How Many Gold Atoms Fit in the Foil Used by Rutherford in His Experiment?

The gold foil used by Rutherford in his historic experiment was notably thin, with a thickness of about 0.0001 cm, or 1 × 10^-6 meters. This foil played a crucial role in his groundbreaking discovery of the atomic nucleus. But have you ever wondered how many gold atoms fit into such a thin layer? Let’s delve into the fascinating world of atomic scales to find out.

The Radius of a Gold Atom

The radius of a gold atom is approximately 2.35 × 10^-10 meters or 235 × 10^-12 meters. Using this information, we can estimate the number of atoms that fit in the thickness of the foil.

Calculation Steps

To calculate the number of atoms in the thickness of the gold foil, we start by determining the diameter of a gold atom:

Diameter 2 × Radius 2 × 2.35 × 10^-10 meters 4.7 × 10^-10 meters

Next, we convert the thickness of the foil to meters:

Thickness of foil 1 × 10^-6 meters

Now, we can find the number of atoms in the thickness of the foil by dividing the thickness of the foil by the diameter of a gold atom:

Number of atoms (frac{text{Thickness of foil}}{text{Diameter of gold atom}} frac{1 times 10^{-6}}{4.7 times 10^{-10}} approx 2127.66)

Therefore, approximately 2128 gold atoms fit in the thickness of the gold foil used in Rutherford's experiment.

The Thickness of the Foil in Atoms

Interestingly, the foil’s thickness was also measured in terms of the number of atoms. If the foil was about 1000 atoms thick, it aligns closely with our calculation, given that the diameter of a gold atom is about 2.7 × 10^-10 meters. This thickness is also equivalent to about a quarter of a micron (1 micron 1 × 10^-6 meters).

Revisiting the Order of Magnitude

There was a mix-up in the initial radius provided, which was mistakenly taken as 235 × 10^-15 meters. However, the correct radius for a gold atom is 2.35 × 10^-10 meters. It's crucial to specify the unit when dealing with very small measurements, as 10^-15 meters correspond to the fermi scale, which is used for nuclear physics, whereas atomic radii are typically given in Angstroms (1 Angstrom 10^-10 meters).

Conclusion

The thickness of the gold foil used in Rutherford's experiment is a testament to the precision and groundbreaking nature of his work. Rutherford's discovery led to a significant shift in our understanding of atomic structure, and his experiments continue to inhabit a central place in the education of future scientists and physicists.