Question

1. what is the range of the radii of most atoms in nanometers (nm)? 5×10⁻²⁰ nm - 2×10⁻¹⁹ nm / 5×10⁻¹¹ m - 2×10⁻¹⁰ m
2. a sample of copper with a mass of 63.5 g contains 6.02×10²³ atoms. calculate the mass of a single copper atom. show your work and include correct units.

Explanation:

Step1: Recall atom - radius range

The typical range of the radii of most atoms is \(5\times 10^{-11}\text{ m}-2\times 10^{-10}\text{ m}\). To convert from meters to nanometers, use the conversion factor \(1\text{ m}=10^{9}\text{ nm}\).

Step2: Convert the range to nanometers

For the lower - bound: \(5\times 10^{-11}\text{ m}\times10^{9}\text{ nm/m}=5\times 10^{-2}\text{ nm}\). For the upper - bound: \(2\times 10^{-10}\text{ m}\times10^{9}\text{ nm/m}=0.2\text{ nm}\). So the range in nanometers is \(5\times 10^{-2}\text{ nm}-0.2\text{ nm}\).

Step3: Calculate the mass of a single copper atom

We know that a sample of copper with a mass of \(m = 63.5\text{ g}\) contains \(N=6.02\times 10^{23}\) atoms. The mass of a single atom \(m_{atom}\) can be found using the formula \(m_{atom}=\frac{m}{N}\).

Step4: Substitute the values

\(m_{atom}=\frac{63.5\text{ g}}{6.02\times 10^{23}}=\frac{63.5}{6.02}\times10^{-23}\text{ g}\approx1.05\times 10^{-22}\text{ g}\)

Answer:

1. The range of the radii of most atoms in nanometers is \(5\times 10^{-2}\text{ nm}-0.2\text{ nm}\).
2. The mass of a single copper atom is approximately \(1.05\times 10^{-22}\text{ g}\).