Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A measurement of the energy E of an intermediate nucleus must be made within the mean lifetime $∆ t$ of the nucleus and necessarily carries an uncertainty $∆ E$ according to the uncertainty principle
$∆ E \cdot ∆ t = h$ .
(a) What is the uncertainty $∆ E$ in the energy for an intermediate nucleus if the nucleus has a mean lifetime of $10^{- 22} s$ ? (b) Is the nucleus a compound nucleus?

The uncertainty in the energy for an intermediate nucleus is 6.6 MeV .
The nucleus is not a compound nucleus.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

Mean lifetime of the nucleus, $t_{a v g} = 10^{- 22} s$

Step 2: Understanding the concept of uncertainty principle

The uncertainty principle given by Heinsberg states that an electron's position and velocity can be measured. At the same time, not even in theory.

A compound nucleus is an unstable nucleus formed by the coalescence of an atomic nucleus with a captured particle.

Formula:

The energy-time uncertainty relation, $∆ E \cdot ∆ t = h o r ∆ E \cdot ∆ t = h / 2 π . . . . . . . . (1)$

where, h is the Planck’s constant.

Step 3: a) Calculation of the uncertainty in energy

Using the given data in equation (1), we can get the uncertainty in energy for an intermediate nucleus as follows:

$∆ E \approx \frac{h / 2 π}{t_{a v g}} = \frac{(6.626 \times 10^{- 34} J . s) / 2 π}{(1.6 \times 10^{- 19} J . eV) (1.0 \times 10^{- 22} s)} \approx 6.6 \times 10^{6} eV = 6.6 MeV$

Hence, the uncertainty in energy is $6.6 MeV$ .

Step 4: b) Calculation for checking if the nucleus is a compound nucleus or not

In order to fully distribute the energy in a fairly large nucleus, and create a compound nucleus” equilibrium configuration, about $10^{- 15}$ s is typically required. A reaction state that exists no more than about $10^{- 22}$ s does not qualify as a compound nucleus.

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Understanding the concept of uncertainty principle

Step 3: a) Calculation of the uncertainty in energy

Step 4: b) Calculation for checking if the nucleus is a compound nucleus or not

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