Particle nature of matter

So far we have discussed the peculiar nature of light and itsbehaviour as both particles and waves.Now we will discuss the nature of matter ……

Particle nature of matterA brief history of matter:430 BC: Leucipus and Democritus propose that matter consisted of indivisibleparticles (atoms)1660s: Newton notes that Boyle’s experiments with gases could be explained ifgases consisted of particles.1800s: Dalton argues that chemical reactions could be explained if all matter of agiven 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 confirman atomic theory of matter. Atoms were associated with quantized positive andnegative charges. The mass and size of these charges were not known.

Particle nature of matter1897: Thomson shows that atoms are made of constituent charged particles(electrons).He measures the charge to mass ratio of charged particles emitted in acathode ray tube:

Electrons emitted from a cathode (negative electrode) are deflected byelectric and magnetic fields

Particle nature of matterThomson’s crossed-field experiment:

If only a magnetic field is applied, it causes the electrons to move in acircular arc upwards:

r can be determined by measuring where the electrons hit the tube.

FB= qvB = ma

r=mv

2

r!

q

m=v

rB

Particle nature of matterThomson’s crossed-field experiment:

The additional electric field causes the electrons to move in a paraboladownwards. When the fields are adjusted so that the electron moves in astraight line,

Thus the charge-mass ratio of the electrons is

FB= qvB = F

E= qE! v =

E

B

q

m=v

rB=

E

rB2

Particle nature of matterAn electron in a cathode ray tube passes between 2.5cm long electrodes that are5mm apart. A 1.0 mT 2.5 cm wide magnetic field is perpendicular to the fieldbetween the plates .The electron passes through undeflected if the voltagebetween the plates is 150V. If the voltage is set to 0, through what angle is theelectron deflected.

v =E

B=!V d

B=

150 V 5.0 "10#3

m

1.0 "10#3

T= 3.0 "10

7 m/s

r =mv

eB=

9.11!10"31 kg( ) 3.0 !107 m/s( )1.6 !10"19 C( ) 1.0 !10"3 T( )

= 0.1708 m

sin! =L

r=

2.5 cm

17.08 cm= 0.1463"! = 8.42°

Particle nature of matterMillikan measures the charge of an electron:

Millikan observed the motion of oil drops falling under gravity. The dropsare also acted on by a drag force proportional to their velocity. At terminalvelocity:

Fg = Fdrag ! mg = Cv

Particle nature of matterMillikan measures the charge of an electron:

If an additional electric field is applied which causes the drops to moveupwards with a constant velocity,

Fg + Fdrag = FE ! mg + C "v = qE

Particle nature of matterMillikan measures the charge of an electron:

Electric field off:

Fg + Fdrag = FE ! mg + C "v = qEFg = Fdrag ! mg = Cv

q =mg

E

v + !vv

"#$

%&'

Electric field on:

Particle nature of matterMillikan measures the charge of an electron:

m = density ! volume = "4

3#a3

q =mg

E

v + !vv

"#$

%&'

r = density, a = radius of oil dropsEach drop can have a different number of electrons. Thus the value of theelementary charge of a single electron can be found by taking the ratio ofdifferent measured charges.

Value of e:

1.60217733!10"19C

Particle nature of matterThomson’s plum-pudding model of the atom: Mass of an atom isuniformly distributed in a positively charged sphere with electronsembedded in it.Rutherford’s scattering experiments challenged this model.Rutherford shot positively charged alpha particles at a gold foil andmeasured the angle of deflection of the alpha particles:

Particle nature of matterRutherford observed large deflection of the alpha particles, includingback scattering (alpha particles deflected backwards).This could only be explained by assuming that the positive charges wereconcentrated in a nucleus around which the electrons orbit:

Plum-pudding model Rutherford nuclear model

Particle nature of matterRutherford nuclear model Using Coulombs law for the repulsive force between

the alpha particles with charge 2e and the nuclearcharge Ze at at distance r:

Rutherford showed that the number of alpha particleshitting the detector per unit time at an angle ϕ is

F =k(2e)(Ze)

r2

!n =k2e4Z2NnA

4R2K2sin

4(" / 2)

k: Coulomb constantN: number of nucleii per unit arean: total number of alpha particlesK: kinetic energy of alpha particles