How many ruthenium atoms can you line up across across the tip of a finger that is 3.6 cm in length. A ruthenium atom has an average atomic radius of 178 pm.

1.0 × 10⁸ ruthenium atoms

Explanation:

Step 1: Calculate the diameter (d) of an atom of ruthenium

The diameter of an atom is twice its radius.

d = 2 × r = 2 x 178 pm = 356 pm

Step 2: Convert "d" to meters

We will use the conversion factor 1 m = 10¹² pm.

356 pm × 1 m/10¹² pm = 3.56 × 10⁻¹⁰ m

Step 3: Convert the distance of the tip of a finger (D) to meters

We will use the conversion factor 1 m = 10² cm.

3.6 cm × 1 m/10² cm = 0.036 m

Step 4: Calculate the number of atoms of ruthenium required

We will use the following expression.

D/d = 0.036 m/3.56 × 10⁻¹⁰ m = 1.0 × 10⁸