTRA
When an atomic gas or vapour is excited at low pressure, usually by
passing an electric current through it, the emitted radiation has a
spectrum which contains certain specific wavelengths only. A spectrum
of this kind is termed as line emission spectrum and it consists of
bright lines on a dark background.
When white light passes through a gas and we analyze the transmitted
light using a spectrometer we find some dark lines in the spectrum.
These dark lines correspond precisely to those wavelengths which were
found in the emission line spectrum of the gas. This is called the
absorption spectrum of the material of the gas.

14. Spectral Series of Hydrogen
 Hydrogen is the simplest atom and therefore, has the simplest spectrum. In the
observed spectrum, however, at first sight, there does not seem to be any
resemblance of order or regularity in spectral lines. Each of these sets is called a
spectral series. In 1885, the first such series was observed by a Swedish, Johann
Jakob Balmer (1825–1898) in the visible region of the hydrogen spectrum. This
series is called Balmer series . The line with the longest wavelength, 656.3 nm
in the red is called Hα; the next line with wavelength 486.1 nm in the bluegreen
is called Hβ, the third line 434.1 nm in the violet is called Hγ; and so on.
 Balmer found a simple empirical formula for the observed wavelengths
Where n= 3,4,5……
 R is a constant called the Rydberg
constant & R = 1.097 x 107 m-1

15.  Other series of spectra for hydrogen were subsequently discovered.
These are known, after their discoverers, as Lyman, Paschen, Brackett,
and Pfund series. These are represented by the formulae:
Lyman Series n=2,3,4….. (Ultraviolet Region)
Paschen Series n=4,5,6…. (Infrared Region)
Brackett Series n=5,6,7…. ( ,,,, )
Pfund Series ( ,,,, )
n=6,7,8….

16. Limitations of Rutherford Atomic Model
• Can’t explain Stability of atom
According to classical electromagnetic theory, an accelerating charged
particle emits radiation in the form of electromagnetic waves. The energy
of an accelerating electron should therefore, continuously decrease. The
electron would spiral inward and eventually fall into the nucleus. Thus,
such an atom can not be stable.
• Can’t explain Line spectra of atom
Further, according to the classical electromagnetic theory, the frequency of
the electromagnetic waves emitted by the revolving electrons is equal to
the frequency of revolution. As the electrons spiral inwards, their angular
velocities and hence their frequencies would change continuously, and so
will the frequency of the light emitted. Thus, they would emit a continuous
spectrum, in contradiction to the line spectrum actually observed.

17. Bohr’s Model of an Atom
 Niels Bohr (1885 – 1962) made certain modifications in this model by
adding the ideas of the newly developing quantum hypothesis.
 Postulates of Bohr’s model:-
 1. Every atom consist of central core called nucleus, in which entire positive
charge and almost entire mass of atom are concentrated. A suitable no. Of
electrons revolve around the nucleus in circular orbits. The centripetal force for
revolution is provided by electrostatic force of attraction between electron and
the nucleus.
 2. Electron revolves around the nucleus only in those orbits for which the angular
momentum is some integral multiple of h/2π where h is the Planck’s constant.
Thus the angular momentum (L) of the orbiting electron is quantised. i.e.
L = nh/2π
 3. An electron might make a transition from one of its specified non-radiating
orbits to another of lower energy. When it does so, a photon is emitted having
energy equal to the energy difference between the initial and final states. The
frequency of the emitted photon is then given by
• hν = Ei – Ef

18.  Radii of Bohr’s stationary orbits
This shows that r ∝ / Z
i.e. radii of stationary orbits are in the ratio 12:22:32: and so on. Clearly,
the stationary orbits are not equally spaced.
Putting values of all constants, we get
This is called The Bohr’s radius.
Velocity of electron in Bohr’s stationary orbit
This shows r ∝ 1/ n
Therefore, orbital velocity of electron in outer orbits is smaller as
compared to its value in the inner orbits.
For hydrogen, Z=1 and for n=1, v= 2.2X106m/s

19.  Frequency of electron in Bohr’s stationary orbit
It is the no. of revolutions completed per second by the electron in a
stationary orbit around nucleus and is given by
i.e. ν ∝ 1/ n
For first orbit of hydrogen atom, ν= 6.57X1015 rps.
Total energy of electron in Bohr’s stationary orbit
putting standard values,
for hydrogen,
For ground state E= -13.6 eV. Therefore, the minimum energy required
to remove the electron from ground state of hydrogen atom is 13.6 eV.
This is called ionisation energy of hydrogen atom.

