Question

Which conservation law is violated in each of these proposed decays? Assume that the initial particle is stationary and the decay products have zero orbital angular momentum.

(a)${\mathit{\mu }}^{\mathbf{-}}\mathbf{\to }{\mathit{e}}^{\mathbf{-}}\mathbf{+}{\mathit{\nu }}_{\mathbf{\mu }}$; (b)${\mathit{\mu }}^{\mathbf{-}}\mathbf{\to }{\mathit{e}}^{\mathbf{+}}\mathbf{+}{\mathit{\nu }}_{\mathbf{e}}\mathbf{+}{{\mathit{v}}^{\mathbf{-}}}_{\mathbf{\mu }}$;(c)${\mathit{\mu }}^{\mathbf{+}}\mathbf{\to }{\mathit{\pi }}^{\mathbf{+}}\mathbf{+}{\mathit{\nu }}_{{\mathbf{\mu }}^{\mathbf{+}}}$

Short answer

(a) decay does not occur.

(b) decay does not occur.

(c) poin energy does not conserve.

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.

Symmetries$\leftrightarrow$Conservation laws.

Rotation$\leftrightarrow$ Angular momentum.

Spin translation$\leftrightarrow$ momentum.

Time translation$\leftrightarrow$ Energy.

(a) Solve μ-→e-+νμ

$$\begin{gathered} {\mu }^{-}\to e^{-}+{\nu }_{\mu } \\ \mathrm{Spin}\text{angular momentum}\frac{\pi }{2}\frac{\pi }{2}\frac{\pi }{2} \\ \text{Electron lepton number}0\text{+10} \end{gathered}$$

Decay does not occur.

Step 3:(b) Solve μ-→e++ve+v-μ

$$\begin{gathered} {\mu }^{-}\to e^{+}+v_{\mathrm{e}}+{v^{-}}_{\mathrm{\mu }} \\ \mathrm{Charge}-\mathrm{e}\text{e00} \\ \text{moun lepton number1-10-1} \end{gathered}$$

Decay does not occur.

(c) solve μ+→π++νμ+

$$\begin{gathered} {\mu }^{+}\to {\pi }^{+}+{\nu }_{{\mu }^{+}} \\ \mathrm{moun}\text{lepton number-10+1} \end{gathered}$$

Mass of poin energy can not be conserved.