Question

A typical atom has a diameter of about 1.32 x 10-10 m.

A) What is this in inches?
B) How many atoms are there along a 21.0cm line?

Answer 1

A) The value of the diameter in inches is 5.19685 × 10⁻⁹ inches

B) There are 1,590,909,091 atoms on a 21.0cm line

Step-by-step explanation:

A) To determine what its diameter is in inches

We will convert 1.32 × 10⁻¹⁰ m to inches

First convert this to centimeters (cm)

1.32 × 10⁻¹⁰m = 1.32 × 10⁻¹⁰ × 10² cm

= 1.32 × 10⁻⁸cm

Now, since 1 inch = 2.54 cm

∴ 1 cm =
`(1)/(2.54)` inches

If 1 cm =
`(1)/(2.54)` inches

Then 1.32 × 10⁻⁸ cm will be

1.32 × 10⁻⁸ ×
`(1)/(2.54)` inches

= 5.19685 × 10⁻⁹ inches

This is the value of the diameter in inches

B) For the number of atoms on a 21.0cm line

The diameter of 1 atom is 1.32 × 10⁻¹⁰m

1.32 × 10⁻¹⁰m = 1.32 × 10⁻⁸cm

Hence, on a 21.0 cm line, we will have

(21.0 / 1.32 × 10⁻⁸) atoms

= 1590909091 atoms

Hence, there are 1,590,909,091 atoms on a 21.0cm line