Question

A silicon chip used in an integrated circuit of a computer has a mass of 5.68 mg. The number of Si atoms present in this chip are

• A. \(1.44\times 10^{20}\) atoms
• B. \(1.8\times 10^{20}\) atoms
• C. \(2.1\times 10^{20}\) atoms
• D. None of these

Hint:

Always ensure mass is in grams when using atomic mass in g/mol. For very small masses, converting to scientific notation and carefully handling powers of 10 is crucial.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The number of atoms in a given mass is found by dividing the mass by the atomic mass to get moles, then multiplying by Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol).

Step 2: Detailed Explanation:
Atomic mass of Silicon (Si) = 28 g/mol. Mass of chip = 5.68 mg = \(5.68 \times 10^{-3}\) g. Number of moles of Si = \(\frac{5.68 \times 10^{-3} \text{ g}}{28 \text{ g/mol}} = 2.0286 \times 10^{-4}\) mol. Number of Si atoms = moles \(\times N_A\) = \(2.0286 \times 10^{-4} \times 6.022 \times 10^{23}\) = \(1.221 \times 10^{20}\) atoms. This can be written as \(1.221 \times 10^{20}\) atoms = \(122.1 \times 10^{18}\) atoms, which is not equal to any of the given options.

Step 3: Final Answer:
The calculated number of atoms is \(1.221 \times 10^{20}\), which does not match options (A), (B), or (C). Hence, the correct answer is (D) None of these.