QQuestionMathematics
QuestionMathematics
Paper thickness varies. Typically, 100 sheets are about 1 cm thick. Atoms typically vary from 1 to 3 angstroms in radius. (An angstrom is 10
−10
m.) Suppose a piece of paper is 0.0072 cm thick. How many atoms span the thickness if the radius of the atom is 1.23 angstroms?
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Answer
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Step 1:Let's solve this problem step by step:
Step 2:: Convert the paper thickness to meters
0.0072 \mathrm{~cm} = 7.2 \times 10^{-4} \mathrm{~m}
Step 3:: Convert the atom radius from angstroms to meters
• 1 angstrom = $$10^{-10} \mathrm{~m}
• Atom radius = 1.23 \times 10^{- 10} \mathrm{~m}
Step 4:: Calculate the number of atoms that span the paper thickness
• Number of atoms = $$\frac{7.2 \times 10^{-4} \mathrm{~m}}{2 \times (1.23 \times 10^{-10} \mathrm{~m})}
• To span the thickness, we'll divide the paper thickness by the atom diameter
Step 5:: Calculate the final result
\frac{7.2 \times 10^{-4}}{2 \times 1.23 \times 10^{-10}} = 2.93 \times 10^{6} \text{ atoms}
Final Answer
Approximately 2,930,000 atoms span the thickness of the paper.
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