Calculate the lifetimes of U238 and Po212, using Equations 1 and 8.25. Hint: The density o...

Calculate the lifetimes of U238 and Po212, using Equations 1 and 8.25. Hint: The density of nuclear matter is relatively constant (i.e., the same for all nuclei), so (r1)3 is proportional to A (the number of neutrons plus protons). Empirically,

[8.29]

FIGURE 8.6: Graph of the logarithm of the lifetime versus 1/√E (where E is the energy of the emitted alpha particle), for uranium and thorium.

The energy of the emitted alpha particle can be deduced by using Einstein's formula (E = mc2):

 [8.30]

where mp is the mass of the parent nucleus, md is the mass of the daughter nucleus, and mα is the mass of the alpha particle (which is to say, the He4 nucleus). To figure out what the daughter nucleus is, note that the alpha particle carries off two protons and two neutrons, so Z decreases by 2 and A by 4. Look up the relevant nuclear masses. To estimate v, use E = (1/2)mav2; this ignores the (negative) potential energy inside the nucleus, and surely underestimates v, but it's about the best we can do at this stage. Incidentally, the experimental lifetimes are 6 x 109 yrs and 0.5 μs, respectively.

Equations 1