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

One barn is equal to:
A. 10−30  m210^{-30}\;m^2
B. 1028  m210^{28}\;m^2
C. 10−28  m210^{-28}\;m^2
D. 1030  m210^{30}\;m^2

Explanation

Solution

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  m10^{-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 = πr2\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  m10^{-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=πr2=π(10−14)2=π×10−28≈10−28  m2=1  barnArea = \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.