Calculate the lifetimes of U²³⁸ and Po²¹², using Equations 9.26 and 9.29.

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

where m_p is the mass of the parent nucleus, m_d is the mass of the daughter nucleus, and m_∝ 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) m_∝v²; 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 6x10⁹ yrs and 0.5 μs, respectively.

Transcribed Image Text:

r(1.07 fm) A¹/3 (9.30)