Chapter 1: Q17. (page 18)

A typical atom has a diameter of about $1.0 \times 10^{- 10} m$ .
(a) What is this in inches?
(b) Approximately how many atoms are along a 1.0 cm line, assuming they just touch?

Short Answer

Expert verified

(a) The typical diameter of an atom is $3.9 \times 10^{- 9}$ inches.

(b) There are $1.0 \times 10^{8}$ atoms along a 1.0 cm line.

Step by step solution

Step 1. Relation between in and m

The unit conversion is a process in which the unit of a particular quantity is changed from one standard to another standard by multiplying or dividing by a fixed factor.

Given data:

The diameter of a typical atom is $1.0 \times 10^{- 10} m$ .

Now,

$\begin{matrix} 1 in = 2.54 cm \\ = 2.54 cm \times \frac{1 m}{100 cm} \\ = 0.0254 m \end{matrix}$

Step 2. Converting the unit of the diameter from m to in

(a) Now, changing the unit from m to in, you get

$\begin{matrix} 1.0 \times 10^{- 10} m = 1.0 \times 10^{- 10} m \times \frac{1 in}{0.0254 m} \\ = 3.9 \times 10^{- 9} in \end{matrix}$

Therefore, the diameter of a typical atom is about $3.9 \times 10^{- 9} in$ .

Step 3. Finding the numbers of atoms along a 1.0 cm line

(b)Let there be N atoms along a 1.0-cm line.

Now, you know that $1.0 cm = 1.0 \times 10^{- 2} m$ .

Assuming they just touch together, you get

localid="1654695946709" $\begin{matrix} N \times (1.0 \times 10^{- 10} m) = 1.0 \times 10^{- 2} m \\ N = \frac{1.0 \times 10^{- 2} m}{1.0 \times 10^{- 10} m} \\ N = 1.0 \times 10^{8} \end{matrix}$

Therefore, there are $1.0 \times 10^{8}$ atoms along a 1.0 cm line.

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A typical atom has a diameter of about $1.0 \times 10^{- 10} m$ .
(a) What is this in inches?
(b) Approximately how many atoms are along a 1.0 cm line, assuming they just touch?

Short Answer

Step by step solution

Step 1. Relation between in and m

Step 2. Converting the unit of the diameter from m to in

Step 3. Finding the numbers of atoms along a 1.0 cm line

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A typical atom has a diameter of about1.0×10-10m.(a) What is this in inches?(b) Approximately how many atoms are along a 1.0 cm line, assuming they just touch?

Short Answer

Step by step solution

Step 1. Relation between in and m

Step 2. Converting the unit of the diameter from m to in

Step 3. Finding the numbers of atoms along a 1.0 cm line

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Electric Charge Field and Potential

Physical Quantities And Units

Torque and Rotational Motion

Electrostatics

Oscillations

Study anywhere. Anytime. Across all devices.

A typical atom has a diameter of about $1.0 \times 10^{- 10} m$ .
(a) What is this in inches?
(b) Approximately how many atoms are along a 1.0 cm line, assuming they just touch?