• Tags: rutherford, alpha-scattering, nucleus
• Difficulty: Foundation

Geiger and Marsden directed alpha particles at a thin gold foil under Rutherford's guidance. Most particles passed through with little deflection, confirming atoms are mostly empty space. About 1 in 8000 bounced back at angles > 90°, indicating a small, dense, positively charged nucleus. The hyperbolic trajectory of the alpha particle near the nucleus gives the impact parameter b = (k$Ze^{2}$ cot(θ/2))/(½$mv^{2}$). The distance of closest approach r_{0} = 2k$Ze^{2}$/(½$mv^{2}$) = k$Ze^{2}$/KE provides an upper limit for nuclear size (~10^{-14} m for gold). The fraction scattered beyond angle θ is proportional to $Z^{2}$ and c$ot^{2}$(θ/2). Rutherford's model couldn't explain stability or discrete spectra.