Question

Which conservation law is violated in each of these proposed reactions and decays? (Assume that the products have zero orbital angular momentum.)

$$\begin{gathered} \mathbf{\left(}\mathbf{a}\mathbf{\right)}{\mathbf{\wedge }}^{\mathbf{0}}\mathbf{\to }{\mathbf{pK}}^{\mathbf{-}}\mathbf{;} \\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}{\mathbf{\Omega }}^{\mathbf{-}}\mathbf{\to }\sum _{}^{-}\mathbf{+}{\mathbf{\pi }}^{\mathbf{0}}\mathbf{(}\mathbf{S}\mathbf{=}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{q}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{m}\mathbf{=}\mathbf{162}\mathbf{MeV}\mathbf{/}{\mathbf{c}}^{\mathbf{2}}\mathbf{,}\mathbf{and}\mathbf{}{\mathbf{m}}_{\mathbf{s}}\mathbf{=}\frac{\mathbf{3}}{\mathbf{2}}\mathbf{for\Omega }\mathbf{)}\mathbf{;} \\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}{\mathbf{K}}^{\mathbf{-}}\mathbf{+}\mathbf{p}\mathbf{\to }\mathbf{\wedge }\mathbf{0}\mathbf{+}{\mathbf{\pi }}^{\mathbf{+}} \end{gathered}$$

Short answer

(a) Energy

(b) Strangeness.

(c) Charge.

Step-by-step solution

Conservation law

A principle that states that a certain physical property does not charge in the course of time within an isolated physical system. or

The law states that the total energy of an isolated system does not change.

Solve.(a)∧0→p+K-

1) Solution.

$$\begin{gathered} {\wedge }^0\to p+K \\ Change0+1-1 \\ Spin\frac{\mathrm{\pi }}{2}\frac{\mathrm{\pi }}{2}\frac{\mathrm{\pi }}{2} \\ Baryonnumber+1+1-1 \\ Strangeness-10-1 \\ Restenergy1115.6938.3493.7 \end{gathered}$$

Hence, Energy cannot be conserved

Solve.(b)Ω-→∑-+π0s=-3,q=-1,m=1672MeV/c2,ms=32forΩ

1) Solution.

$$\begin{gathered} {\Omega }^{-}\to \sum _{}^{-}+{\mathrm{\pi }}^0 \\ \mathrm{Charge}-1-10 \\ \mathrm{Baryon}\mathrm{number}+10+100 \\ \mathrm{Spin}\frac{\mathrm{\pi }}{2}\frac{\mathrm{\pi }}{2}0 \\ \mathrm{Strangeness}-3-10 \\ \mathrm{Rest}\mathrm{energy}16801197.313.5 \end{gathered}$$

Hence, Charge can not be conserved.

Solve(c)K-+p→∧0+π+

1) Solution.

$$\begin{gathered} K^{-}+p\to {\wedge }^0+{\mathrm{\pi }}^{+} \\ \mathrm{Rest}\mathrm{energy}493.7938.31115.6139.6 \\ \mathrm{Strangeness}-10-10 \\ \mathrm{Spin}0\frac{\mathrm{\pi }}{2}\frac{\mathrm{\pi }}{2}0 \\ \mathrm{Baryon}\mathrm{number}0+1+10 \\ \mathrm{Charge}-1+10+1 \end{gathered}$$

Hence, Charge can not be conserved.