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Scattering of Particles. Rutherford-Bohr Atom

Problem 6.15

A narrow beam of protons with kinetic energy T=1.4MeVT=1.4 \mathrm{MeV} falls normally on a brass foil whose mass thickness ρd=1.5mg/cm2\rho d=1.5 \mathrm{mg} / \mathrm{cm}^{2}. The weight ratio of copper and zinc in the foil is equal to 7: 3 respectively. Find the fraction of the protons scattered through the angles exceeding θ0=30∘.\theta_{0}=30^{\circ} .

Reveal Answer
 6.15. ΔN/N=πe44T2(0.7Z12M1+0.3Z22M2)ρdNAcot⁡2θ2=1.4⋅10−3 \text { 6.15. } \Delta N / N=\frac{\pi e^{4}}{4 T^{2}}\left(0.7 \frac{Z_{1}^{2}}{M_{1}}+0.3 \frac{Z_{2}^{2}}{M_{2}}\right) \rho d N_{A} \cot ^{2} \frac{\theta}{2}=1.4 \cdot 10^{-3} where Z1Z_{1} and Z2Z_{2} are the atomic numbers of copper and zinc, M1M_{1} and M2M_{2} are their molar masses, NAN_{A} is Avogadro's number.
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