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Found in: Page 1363

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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

(a) decay does not occur.

(b) decay does not occur.

(c) poin energy does not conserve.

See the step by step solution

## Step 1: 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$↔$Conservation laws.

Rotation $↔$ Angular momentum.

Spin translation$↔$ momentum.

Time translation $↔$ Energy.

## Step 2: (a) Solve μ-→e-+νμ

${\mu }^{-}\to {e}^{-}+{\nu }_{\mu }\phantom{\rule{0ex}{0ex}}\mathrm{Spin}\text{angular momentum}\frac{\pi }{2}\text{}\frac{\pi }{2}\text{}\frac{\pi }{2}\phantom{\rule{0ex}{0ex}}\text{Electron lepton number}0\text{+1 0}\phantom{\rule{0ex}{0ex}}$

Decay does not occur.

## Step 3:(b) Solve μ-→e++ve+v-μ

${\mu }^{-}\to {e}^{+}+{v}_{\mathrm{e}}+{{v}^{-}}_{\mathrm{\mu }}\phantom{\rule{0ex}{0ex}}\mathrm{Charge}\text{}-\mathrm{e}\text{e 0 0}\phantom{\rule{0ex}{0ex}}\text{moun lepton number 1 -1 0 -1}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

Decay does not occur.

## Step 4: (c) solve μ+→π++νμ+

$\text{}{\mu }^{+}\to {\pi }^{+}+{\nu }_{{\mu }^{+}}\phantom{\rule{0ex}{0ex}}\mathrm{moun}\text{lepton number -1 0 +1}\phantom{\rule{0ex}{0ex}}$

Mass of poin energy can not be conserved.