Structure of the Atom

Page
2

If an α particle were scattered by many electrons and N electrons results in .

The number of atoms across the thin gold layer of 6 × 10−7 m:

Assume the distance between atoms is

and there are .

That gives .

Slide 8

Rutherford’s Atomic Model

even if the α particle scattered from all 79 electrons in each atom of gold.

The experimental results were not consistent with Thomson’s atomic model.

Rutherford proposed that an atom has a positively charged core (nucleus) surrounded by the negative electrons.

The positive charge is concentrated in

a nucleus with a radius much smaller than 10-10 m

Slide 9

Rutherford Scattering

Scattering experiments help us study matter too small to be observed directly.

There is a relationship between the impact parameter b and the scattering angle θ.

When b is small,

r gets small.

Coulomb force gets large.

θ can be large and the particle can be repelled backward.

4.2:

Slide 10

Any particle inside the circle of area πb02 will be similarly scattered.

The cross section σ = πb2 is related to the probability for a particle being scattered by 1 nucleus.

The number of scattering nuclei per unit area .

The fraction of incident particles scattered is

f = ntAs/A

Rutherford Scattering

Slide 11

In actual experiment a detector is positioned from θ to θ + dθ that corresponds to incident particles between b and b + db.

The number of particles scattered per unit area is

Rutherford Scattering Equation

Slide 12

The Classical Atomic Model

4.3:

Let’s consider atoms as a planetary model.

The force of attraction on the electron by the nucleus and Newton’s 2nd law give

where v is the tangential velocity of the electron.

The total energy is

Slide 13

The Classical Atomic Model

Consider an atom as a planetary system.

The Newton’s 2nd Law force of attraction on the electron by the nucleus is:

where v is the tangential velocity of the electron:

The total energy is then:

This is negative, so the system is bound, which is good.

Slide 14

The Planetary Model is Doomed

From classical E&M theory, an accelerated electric charge radiates energy (electromagnetic radiation) which means total energy must decrease. Radius r must decrease!!