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Fundamentals Of Physics
Found in: Page 1306

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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


(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?

  1. The uncertainty in the energy for an intermediate nucleus is 6.6 MeV .
  2. The nucleus is not a compound nucleus.
See the step by step solution

Step by Step Solution

Step 1: Given data

Mean lifetime of the nucleus, tavg=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.


The energy-time uncertainty relation, E·t=h or E·t=h/2π........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:

Eh/2πtavg =6.626×10-34 J.s/2π1.6×10-19 J.eV1.0×10-22 s 6.6×106 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 10-22s does not qualify as a compound nucleus.


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