Tru Physics

Rutherford Scattering

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Introduction

Rutherford scattering is a phenomenon in physics that was used by Ernest Rutherford in 1911 to infer the presence of a positively charged nucleus at the center of the atom. The process refers to the scattering of particles by an atomic nucleus, leading to a deflection of the particles in various directions.

Principles of Rutherford Scattering

The key principle of Rutherford scattering is the deflection of a charged particle by the Coulomb force when it approaches a heavy nucleus.

The Coulomb force between a particle of charge q_{1} and a nucleus of charge q_{2} is given by:

F = k \dfrac{q_{1}q_{2}}{r^{2}}

where k is Coulomb’s constant and r is the distance between the particle and the nucleus.

Rutherford Scattering Formula

The Rutherford scattering formula describes the distribution of scattered particles as a function of angle. It is given by:

\dfrac{d\sigma}{d\Omega} = \left(\dfrac{k^2Z^2e^4}{16E^{2}sin^{4}\left(\dfrac{\theta}{2}\right)}\right)

where d\sigma/d\Omega is the differential cross-section, k is Coulomb’s constant, Z is the atomic number of the target, e is the charge of an electron, E is the energy of the incident particle, and \theta is the scattering angle.

Rutherford’s Gold Foil Experiment

Rutherford’s famous gold foil experiment involved firing alpha particles (helium nuclei) at a thin gold foil. Most particles passed through the foil with little or no deflection, but a small number were deflected at large angles. This led Rutherford to propose that most of the atom’s mass and positive charge are concentrated in a small nucleus.

Implications and Applications

Rutherford scattering provides the basis for the Rutherford model of the atom, which was a precursor to the Bohr model and the modern quantum mechanical model. Today, techniques based on Rutherford scattering are used to probe the properties of materials, including Rutherford backscattering spectrometry (RBS).

Conclusion

Rutherford scattering is a fundamental concept in nuclear physics, leading to the development of modern atomic theory. The technique has many practical applications in materials science and is still an active area of research.

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