20. Bohr’s Explanation of Spectral Series
 Acc. to 3rd postulate of Bohr’ theory, when an electron
makes a transition form orbit of higher energy to lower
energy orbit, a light photon is emitted.
 When an electron jumps to 1st orbit (n=1) from any other
orbit (n=2,3,4,….), Lyman Series is obtained which lies in
ultraviolet region.
 Similarly, When an electron jumps to 2nd orbit (n=2) from
any other orbit (n=3,4,5,….), Balmer Series is obtained
which lies in Visible region.

21.  When an electron jumps to 3rd orbit (n=3) from any other
orbit (n=4,5,6, ….), Paschen Series is obtained which lies
in Infrared region.
 When an electron jumps to 4th orbit (n=4) and 5th orbit
from any other orbit (n=5,6,7 ….) and (n=6,7,8, …) Brackett
and Pfund Series are obtained
respectively which also lies in
Infrared region.
and

22. ENERGY LEVEL DIAGRAM
 A diagram which represents
the total energies of electron
in different stationary orbits
of an atom is called energy
level diagram.
An electron can have any total
energy above E=0 eV. In such
a case, the electron is free.

23.  Excitation energy:- The minimum energy required to excite an
atom in the ground state to one of the higher stationary states is called
excitation energy.
e.g. in case of hydrogen, to lift an electron from ground state (E= -13.6
eV) to first excited state (E= -3.4 eV), energy is
E= -3.4-(-13.6)= 10.2 eV
Excitation Potential:- The minimum potential which provides an
electron energy sufficient to jump from ground state to one of the
higher states is called excitation potential.
excitation potential= = 10.2 V
Ionisation Energy:- The minimum energy required to ionise an
electron is called ionisation energy.
Ionisation Potential:- The minimum potential which would
provide an energy to just remove an electron from atom is called
ionisation potential.

24. de Broglie’ View of Bohr’s 2nd postulate.
 It states that the angular momentum of the electron orbiting around the
nucleus is quantized (that is, L = nh/2π; n = 1, 2, 3 …). Why should the angular
momentum have only those values that are integral multiples of h/2π? The
French physicist Louis de Broglie explained this puzzle in 1923, ten years after
Bohr proposed his model. We know that when a string is plucked, a vast
number of wavelengths are excited. However only those wavelengths survive
which have nodes at the ends. It means that in a string, standing waves are
formed when the total distance travelled by a wave down the string and back
is one wavelength, two wavelengths, or any integral number of wavelengths.
For an electron moving in nth circular orbit of radius rn , the total distance is
the circumference of the orbit, 2πrn.
2π rn = nλ, n = 1, 2, 3...
Now, λ = h/mvn , we have 2π rn = n h/mvn
m vn rn = nh/2π
i.e. L = nh/2π

25. Limitations of Bohr’s Model
 1. The Bohr model is applicable to hydrogenic atoms. It
cannot be extended even to mere two electron atoms such
as helium. Difficulty lies in the fact that each electron
interacts not only with the positively charged nucleus but
also with all other electrons.
 2. While the Bohr’s model correctly predicts the frequencies
of the light emitted by hydrogenic atoms, the model is
unable to explain the relative intensities of the frequencies
in the spectrum

26. LASER LIGHT
 The acronym LASER stands for Light Amplification by Stimulated
Emission of Radiation.
 Since its development in 1960, it has entered into all areas of science
and technology. It has found applications in physics, chemistry,
biology, medicine, surgery, engineering, etc.
There are low power lasers, with a power
of 0.5 mW, called pencil lasers, which serve
as pointers. There are also lasers of different
power, suitable for delicate surgery of eye or
glands in the stomach. Finally, there are lasers
which can cut or weld steel.