Particle nature of matter
So far we have discussed the peculiar nature of light and its
behaviour as both particles and waves.
Now we will discuss the nature of matter ……
Particle nature of matter
A brief history of matter:
430 BC: Leucipus and Democritus propose that matter consisted of indivisible
particles (atoms)
1660s: Newton notes that Boyle’s experiments with gases could be explained if
gases consisted of particles.
1800s: Dalton argues that chemical reactions could be explained if all matter of a
given chemical element was made up of identical atoms.
1800s: Avogadro postulates that atoms can stick together to make molecules.
1833: Faraday performs groundbreaking electrolysis experiments which confirm
an atomic theory of matter. Atoms were associated with quantized positive and
negative charges. The mass and size of these charges were not known.
Particle nature of matter
1897: Thomson shows that atoms are made of constituent charged particles
(electrons).
He measures the charge to mass ratio of charged particles emitted in a
cathode ray tube:
Electrons emitted from a cathode (negative electrode) are deflected by
electric and magnetic fields
Particle nature of matter
Thomson’s crossed-field experiment:
If only a magnetic field is applied, it causes the electrons to move in a
circular arc upwards:
mv 2
q
v
FB = qvB = mar =
! =
r
m rB
r can be determined by measuring where the electrons hit the tube.
Particle nature of matter
Thomson’s crossed-field experiment:
The additional electric field causes the electrons to move in a parabola
downwards. When the fields are adjusted so that the electron moves in a
straight line,
E
FB = qvB = FE = qE ! v =
Thus the charge-mass ratio of the electrons is
B
q
v
E
=
= 2
m rB rB
Particle nature of matter
An electron in a cathode ray tube passes between 2.5cm long electrodes that are
5mm apart. A 1.0 mT 2.5 cm wide magnetic field is perpendicular to the field
between the plates .The electron passes through undeflected if the voltage
between the plates is 150V. If the voltage is set to 0, through what angle is the
electron deflected.
E !V d 150 V 5.0 " 10#3 m
v= =
=
= 3.0 " 107 m/s
#3
B
B
1.0 " 10 T
(
)(
)(
)
9.11 ! 10"31 kg 3.0 ! 107 m/s
mv
r=
=
= 0.1708 m
"19
"3
eB
1.6 ! 10 C 1.0 ! 10 T
sin ! =
(
)
L
2.5 cm
=
= 0.1463 " ! = 8.42°
r 17.08 cm
Particle nature of matter
Millikan measures the charge of an electron:
Millikan observed the motion of oil drops falling under gravity. The drops
are also acted on by a drag force proportional to their velocity. At terminal
velocity:
Fg = Fdrag ! mg = Cv
Particle nature of matter
Millikan measures the charge of an electron:
If an additional electric field is applied which causes the drops to move
upwards with a constant velocity,
Fg + Fdrag = FE ! mg + Cv" = qE
Particle nature of matter
Millikan measures the charge of an electron:
Electric field off:
Electric field on:
Fg = Fdrag ! mg = Cv
Fg + Fdrag = FE ! mg + Cv" = qE
q=
mg " v + v! %
$
'
E # v &
Particle nature of matter
Millikan measures the charge of an electron:
q=
mg " v + v! %
$
'
E # v &
4 3
m = density ! volume = " # a
3
r = density, a = radius of oil drops
Each drop can have a different number of electrons. Thus the value of the
elementary charge of a single electron can be found by taking the ratio of
different measured charges.
Value of e:
1.60217733 ! 10 "19 C
Particle nature of matter
Thomson’s plum-pudding model of the atom: Mass of an atom is
uniformly distributed in a positively charged sphere with electrons
embedded in it.
Rutherford’s scattering experiments challenged this model.
Rutherford shot positively charged alpha particles at a gold foil and
measured the angle of deflection of the alpha particles:
Particle nature of matter
Rutherford observed large deflection of the alpha particles, including
back scattering (alpha particles deflected backwards).
This could only be explained by assuming that the positive charges were
concentrated in a nucleus around which the electrons orbit:
Plum-pudding model
Rutherford nuclear model
Particle nature of matter
Rutherford nuclear model Using Coulombs law for the repulsive force between
the alpha particles with charge 2e and the nuclear
charge Ze at at distance r:
k(2e)(Ze)
r2
Rutherford showed that the number of alpha particles
hitting the detector per unit time at an angle ϕ is
F=
k 2 e 4 Z 2 NnA
!n =
4 R 2 K 2 sin 4 (" / 2)
k: Coulomb constant
N: number of nucleii per unit area
n: total number of alpha particles
K: kinetic energy of alpha particles