Question

Total columnar ozone in the atmosphere is measured in Dobson units. One Dobson unit corresponds to ..............

• A. $\frac{1}{10}\text{ of mm}$
• B. $\frac{1}{100}\text{ of mm}$
• C. $\frac{1}{1000}\text{ of mm}$
• D. $\frac{1}{100}\text{ of cm}$

Hint:

Dobson Unit Conversion Formulas:
$1\text{ DU} = 0.01\text{ mm} = \frac{1}{100}\text{ mm} = 10^{-5}\text{ m}$ (at STP).
$1\text{ DU} = 2.69 \times 10^{16}\text{ molecules/cm}^2$.
An ozone hole is defined when total ozone levels drop below $220\text{ DU}$.

Answer 1

The Correct Option is B

Concept:
Total columnar ozone refers to the total number of ozone molecules present in a vertical atmospheric column extending from the Earth's surface to the top of the atmosphere.
It is conventionally expressed in Dobson Units (DU), named in honor of Gordon Dobson, who designed the first spectrophotometer to measure stratospheric ozone.

Step 1: Physical Definition of a Dobson Unit:
A Dobson Unit is defined by compressing all ozone molecules in a vertical column of air into a pure, uniform layer at Standard Temperature and Pressure (STP, defined as $T = 0^\circ\text{C}$ or $273.15\text{ K}$ and $P = 1\text{ atm}$ or $101.325\text{ kPa}$).
Under these conditions, a layer thickness of $1\text{ mm}$ of pure ozone corresponds to $100\text{ DU}$.

Step 2: Mathematical Conversion to Millimeters:
Using this relationship:
\[ 100\text{ DU} = 1\text{ mm of pure ozone at STP} \] Dividing both sides by 100:
\[ 1\text{ DU} = \frac{1}{100}\text{ mm} = 0.01\text{ mm} = 10\,\mu\text{m} \] In terms of molecular areal density, $1\text{ DU}$ is equivalent to approximately $2.69 \times 10^{16}\text{ molecules of ozone per square centimeter}$ ($2.69 \times 10^{20}\text{ molecules/m}^2$).
For reference, typical atmospheric ozone concentrations average roughly $300\text{ DU}$, which corresponds to a pure ozone layer only $3\text{ mm}$ thick at sea-level pressure.
Final Answer:
One Dobson unit corresponds to $\frac{1}{100}\text{ of mm}$ of pure ozone at STP, which corresponds to option (B).