Which of the following reactions cannot because the law of conservation of strangeness is violated? (a) \(\mathrm{p}+\mathrm{n} \rightarrow \mathrm{p}+\mathrm{p}+\pi^{-}\) (b) \(\mathrm{p}+\mathrm{n} \rightarrow \mathrm{p}+\mathrm{p}+\mathrm{K}^{-}\) (c) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \mathrm{K}^{-}+\sum^{+}\) (d) \(\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{+}+\sum^{-}\) (e) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \Xi^{0}+\mathrm{K}^{+}+\pi^{-}\) (f) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \Xi^{0}+\pi^{-}+\pi^{-}\) (g) \(\pi^{+}+\mathrm{p} \rightarrow \Sigma^{+}+\mathrm{K}^{+}\) (h) \(\pi^{-}+\mathrm{n} \rightarrow \mathrm{K}^{-}+\Lambda^{0}\)

Short Answer

Expert verified
Thus, the reaction that violated the law of conservation of strangeness is (g).

Step by step solution

01

Understand strangeness of each particle

Firstly, the concept of strangeness is understood. Strangeness is a property of particles, expressed as a number, which is conserved in all particle physics reactions. Each particle has its own 'strangeness value' as follows: Proton (p) and Neutron (n): 0, Pion: 0, Kaon (K-): -1, Anti-Kaon (K+): +1, Sigma: 0, Xi: 0, Lambda: 0.
02

Calculate total strangeness for each reaction

Next, for each of the given reactions, the total strangeness at the start of the reaction (left side of the equation) is compared to the total strangeness at the end of the reaction (right side of the equation). If these values are not the same, then the law of conservation of strangeness is violated.
03

Identify violating reactions

(a) and (b) reactions are proton-neutron reactions. Since protons and neutrons have zero strangeness, the left side of the equation has zero total strangeness. The right side of both equations also has zero strangeness (protons = 0, pion = 0, kaon = -1 and anti-kaon = +1 add up to a total of 0), hence both conserve strangeness. (c), (d), (e), and (f) involve kaon and pion reactions which also conserve strangeness. But, in (g), \( \pi^{+}+\mathrm{p} \rightarrow \Sigma^{+}+\mathrm{K}^{+} \), the initial total strangeness is 0, however the total strangeness of the final particles is +1 (because of anti-kaon, K+), therefore this violates the law of strangeness conservation. Lastly, (h) also conserves strangeness.

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