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the radius of a palladium atom is 137 pm. how many palladium atoms would have to be laid side by side to span a distance of 2.29 mm?

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Final answer:

To span a distance of 2.29 mm, approximately 8,357 palladium atoms, each with a diameter of 274 pm, would be required when laid side by side.

Step-by-step explanation:

To determine how many palladium atoms are needed to span a distance of 2.29 mm, we first need to convert the distance into picometers (pm) since the radius of a palladium atom is given in picometers (1 mm = 1,000,000 pm). Therefore, 2.29 mm is equal to 2.29 × 1,000,000 pm = 2,290,000 pm. If the radius of a palladium atom is 137 pm, the diameter of one atom would be 2 × 137 pm = 274 pm.

Next, calculate the number of diameters that fit into the total distance

  • Total distance in picometers: 2,290,000 pm
  • Diameter of one palladium atom: 274 pm
  • Number of palladium atoms required to span 2.29 mm:

№ of palladium atoms = Total distance / Diameter of one atom

№ of palladium atoms = 2,290,000 pm / 274 pm

№ of palladium atoms = approximately 8,357

So, roughly 8,357 palladium atoms would be needed to span a distance of 2.29 mm.

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