if the diameter of a sodium atom is 3.14×10−8 cm, how many sodium atoms would fit along a line exactly 1.00 inch long?
How far apart are they? Do they touch. If so,
Make a proportion.
(3.14E-8cm/1 atom) = (2.54cm/x atoms).
Solve for x.
8.08E7
1 Inch = 2.54 cm
1 Na atom has a diameter of 3.4 x 10^-8 cm
X Na atoms = 2.54 cm
(3.4 x 10^-8)x = 2.54
Find X= ?
X= 8.09 x 10^7 Na atoms.
To find out how many sodium atoms would fit along a line exactly 1.00 inch long, we need to convert the given diameter to inches and then divide the 1.00 inch length by the converted diameter.
First, let's convert the diameter of the sodium atom from cm to inches:
1 cm = 0.3937 inches
So, the diameter in inches would be:
3.14 × 10^(-8) cm * 0.3937 inches/cm = 1.236 × 10^(-8) inches
Now that we have the diameter of a sodium atom in inches, we can calculate the number of atoms that would fit along a 1.00 inch line:
Number of atoms = Length of line / Diameter of a single atom
Number of atoms = 1.00 inch / 1.236 × 10^(-8) inches
Number of atoms ≈ 8.10 × 10^7 atoms
Therefore, approximately 8.10 × 10^7 sodium atoms would fit along a line exactly 1.00 inch long.