Question

If 5.76 x 1013 neon atoms (spherical) were laid in a line, each touching the next, the line would measure 2.54 miles. what is the diameter of a neon atom in å?

Answer 1

The diameter of a neon atom, calculated from the length of a line of atoms and the number of atoms within that line, is approximately 0.70946 angstroms (Å).

Step-by-step explanation:

To determine the diameter of a neon atom in angstroms (Å), we can use the information provided about the length of a line of atoms and the number of atoms in that line. Since the line measures 2.54 miles and we know that 1 mile equals 1.609344 kilometers (km), we first convert the length of the line to meters (m). There are 1,000 meters in a kilometer, so:

2.54 miles = 2.54 × 1.609344 km/mile × 1000 m/km = 4,086.7136 m

Now, as we have 5.76 × 1013 atoms in this length, we divide the total length in meters by the number of atoms to find the length occupied by one atom:

4,086.7136 m / 5.76 × 1013 atoms = 7.0946 × 10-11 m/atom

Since 1 Å is 10-10 m, we convert this measurement to angstroms:

7.0946 × 10-11 m/atom × (1010 Å/1 m) = 0.70946 Å/atom

Therefore, the diameter of a neon atom is approximately 0.70946 Å.