The radius of a spherical aluminum atom is 140 picometers. How many aluminum atoms could be lined up across a length of 27.9 cm.

9.96 × 10⁸

Explanation:

Step 1: Calculate the diameter of 1 aluminum atom

The diameter of a sphere is 2 times the radius.

d = 2 × 140 pm = 280 pm

Step 2: Convert "d" to m

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

280 pm × 1 m/10¹² pm = 2.80 × 10⁻¹⁰ m

Step 3: Convert the total length (L) to m

We will use the conversion factor 1 m = 100 cm.

27.9 cm × 1 m/100 cm = 0.279 m

Step 4: Calculate the number of atoms of aluminum required

We will use the following expression.

L/d = 0.279 m/2.80 × 10⁻¹⁰ m = 9.96 × 10⁸