A measurement of the energy E of an intermediate nucleus must be made within the mean lifetime of the nucleus and necessarily carries an uncertainty according to the uncertainty principle
(a) What is the uncertainty in the energy for an intermediate nucleus if the nucleus has a mean lifetime of ? (b) Is the nucleus a compound nucleus?
Mean lifetime of the nucleus,
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,
where, h is the Planck’s constant.
Using the given data in equation (1), we can get the uncertainty in energy for an intermediate nucleus as follows:
Hence, the uncertainty in energy is .
In order to fully distribute the energy in a fairly large nucleus, and create a compound nucleus” equilibrium configuration, about s is typically required. A reaction state that exists no more than about s does not qualify as a compound nucleus.
The strong neutron excess (defined as ) of high-mass nuclei is illustrated by noting that most high-mass nuclides could never fission into two stable nuclei without neutrons being left over. For example, consider the spontaneous fission of a nucleus into two stable daughter nuclei with atomic numbers and . From Appendix F, determine the name of the (a) first and (b) second daughter nucleus. From Fig. 42-5, approximately how many neutrons are in the (c) first and (d) second? (e) Approximately how many neutrons are left over?
Characteristic nuclear time is a useful but loosely defined quantity, taken to be the time required for a nucleon with a few million electron-volts of kinetic energy to travel a distance equal to the diameter of a middle-mass nuclide. What is the order of magnitude of this quantity? Consider 5 MeV neutrons traversing a nuclear diameter of ; use Eq. 42-3.
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