Rutherford scattering

Rutherford scattering is a phenomenon that was explained by Ernest Rutherford in 1911, and led to the development of the orbital theory of the atom. It is now exploited by the materials analytical technique Rutherford backscattering. Rutherford scattering is also sometimes referred to as Coulomb scattering because it relies on static electric (Coulomb) forces. A similar process probed the insides of nuclei in the 1960s, called Deep Inelastic Scattering.

Details of calculating nuclear size

For head on collisions between alpha particles and the nucleus, all the kinetic energy (rac{1}{2}mv^2) of the alpha particle is turned into potential energy and the particle is at rest. The distance from the centre of the electron to the centre of the nucleus (b) is approximately then the radius.

Related Topics:
Kinetic energy - Potential energy

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Applying the inverse-square law between the charges on the electron and nucleus, one can write:

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rac{1}{2} mv^2 = rac{1}{4pi epsilon_0} cdot rac{q_1 q_2}{b}

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Rearranging:

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b = rac{1}{4pi epsilon_0} cdot rac{2 q_1 q_2}{mv^2}

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For an alpha particle:

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• m (mass) = 6.7×10⁻²⁷ kg
• q₁ = 2×(1.6×10⁻¹⁹) C
• q₂ (for gold) = 79×(1.6×10⁻¹⁹) C
• v (initial velocity) = 2×10⁷ m/s

Substituting these in gives the value of about 2.7×10−14 m.

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