The radius of a strontium atom is 215 pm. How many strontium atoms would have to be laid side by side to span a distance of 4.47 mm?
To solve this problem, we need to determine the number of strontium atoms that can fit within the given distance. Here's how we can do it:
Step 1: Convert the radius to meters
1 pm (picometer) is equal to 1 x 10^-12 meters.
So, to convert the radius of 215 pm to meters, we divide it by 10^12:
215 pm = (215 / 10^12) meters = 2.15 x 10^-10 meters.
Step 2: Calculate the diameter of a strontium atom
The diameter of a sphere is twice the radius. So, the diameter of a strontium atom is:
2 x (2.15 x 10^-10) meters = 4.3 x 10^-10 meters.
Step 3: Determine the number of atoms that can fit in the given distance
To find the number of atoms that can fit in 4.47 mm, we need to divide the distance by the diameter of a single atom:
Number of atoms = (4.47 mm) / (4.3 x 10^-10 m).
First, let's convert 4.47 mm to meters:
1 mm (millimeter) is equal to 1 x 10^-3 meters.
So, 4.47 mm = (4.47 x 10^-3) meters.
Now, we can calculate the number of atoms using the formula:
Number of atoms = (4.47 x 10^-3) / (4.3 x 10^-10).
Divide the two values:
Number of atoms ≈ 1.04 x 10^7.
Therefore, approximately 10,400,000 strontium atoms would have to be laid side by side to span a distance of 4.47 mm.
To determine how many strontium atoms would have to be laid side by side to span a distance of 4.47 mm, we need to calculate the number of atoms that fit within this distance.
First, we need to convert the radius of a strontium atom from picometers (pm) to millimeters (mm):
1 pm = 0.000001 mm
So, the radius of a strontium atom in millimeters is:
215 pm * 0.000001 mm/pm = 0.000215 mm
Next, we can calculate the number of atoms that fit within the given distance:
Number of atoms = distance / (2 * radius)
Number of atoms = 4.47 mm / (2 * 0.000215 mm)
Number of atoms = 4.47 mm / 0.00043 mm
Number of atoms = 10,395.34
Therefore, approximately 10,395 strontium atoms would need to be laid side by side to span a distance of 4.47 mm.
A radius of 215 pm = diameter of 430 pm and that is 430E-12m.
The distance to be covered is 4.47mm or 4.47E-3m.
So 430E-12m x #atoms = 4.47E-3 m
Solve for # atoms.