Step 1: Understanding the Question:
We need the thickness equal to one Dobson unit.
Step 2: Use a known number:
The average ozone column is about 300 DU, and it makes a layer about 3 mm thick under standard conditions.
Step 3: Divide:
One unit is \(\frac{3\text{ mm}}{300} = 0.01\) mm \(= \frac{1}{100}\) mm.
Step 4: Unit check on option 4:
0.01 cm is 0.1 mm, so it does not match 0.01 mm.
Step 5: Check options 1 and 3:
0.1 mm and 0.001 mm are off by a factor of 10 in either direction.
Step 6: Match:
Only option 2 gives 0.01 mm.
Quick Recap:
Recap: the Dobson unit is a thickness measure, so the answer must be a length. Only 0.01 mm is correct, and the other lengths in the options are ten times larger or smaller.
Final Answer:
\[\boxed{2}\]