The radius of a niobium atom is 131 pm. How many niobium atoms would have to be laid side by side to span a distance of 3.20 mm?
To find out how many niobium atoms would have to be laid side by side to span a distance of 3.20 mm, we need to calculate the number of atoms that can fit within this distance.
First, let's convert the radius of the niobium atom from picometers (pm) to millimeters (mm). Since 1 pm = 1 x 10^-3 mm, we can calculate:
Radius in mm = 131 pm x (1 x 10^-3 mm/1 pm) = 0.131 mm
Next, we need to determine the distance covered by a single niobium atom. Since the diameter of an atom is twice the radius, the distance covered by a single atom would be:
Distance covered by a single atom = 2 x radius = 2 x 0.131 mm = 0.262 mm
Now we can calculate the number of niobium atoms that can fit within a distance of 3.20 mm by dividing the total distance by the distance covered by a single atom:
Number of atoms = Total distance / Distance covered by a single atom = 3.20 mm / 0.262 mm
So, the number of niobium atoms that would have to be laid side by side to span a distance of 3.20 mm is approximately:
Number of atoms ≈ 12.21 atoms
Therefore, we would need approximately 12.21 niobium atoms to span a distance of 3.20 mm.
To find out how many niobium atoms would have to be laid side by side to span a distance of 3.20 mm, we need to calculate the number of atoms that can fit within this distance.
Here's the step-by-step process:
Step 1: Convert the radius of the niobium atom from picometers (pm) to meters (m).
1 pm = 1x10^-12 meters
Given the radius of the niobium atom: 131 pm
Radius in meters = 131 pm * (1x10^-12 m/pm) = 131x10^-12 m
Step 2: Calculate the diameter of the niobium atom:
Diameter of the niobium atom = 2 * radius
Diameter = 2 * (131x10^-12 m) = 262x10^-12 m
Step 3: Convert the distance to meters:
Given distance = 3.20 mm
Distance in meters = 3.20 mm * (1x10^-3 m/mm) = 3.20x10^-3 m
Step 4: Divide the distance by the diameter of a niobium atom to find the number of niobium atoms that can fit.
Number of atoms = Distance / Diameter
Number of atoms = (3.20x10^-3 m) / (262x10^-12 m)
Calculating this, we find:
Number of atoms = 1.22x10^10 niobium atoms
Therefore, approximately 1.22x10^10 niobium atoms would have to be laid side by side to span a distance of 3.20 mm.