Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Calculate the disintegration energy of the reactions
$(a) π^{+} + p \to \sum^{+} + K^{+} and (b) K^{-} + p \to Λ^{0} + π^{0}$

(a) The value $π^{+} + p \to \sum^{+} + K^{+}$ is $605.2 Mev$ .

(b)The value $K^{-} + p \to Λ^{0} + π^{0}$ is $- 181.4 Mev$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Disintegration energy

Disintegration energy is lost by the nucleus undergoing radioactive decay. During radioactive decay, an element loses mass and energy by emitting radiation and ionizing particles. During this process of radioactive decay. an atom is transformed into another element.

The chemical species undergoing radioactive decay is called the parent nuclide, and the new chemical species is called the daughter nuclide.

. $Q = - Δ m . c^{2}$

Step 2 (a) : Solve π++p→∑++ K+

(1) Explanation

$m_{π^{+}} \to 139.6 MeV m_{p} \to 938.3 MeV m_{\sum^{+}} \to 1189.4 MeV m_{K^{+}} \to 493.7 MeV$

(2) Solution

$Q = - Δ m . c^{2}$ ….. (1)

Put the value in equation (1)

$\begin{array}{rcl} Q & = & (m_{\sum^{+}} + m_{K^{+}} - m_{π^{+}} - m_{p}) c^{2} \\ = & (1189.4 + 493.7 - 139.6 - 938.3) MeV \\ = & (1683.1 - 1077.9) MeV \\ = & 605.2 Mev \end{array}$

Hence the value $π^{+} + p \to \sum^{+} + K^{+}$ is $605.2 Mev$ .

Step 3 (b): Solve K-+p→Λ0+π0

(1) Explanation

$m_{K^{-}} \to 493.7 MeV m_{p} \to 938.3 MeV m_{Λ^{0}} \to 1115.6 Mev m_{π^{0}} \to 135.0$

(2) Solution.

$\begin{array}{rcl} Q & = & - Δ m . c^{2} \\ Q & = & (m_{Λ^{0}} + m_{π^{0}} - m_{K^{-}} - m_{p}) c^{2} \\ = & (1115.6 + 135.0 - 493.7 - 938.3) MeV \\ = & (1250.6 - 1432) MeV \\ = & - 181.4 Mev \end{array}$

Hence, the value $K^{-} + p \to Λ^{0} + π^{0}$ is $- 181.4 Mev$ .

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Fundamentals Of Physics

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Short Answer

Calculate the disintegration energy of the reactions
$(a) π^{+} + p \to \sum^{+} + K^{+} and (b) K^{-} + p \to Λ^{0} + π^{0}$

Step by Step Solution

Step 1: Disintegration energy

Step 2 (a) : Solve π++p→∑++ K+

Step 3 (b): Solve K-+p→Λ0+π0

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Calculate the disintegration energy of the reactions(a)π++p→∑++ K+ and (b)K-+p→Λ0+π0

Step by Step Solution

Step 1: Disintegration energy

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Step 3 (b): Solve K-+p→Λ0+π0

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Calculate the disintegration energy of the reactions
$(a) π^{+} + p \to \sum^{+} + K^{+} and (b) K^{-} + p \to Λ^{0} + π^{0}$