Question

A man writes his biodata with a carbon pencil on plane paper having a mass of 150 mg. After writing his biodata, he weighs the written paper and finds its mass is 152 mg. What is the number of carbon atoms present in the paper?

• A. \(1.0036\times 10^{20}\)
• B. \(5.02\times 10^{20}\)
• C. \(1.0036\times 10^{23}\)
• D. \(0.502\times 10^{20}\)

Hint:

Remember to subtract the initial mass from the final mass to find the mass of the substance that was added (in this case, carbon). Always ensure masses are in the same units.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The increase in mass of the paper is due to the carbon deposited by the pencil. The number of carbon atoms is then calculated from this mass using the atomic mass of carbon and Avogadro's number.

Step 2: Detailed Explanation:
Mass of carbon atoms deposited = final mass - initial mass = 152 mg - 150 mg = 2 mg = \(2\times 10^{-3}\) g. Atomic mass of carbon = 12 g/mol. Number of moles of carbon = \(\frac{2\times 10^{-3} \text{ g}}{12 \text{ g/mol}} = 1.6667\times 10^{-4}\) mol. Number of carbon atoms = moles \(\times N_A\) = \(1.6667\times 10^{-4} \times 6.022\times 10^{23}\) = \(1.0036\times 10^{20}\) atoms.

Step 3: Final Answer:
The number of carbon atoms is \(1.0036\times 10^{20}\), which corresponds to option (A).