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.