Cornell Note (Pinned): Rutherford's Alpha-Scattering Experiment

type: cornell_note | pinned: true | subtopic: Rutherford Experiment

Apparatus Image: Geiger-Marsden Apparatus Source: Wikimedia Commons — Geiger-Marsden Experiment (expected vs. actual results)

Cue Column | Note-Taking Area

Cue	Notes
What was the experiment?	Alpha particles (He-4 nuclei) fired at a thin gold foil (0.00004 cm thick). Zinc sulfide (ZnS) screen detected scattered particles at various angles.
What was observed?	(1) Most alphas: undeflected (straight through). (2) ~1 in 8000: deflected at large angles. (3) Very rarely (1 in ~20,000): bounced nearly straight back (~180°).
Conclusion 1	Most of the atom is empty space (explains undeflected majority).
Conclusion 2	All positive charge and most mass concentrated in a tiny nucleus (~10^{-15} m, called the nucleus).
Conclusion 3	Electrons orbit far from nucleus (~10^{-10} m).
Distance of closest approach	d = 2k $Ze^{2}$ /KE_α. At this point, all KE converts to electrostatic PE. Gives upper limit on nuclear size.
Formula d	d = 2k $Ze^{2}$ /KE where k = $9 \times 10^{9}$ N $m^{2}$$C^{-2}$ , Z = target atomic number, e = $1.6 \times 10^{-19}$ C.
For 5 MeV on Au(Z=79)	d = 2× $9 \times 10^{9}$ ×79×( $1.6 \times 10^{-19}$ )^{2} / ( $5 \times 10^{6}$ × $1.6 \times 10^{-19}$ ) ≈ 45.5 fm
Units	[d] = [L]; SI unit: metres (m); typical value: ~10^{-14} m = tens of fm
Why Rutherford was shocked	Classical expectation: all alphas should pass through (Thomson "plum pudding" model). Back-scattering was "as if you fired shells at tissue paper and they came back."

Summary (in own words):

Rutherford's experiment shattered the Thomson model. The overwhelming majority of alpha particles sailed through the gold foil without deflection, confirming the atom is mostly empty space. The rare back-scattering events were explained only if positive charge was concentrated in an incredibly tiny, dense nucleus. The distance of closest approach (d = 2k $Ze^{2}$ /KE) gives the maximum radius of the nucleus.

NEET Focus: The formula d = 2k $Ze^{2}$ /KE and its application to find nuclear size is frequently tested. Also tested: what each observation concludes.