When Rutherford performed his gold foil experiment the alpha particles (which ar

Question

When Rutherford performed his gold foil experiment the alpha particles (which are comprised of 2 protons and 2 neutrons) either passed through the gold foil or bounced off the gold nuclei. In other words, the alpha particles were behaving like particles. The distance between neighboring gold atoms in the foil is about 136 pico meters (1pm = 10^-12m)

A) explain why an interference pattern did not show up in Rutherford's experiment. After all, when Davisson and Germer fired electrons at a crystal an interference pattern did show up

B) Estimate the speed at which the alpha particles would need to be traveling so that an interference pattern would appear.

Explanation / Answer

Matter will only show wavelike behavior when it interacts with objects within about a factor of 1000 of its de Broglie wavelength. Because the alpha particle is so large compared to the electron, its de Broglie wavelength will be smaller: h h p mv It must have been that the de Broglie wavelength of the alpha particles in Rutherfords experiment was shorter than 136 1012 m 136 1015 m 1.36 1013 m . In order for the alpha particles to have a wavelength longer than this 1000 (and would therefore begin showing significant interference effects) they would have to traveling no faster than: v h 6.63 1034 J s 7.30 105 m s 27 13 m 4 1.67 10 kg 1.36 10 m Rutherford was using alpha particles produced by the radioactive decay of heavy elements. Alpha particles produced in this way typically have speeds 20 times greater than this which is why he did not observe any interference effec ts.

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