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### Fundamentals Of Physics

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

# A ${\mathbf{220}}{\mathbf{\text{\hspace{0.17em}MeV}}}$ ${{\sum }}^{{-}}$particle decays: ${{\mathbf{\sum }}}^{{\mathbf{-}}}{\mathbf{\to }}{{\mathbit{\pi }}}^{{\mathbf{-}}}{\mathbf{+}}{\mathbit{n}}$. Calculate the total kinetic energy of the decay products.

The total kinetic energy of the decay energy is.$338\text{\hspace{0.17em}Mev}$

See the step by step solution

## Step 1: Law of conservation of energy.

The law of conservation of energy is define as the energy can neither be created nor destroyed, only converted from one form of energy to another form.

## Step 2: Calculate the total kinetic energy of the decay energy

The given reaction is written as:

${\sum }^{-}\to {\pi }^{-}+n$

Solve the total kinetic energy of the decay energy as follows:

$\begin{array}{c}Q={\left(BE\right)}_{p}~{\left(BE\right)}_{R}\\ =-\Delta m{c}^{2}+{Q}_{initial}\\ =\left({m}_{{\Lambda }^{0}}-{m}_{p}-{m}_{{\pi }^{-}}\right){c}^{2}+{Q}_{initial}\end{array}$

Substitute the values from the standard data

$\begin{array}{c}Q=\left(1197.3-139.6-939.6+220\right)\text{Mev}\\ =338\text{\hspace{0.17em}Mev}\end{array}$

Thus, the total kinetic energy of the decay energy is.$338\text{\hspace{0.17em}Mev}$