bei48482_FM

Here is the alpha-particle velocity in m/s and Eits energy in MeV, R 0 is the nuclear

radius in fermis, and Zis the atomic number of the daughter nucleus. Figure 12.9 is a

plot of log 10 versus ZE^1 ^2 for a number of alpha-radioactive nuclides. The straight

line fitted to the experimental data has the1.72 slope predicted throughout the entire

range of decay constants. We can use the position of the line to determine R 0 , the nuclear

radius. The result is just about what is obtained from nuclear scattering experiments.

This approach thus constitutes an independent means of determining nuclear sizes.

Equation (12.14) predicts that the decay constant , and hence the half-life, should

vary strongly with the alpha-particle energy E. This is indeed the case. The slowest

decay is that of^23290 Th, whose half-life is 1.3  1010 y, and the fastest decay is that of

212

84 Po, whose half-life is 3.0 ^10

 (^7) s. Whereas its half-life is 10 (^24) greater, the alpha-
particle energy of^23290 Th (4.05 MeV) is only about half that of^21284 Po (8.95 MeV).
12.5 BETA DECAY
Why the neutrino should exist and how it was discovered
Like alpha decay, beta decay is a means whereby a nucleus can alter its composition
to become more stable. Also like alpha decay, beta decay has its puzzling aspects: the
436 Chapter Twelve
25
Berkeley :
for serif labels
30 35 40 45

• 20


• 10

0

10

ZE–1/2

log

10

λ

Figure 12.9Experimental verification of the theory of alpha decay.

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