Question

The diameter of a cream-filled cookie is approximately 44 millimeters (mm). An atom of bismuth (Bi) is approximately 320. picometers (pm) in diameter. Calculate the number of bismuth atoms needed to span the diameter of a cream-filled cookie in a line. Express your answer in scientific notation, showing the correct number of significant figures. (Enter your answer using one of the following formats: 1.2e-3 for 0.0012 and 1.20e+2 for 120. 1 m = 103 mm = 1012 pm)

Bi atoms?

Answer 1

1.4e+8 bismuth atoms

Step-by-step explanation:

If 10³ mm = 10¹² pm

then 44 mm = X pm

X = (44 × 10¹²) / 10³ = 44 × 10⁹ pm (which is the cookie diameter in picometers)

Now we can calculate the number of bismuth atoms needed to span the diameter of the cookie:

number of bismuth atoms = cookie diameter / bismuth atom diameter

number of bismuth atoms = 44 × 10⁹ / 320 = 0.1375 × 10⁹ atoms = 1.375 × 10⁸ atoms

And now to respect the answer format requested by the problem:

1.375 × 10⁸ = 1.375e+8 ≈ 1.4e+8