The radius of a chromium atom is 125 pm. How many chromium atoms would have to be laid side by side to span a distance of 4.14 mm?
To determine how many chromium atoms would have to be laid side by side to span a distance of 4.14 mm, we need to first convert the given radius of 125 pm to millimeters.
Given:
Radius of chromium atom = 125 pm
Distance to span = 4.14 mm
1 pm = 1 × 10^-12 m
1 mm = 1 × 10^-3 m
Converting pm to mm:
125 pm * (1 × 10^-12 m/1 pm) * (1 mm/1 × 10^-3 m) = 1.25 × 10^-7 mm
Now, we can determine the number of atoms required to span 4.14 mm by dividing the distance by the equivalent length of a single chromium atom:
Number of chromium atoms = 4.14 mm / 1.25 × 10^-7 mm
Number of chromium atoms = 33,120,000
Therefore, approximately 33,120,000 chromium atoms would have to be laid side by side to span a distance of 4.14 mm.
To determine the number of chromium atoms needed to span a distance of 4.14 mm, we need to calculate the length of a single chromium atom and then divide the total distance by this length.
Given:
Radius of a chromium atom = 125 pm (picometers)
Total distance = 4.14 mm
1 picometer (pm) = 1 × 10^-12 meters (m)
1 millimeter (mm) = 1 × 10^-3 meters (m)
Step 1: Convert the radius of a chromium atom from picometers (pm) to meters (m):
125 pm * (1 × 10^-12 m/1 pm) = 1.25 × 10^-10 m
Step 2: Convert the total distance from millimeters (mm) to meters (m):
4.14 mm * (1 × 10^-3 m/1 mm) = 4.14 × 10^-3 m
Step 3: Calculate the length of a single chromium atom:
The radius is half of the diameter, so the diameter of a chromium atom is: 2 * 1.25 × 10^-10 m = 2.5 × 10^-10 m
Step 4: Divide the total distance by the length of a single chromium atom to find the number of atoms needed:
4.14 × 10^-3 m / (2.5 × 10^-10 m) = 1.656 × 10^7
Therefore, approximately 1.656 × 10^7 (or 16,560,000) chromium atoms would need to be laid side by side to span a distance of 4.14 mm.
Convert 250 pm diameter to mm.
?mm diameter/atom x # atoms = 4.14 mm
Solve for # atoms.