bei48482_FM

To illustrate this point, we can compute, from the known masses of each particle

and the parent and daughter nuclei, the energy Qreleased when various particles are

emitted by a heavy nucleus. This is given by

Q(mimfmx)c^2 (12.10)

where mimass of initial nucleus

mfmass of final nucleus

mxparticle mass

We find that the emission of an alpha particle in some cases is energetically possible,

but other decay modes would need energy supplied from outside the nucleus. Thus

alpha decay in^23292 U is accompanied by the release of 5.4 MeV, while 6.1 MeV would

be needed for a proton to be emitted and 9.6 MeV for a^32 He nucleus to be emitted.

The observed disintegration energies in alpha decay agree with the predicted values

based upon the nuclear masses involved.

The kinetic energy KEof the emitted alpha particle is never quite equal to the

disintegration energy Qbecause, since momentum must be conserved, the nucleus

recoils with a small amount of kinetic energy when the alpha particle emerges. It is

easy to show (see Exercise 23) from momentum and energy conservation that KEis

related to Qand the mass number Aof the original nucleus by

KE Q (12.11)

The mass numbers of nearly all alpha emitters exceed 210, and so most of the disin-

tegration energy appears as the kinetic energy of the alpha particle.

Example 12.7

The polonium isotope^21084 Po is unstable and emits a 5.30-MeV alpha particle. The atomic mass

of^21084 Po is 209.9829 u and that of^42 He is 4.0026 u. Identify the daughter nuclide and find its

atomic mass.

Solution

(a) The daughter nuclide has an atomic number of Z 84  2 82 and a mass number of

A 210  4 206. Since Z82 is the atomic number of lead, the symbol of the daughter

nuclide is^20682 Pb.

(b) The disintegration energy that follows from an alpha-particle energy of 5.30 MeV is

Q KE(5.30 MeV)5.40 MeV

The mass equivalent of this Qvalue is

mQ0.0058 u

Hence

mfmimmQ209.9829 u4.0026 u0.0058 u205.9745 u

5.40 MeV



931 MeV/u

210



210  4

A



A 4

A 4



A

Alpha-particle

energy

Disintegration

energy

Nuclear Transformations 433

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