Tru Physics

Geiger-Marsden Experiment

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Introduction

The Geiger-Marsden experiment, also known as the Gold Foil experiment or the Rutherford experiment, was an experiment conducted by Hans Geiger and Ernest Marsden under the direction of Ernest Rutherford in the early 20th century. It drastically improved our understanding of atomic structure.

The Experiment

The experiment involved firing a stream of alpha particles, which are positively charged, at a thin sheet of gold foil. The alpha particles were detected using a fluorescent screen. The key observation was that while most alpha particles passed straight through the foil, a small number were deflected, and some even bounced back toward the source.

Interpretation and Impact

The observations from the Geiger-Marsden experiment were incompatible with the then-prevailing plum pudding model of the atom, which envisioned the atom as a positively charged sphere with electrons embedded within it. Instead, Rutherford proposed a new model for the atom, which came to be known as the Rutherford model or the nuclear model. In this model, the atom consists of a tiny, dense, positively charged nucleus surrounded by electrons that move in the space outside the nucleus.

The mathematical expression of the scattering of alpha particles in terms of angle \theta is given by Rutherford’s scattering formula:

\dfrac{d\sigma}{d\Omega} = \left(\dfrac{Z_1 Z_2 e^2}{8\pi\varepsilon_0 m v^2}\right)^2 \dfrac{1}{\sin^4(\theta/2)}

Here, Z_1 and Z_2 are the atomic numbers of the alpha particle and the gold atom, respectively, e is the elementary charge, \varepsilon_0 is the permittivity of free space, m is the mass of the alpha particle, v is the speed of the alpha particle, and \theta is the scattering angle.

Conclusion

The Geiger-Marsden experiment was a landmark experiment in nuclear physics. The results led to the development of the nuclear model of the atom and paved the way for the modern field of nuclear physics. Its importance lies in both its direct findings and its role in challenging the scientific community to rethink the structure of the atom.

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