QQuestionChemistry
QuestionChemistry
The radius of an atom of gold (Au) is about 1.35 Å (angstrom).
a. Express this distance in nanometers (nm) and in picometers (pm).
b. How many gold atoms would have to be lined up to span 1.0 mm?
c. If the atom is assumed to be a sphere, what is the volume in cm^3 of a single Au atom?
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Convert the radius from Å to nm
• 1 Å = $$10^{-1}$$ nm
• Radius = 1.35 Å \times \frac{1}{10} nm/Å = 0.135 nm
Step 3:: Convert the radius from Å to pm
• Radius = 1.35 Å $$\times 100$$ pm/Å = 135 pm
• 1 Å = 100 pm
Step 4:: Calculate number of atoms spanning 1.0 mm
• 1.0 mm = $$10^{-3}$$ m = $$10^{4}$$ nm
• Number of atoms = \frac{10^{4} \text{ nm}}{0.135 \text{ nm/atom}} = 7.41 \times 10^{4} atoms
Step 5:: Calculate atomic volume
• Volume = $$\frac{4}{3}\pi(1.35 \times 10^{-10})^{3} = 1.03 \times 10^{-29}$$ cm³
• Radius = 0.135 nm = 1.35 \times 10^{- 10} m
Final Answer
a. 0.135 nm, 135 pm b. 7.41 \times 10^{4} atoms c. 1.03 \times 10^{- 29} cm³
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