Question

One barn is equal to:
A. $10^{-30}\;m^2$
B. $10^{28}\;m^2$
C. $10^{-28}\;m^2$
D. $10^{30}\;m^2$

Answer 1

Hint: Barn is the metric unit of area, specifically the cross-sectional area, presented by an average nucleus. Recall that the radii of typical nuclei are of the order $10^{-14}\;m$. Assuming a spherically shaped nucleus, calculate the area of the nucleus given its radius. This is what one barn is equivalent to.

Formula used: Area of a spherical nucleus = $\pi r^2$, where r is the average radius of nuclei.

Complete step by step answer:
A barn is a unit of area abbreviated as “bn”. Though it is not an official SI unit, it is used by nuclear physicists as a convenient measure for expressing the cross-sectional area of nuclei and nuclear reaction. Today, it is used in all fields of high-energy physics to express the cross-sections of any scattering process.
A barn is approximately the cross-sectional area of a uranium nucleus.
A typical nucleus has an average radius of $10^{-14}\;m$. We know that a nucleus has more or less a spherical shape to maintain stability and keep all its dimensions as small as possible.
Since barn is a measure for expressing the cross-sectional area of a nucleus, the area of the nucleus is thus given by:
$Area = \pi r^2 = \pi (10^{-14})^2 = \pi \times 10^{-28} \approx 10^{-28}\;m^2 =1\;barn$.

So, the correct answer is “Option C”.

Additional Information: It is interesting to note that this unit of barn came into being during the Manhattan Project research on the atomic bomb during World War 2. American physicists needed a secretive unit to describe the approximate cross-sectional area presented by a nucleus, and they decided on a barn, named after the broad side of a barn, which is basically a large area. This was meant to obscure confidential information regarding nuclear developments but eventually this unit came to be used widely in nuclear and particle physics.

Note: It is important to understand that the cross-sectional area here does stand true to its literal meaning. It is more of an analogy and forms a basis for understanding its definition but a cross-sectional area in this context has a different meaning in the physical sense. A nuclear cross section basically gives the probability that a nuclear reaction will occur. Like we mentioned, this concept can be quantified as a characteristic area, where a larger area is synonymous to a larger probability of interaction.