PLUS TWO

PHYSICS

ATOMS
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  A very small fraction of incident alpha
particle retraced its path
ATOMS

Scattering of alpha particle

Geiger Marsden experiment

Experimental set up
 Radioactive source of alpha particle is kept
inside an lead cavity with a narrow opening
 5.5MeV a-particles emitted by the source
are made into a narrow well collimated
beam using led slits. Beam is allowed to fall
on a thin gold foil of thickness 2.1 × 10 m
 The alpha particle scattered in different di-
rection can be absorbed by using the rotat-
able Zinc sulphide screen and microscope
Conclusions
arrangement.
 Since most of the alpha particle passed
 These alpha particle produce light flashes through the foil undeflected, it is concluded
on the screen so the number of alpha par- that major part of an atom is empty.
ticle scattered at different angles can be
counted  A few of the alpha particle suffer a large an-
gle deviation and are very small fraction re-
traced its path.
Observations  since the alpha particle itself 7350 times
heavier than the electron, neither an elec-
 The most of alpha particle passed through
tron nor similar positive charged particle
the foil straight or with very small deviation
could cause such a large angle deviation.
 About 0.14 percentage of incident a-particle
scattered by more than 1∘  Rutherford argued that, the alpha particle
 About one in 8000 get deflected through 90∘ must had encountered a very heavy posi-
or more. tive particle on its path.

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  The electrostatic force of repulsion between  As it approaches the nucleus its velocity
the alpha particle and this heavy positive (kinetic energy )progressively decreases
core causes such a large angle deviation due to electrostatic force of repulsion from
the nucleus.
 This central positive core is named as nu-
cleus  At some distance d from the nucleus the
alpha particle come to rest for moment
 Very rarely an alpha particle travels head and then retraces its path.
on towards the nucleus. these alpha parti-  At the distance 𝑑, when the a particle is
cle re-traces its path. The size of the nucleus at rest, it's kinetic energy is completely
is very small converted into the electrostatic potential
energy.

Impact parameter The distance 𝑑 is called distance of closest

approach.
Impact parameter is the perpendicular dis-
tance of the initial velocity vector of the alpha Ze
particles from the centre of the nucleus.

01. An a-particle having a kinetic energy

5MeV is found to be scattered by a gold
nucleus through 180∘. Calculate the
 Those with small impact parameter sufferer
large scattering.
distance of closest approach. 𝑍 = 79 for
 a- particle with large impact parameter get gold
scattered through smaller angles
 In the case of head on collision,impact pa-
rameter is zero and a-particles rebound
back.

Rutherford’s Nuclear
Distance of closest approach model of atom
 Consider an alpha particle of mass m and On the basis of the alpha particle scattering ex-
initial velocity v moves towards the nucleus periment in 1911 Rutherford proposed his nuclear
of charge is Ze. model of an atom. nuclear model which is also
known as planetary atom model.

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 An atom maybe regarded as a sphere of Radius of nth orbit
size 10−10 m. The entire positive charge and
most of the mass is concentrated at the
central core called nucleus. Which means the radii of the stationary or-
 The electrons have no place inside the nu- bit are in the ratio 1: 4: 9: 16..
cleus they revolve around the nucleus at
some distance away. The centripetal force
for the revolution is provided by the electro-
static force of attraction between the nucle-
us and electrons.
02. In bore model of hydrogen atom which
 The amount of positive charge of the nucle- of the following is quantised?
us is exactly equal to the amount of nega-
tive charges on all the electrons of the atom. (a) Linear momentum of the electron
That means the atom is electrically neutral. (b) Angular momentum of the electron
(c) Linear velocity of the electron
Drawbacks of Rutherford's atom (d) Angular velocity of the electron

model
 In Rutherford's atom model it is assumed
that the electrons revolve around the nu-
cleus in circular orbit and it experiences a
centripetal acceleration.
 According to the electromagnetic theory,
an accelerated electric charge should emit
electromagnetic radiation therefore the re- 03. In the Bohr’s hydrogen atom model, the
volving electron should emit radiation. radius of the stationary orbit is directly
proportional to the principal quantum
 If the radiation is continuously emitted it's an number n as
energy will decrease and electrons would
finally fall into the nucleus. That means an (a) 𝑛−2 (b) 𝑛2
atom cannot be stable. (c) n (d) n–

Bohr atom model

In an atom the electrons cannot revolve around
the nucleus in all paths. They can only Revolve
through certain stationary orbit in which the
angular momentum of the revolving electron is
an integer multiple of ℎ/2𝜋 04. In Bohr’s atom model the orbit radii are
in the rat
Where h is the Plank's constant
(a) 1: 2: 3 (b) 1: 3: 5
n = 1,2,3,.. is the principal quantum numbers (c) 1: 4: 9 (d)2: 4: 6
𝑚 = mass of the electron

𝑣 = orbital velocity of electron

𝑟 = radius of the orbit

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The line spectra of
hydrogen atom A. Name different series obtained in hy-
drogen spectrum?
According to bohr postulate, when an electron B. Draw energy level diagram of hydrogen
make a transition from the outer orbit ni of the atom
energy Ei to inner orbit nf of energy Ef a photon
of energy 𝐸𝑖 − 𝐸𝑓 is emitted
 For Lyman series, 𝑛𝑓 = 1, 𝑛𝑖 = 2,3,4 …
 For Balmer series, 𝑛𝑓 = 2, 𝑛𝑖 = 3,4,5 …
 For Paschen series, 𝑛𝑓 = 3, 𝑛𝑖 = 4,5,6 ….
 For Brackett series, 𝑛𝑓 = 4, 𝑛𝑖 = 5,6,7

de Broglie explanation of Bohr

postulate of Quantisation
From Bohr's postulate the angular momentum
of orbiting electron is

de Broglie suggested that the electron in their

permitted orbits should be seen as a particle
wave. Just like waves travelling on a string.

A. An electron is revolving around the nu-

cleus of hydrogen atom in an orbit of ra-
dius 9 times the radius of the first orbit.
Angular momentum of the electron in Therefore the circumference of the orbit must
this orbit is... be an integral multiple of the particle wave-
length.
B. Sketch the energy level diagram of hy-
drogen atom and sketch the transition
corresponding to Balmer series

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