Step 1: Understanding the Question:
We need to find the edge length ($a$) of a simple cubic unit cell given the atomic radius ($r = 170$ pm). Step 2: Key Formula or Approach:
For a simple cubic (SC) unit cell, the relation between edge length $a$ and radius $r$ is:
\[ a = 2r \]
Step 3: Detailed Explanation:
Given: $r = 170$ pm
\[ a = 2 \times 170\text{ pm} = 340\text{ pm} \]
To convert picometers to centimeters:
\[ 1\text{ pm} = 10^{-10}\text{ cm} \]
\[ a = 340 \times 10^{-10}\text{ cm} \]
\[ a = 3.40 \times 10^{-8}\text{ cm} \]
Step 4: Final Answer:
The edge length is $3.40 \times 10^{-8}$ cm.