Lab Report: Rutherford Scattering Experiment

Abstract

After recreating Ernest Rutherford’s scattering experiment, the results calculated closely resembled the expected trend based on theory, however with a noticeable x-axis shift that was still permissible given the uncertainties involved. This experiment also proved that most α-particles are detected when the scattering angle is at 0°, and the least are observed at around ± 30° onwards.

1. Introduction and Background

Arguably one of the most famous experiments in physics, Ernest Rutherford’s scattering experiment was originally performed in 1911 [1] and developed on the work previously done by Hans Geiger and Ernest Marsden in 1909 [2].

Rutherford’s experiment stemmed from the confusion relating to the behavior of α-particles in Geiger and Marsden’s experiment where the α-particles’ behavior was extremely different from the β-particles also being observed. Some α-particles were being scattered back to the side where they originated from. Rutherford then performed his own experiment on this phenomenon in which α-particles are fired at a thin gold foil. Some passed through the foil undeflected, whereas others had some angle of deflection.

Get quality help now

Writer Lyla

Verified writer

Proficient in: Physics

5 (876)

“ Have been using her for a while and please believe when I tell you, she never fail. Thanks Writer Lyla you are indeed awesome ”

+84 relevant experts are online

Hire writer

Again, some were seen to have never made it past the foil at all and were fully deflected back.

This experiment also debunked J. J. Thomson’s ‘Plum Pudding’ model of the atom and introduced the ‘Nuclear Model’ where negative electrons surround a positive nucleus, rather than both being merged together.

2. Experimental Procedure

Firstly, find the discriminator voltage by ensuring that the radioactive source is not in the chamber. The chamber does not have to be pumped, but it must be covered by a black-out cloth.

The source can now be added, and the chamber pumped with the gold foil at 0°. Once the counter starts to register activity, the foil can be moved to -30° (30° right of the 0° position) once the counter has been set up to count for the desired period. Place a black-out cover over the chamber and start the counter. After the designated time (the counter may stop automatically) record the value then move the foil to -25°. Repeat the above in increments of 5° up to 30° to the left of zero.

Repeat numerous times in order to take an average value of all the results per angle measured.

3. Results and Analysis

3.1 Results

All results are obtained from a base discriminator value of 0.5 ± 0.01 V.

Overall, the experimental results do not take into consideration the discriminator value, but all angles are observed with an uncertainty of ± 0.1°. Counts are assumed to be errorless as they are whole numbers but are discussed later in the Letter. t(ϴ) is always 100 seconds.

Uncertainties of the five sets of integer counts per value of ϴ are calculated from the standard deviation.

3.2 Data Processing

The above averages are processed via equations (1) and (2), and the result is then compared graphically to the products of equation (3) (Fig. 4). N_d(ϴ) is the theoretical 2-dimensional function of average counts per unit time – the plane scattering rate - which is then scaled to a 3-dimensional function, N(ϴ), which is the spatial scattering rate.

$$N_d(ϴ) = frac{N_m(ϴ)}{t(ϴ)}$$

Where N_m(ϴ) is the average number of counts and t(ϴ) is the time, always 100 seconds for the purposes of this Letter.

$$N(ϴ) = 2π sin(ϴ) N_d(ϴ)$$

Equation (3) gives the equation for the theoretical curve.

$$f(ϴ) = frac{A}{sin^4((B-1)/2)}$$

Where A and B are proportionality factors designated to y-axis shift and x-axis displacement respectively. These are found through trial and error and were found to be A= 0.01 and B= 3.

4. Discussion of Results

4.1 General Discussion

Overall, the results show a similar trend as expected from theory with one noticeable discrepancy. The horizontal shift arising in f(ϴ). The used values of A and B were the tested values that provided the most similar graph. Increasing the value of A logarithmically gave ‘y-axis’ values that were exceedingly large, so much so that the plot of N(ϴ) was reduced to a straight line on the ‘x-axis’. The value of B changing in integer steps either reversed f(ϴ) (B= 2) or changed the ‘y-axis’ so that N(ϴ) could again no longer be seen (B= 1,4).

This slight deviation from theory could stem from the 2D to 3D scaling of the incident beam of α-particles with its uncertainties of dϴ and dΩ (equation 4).

$$dΩ = 2π sin(ϴ) dϴ$$

Where dϴ (interpreted to be ± 0.1°) is the 2D angular uncertainty and dΩ is the 3D spatial angular uncertainty.

From equation (4), this ranges from 0 to 0.3°. However, even without taking this into consideration, the errors from f(ϴ) indicate that the trend of N(ϴ) is within its uncertainty (and vice versa) meaning that the experimental graph is allowed within, and abides to, the trend of the theoretical graph.

4.2 Importance in Modern Physics

At first, it may seem like a "simple" experiment, but the implications of this experiment extend even into modern physics in many fields. Rutherford scattering has a great prevalence and is now being used in the fields of astrophysics [4], wave optics [5], and in the field of quantum mechanics [6]. Rutherford scattering has ascended from using α-particles to using photons. Countless experiments and seemingly endless research have stemmed from this one experiment alone, resulting in numerous discoveries.

5. Conclusion

The experiment performed shows a close relation to the theory of the highly famous and important experiment originally done in 1911 by Ernest Rutherford. Having the gold foil at larger angles causes a decrease in the number of α-particles detected, with the most being detected at 0° (Fig. 3) as expected and expressed from theory. In addition, the graphed function of N(ϴ) matched closely to f(ϴ) with a major discrepancy being the shift in the ‘x-axis,’ however, with uncertainties being considered, this slight deviation is permitted, still following the expected trend.

References

1. E. Rutherford, “Scattering of α and β by Matter and the Structure of the Atom,” Philos. Mag. 26, 669–688 (1911).
2. H. Geiger and E. Marsden, “On a Diffuse Reflection of the α-Particles,” Proc. R. Soc. A 82, 495-500 (1909).
3. J. J. Thomson, “On the Structure of the Atom,” Philos. Mag. 17, 237-265 (1904).
4. M. Marta, et al., “Study of Beam Heating Effect in a Gas Target Through Rutherford Scattering,” Nucl. Instrum. Meth. A 569(3), 727-731 (2016).
5. M. Selmke and F. Cichos, “Photonic Rutherford Scattering: A Classical and Quantum Mechanical Analogy in Ray and Wave Optics,” Am. J. Phys. 81(6), (2013).
6. M. Selmke and F. Cichos, “Photothermal Single Particle Rutherford Scattering Microscopy,” Phys. Rev. Lett. (2013).