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 4.53 mm?
atoms
radius is 131 pm
diameter is 2*131 pm
2*131 pm x (1 mm/10^9) x #atoms = 4.53 mm
Solve for # atoms
1.04x10^-7
To calculate the number of niobium atoms required to span a distance of 4.53 mm, we need to know the length of a single niobium atom.
Given that the radius of a niobium atom is 131 pm (picometers), we can calculate the diameter of the atom by doubling the radius:
Diameter = 2 * radius = 2 * 131 pm = 262 pm
Now, we need to convert the diameter from picometers to millimeters since the given distance is in millimeters:
1 pm = 1 × 10^-3 nm = 1 × 10^-6 mm
Therefore, the diameter of a niobium atom is:
262 pm = 262 × 10^-6 mm
Now, we can calculate the number of niobium atoms required to span a distance of 4.53 mm:
Number of atoms = (Total distance) / (Diameter of a single atom)
Number of atoms = 4.53 mm / (262 × 10^-6 mm)
Number of atoms = (4.53 mm) / (2.62 × 10^-4 mm)
Number of atoms = 17,297.71 atoms
Rounding the result to the nearest whole number, we would need 17,298 niobium atoms laid side by side to span a distance of 4.53 mm.
To find out how many niobium atoms would have to be laid side by side to span a distance of 4.53 mm, we need to calculate the total length covered by the given number of atoms.
First, we need to convert the radius of a niobium atom from picometers (pm) to meters (m):
1 pm = 1 x 10^-12 m
So, the radius of a niobium atom in meters would be:
131 pm * (1 x 10^-12 m/1 pm) = 131 x 10^-12 m
Now, we can calculate the length of a niobium atom by doubling the radius:
Length of a niobium atom = 2 * (131 x 10^-12 m) = 262 x 10^-12 m
Next, we convert the given distance of 4.53 mm to meters:
1 mm = 1 x 10^-3 m
So, the given distance in meters would be:
4.53 mm * (1 x 10^-3 m/1 mm) = 4.53 x 10^-3 m
Finally, we divide the total distance by the length of a niobium atom to find the number of atoms required:
Number of niobium atoms = (4.53 x 10^-3 m) / (262 x 10^-12 m)
Now, simplify the expression:
Number of niobium atoms = (4.53 x 10^-3 m) * (1 / (262 x 10^-12 m))
Number of niobium atoms = (4.53 x 10^-3 m) * (1 / (262 x 10^-12 m))
= (4.53 x 10^-3) / (262 x 10^-12)
= (4.53 / 262) * (10^-3 / 10^-12)
= 0.0172973 * 10^9
≈ 1.72973 * 10^7
Therefore, approximately 1.72973 * 10^7 (or 17,297,300) niobium atoms would have to be laid side by side to span a distance of 4.53 mm.