# 1. History Flashcards

Plum-Pudding Model

- prior to the discovery of the nucleus, the most widely accepted model of the atom was the plum-pudding model
- electrons embedded in a diffuse cloud of positive charge
- a reasonably successful model though it failed to explain emission spectra

Rutherford Experiment

Description

- alpha particles (helium nuceli) fired at a thin piece of gold foil
- deflections were observed using a fluorescent screen

Rutherford Experiment

Conservation of Energy

-consider the scattering process of a moving alpha particle off a stationary target:

1/2 mα vo² = 1/2mα vα² + 1/2mt vt²

-rearranging:

vo² = vα² + mt/mα * vt²

Rutherford Experiment

Conservation of Momentum

-consider the scattering process of a moving alpha particle off a stationary target:

mα*vo = mα*vα + mt*vt

Rutherford Experiment

Combining Conservations of Energy and Momentum

vt² (1 - mt/mα) = 2vα . vt =

2 |vα| |vt| cosθ

Rutherford Experiment

target mass less than α mass

-if the target mass is much less than the α mass (e.g. α scattered off an electron), mt/mα«1 then:

vt² ≈ 2 |vα| |vt| cosθ

-this makes cosθ > 0 (θ

Rutherford Experiment

target mass greater than α mass

-if the target mass is much greater than the α particle mass, the α particle can recoil sharply backwards in the direction it originally came from

Rutherford Experiment

Observations and Implications

- Rutherford found that the α particles occasionally recoiled from the gold foil
- the plum pudding model was unable to account for this
- instead we need an atomic model with high-mass objects
- since the large angle deflections were rare, the heavy object must be small

Nuclear Model of the Atom

- heavy dense nucleus
- electrons in large orbitals
- mostly empty space

Impact Parameter

- consider an α particles trajectory as it collides with a gold nucleus
- the perpendicular displacement of the initial trajectory from perfect head-on collision is called the impact parameter, b

Large b

-for larger b, the Coulomb repulsion is low

Small b

-for very small b, the α particle moves through the nucleus and is therefore subject to a smaller effective charge

b of order of the nuclear radius

-for b of the order of the gold nucleus’s radius, the deflection is maximum

Calculating Deflection

Approximation

-in an approximate calculation we can take the Coulomb repulsion to act in a direction perpendicular to the initial trajectory, and only over a distance b

-so for an α particle velocity v, we assume the force only acts for a time:

Δt = b/v

Calculating Deflection

Coulomb Force

F = 1/4πεo * (2e)(Ze)/b²

- where 2e is the charge on the α particle
- and Ze is the charge on the gold nucleus