^7Be is a radioactive element with a half-life of 53.37 days. When isotope 7 of beryllium is heated to a few thousand degrees, its half-life changes. What is the explanation for this?

Question

[latex] ^7 [/latex]Be is a radioactive element with a half-life of [latex] 53.37 [/latex] days. When isotope [latex] 7 [/latex] of beryllium is heated to a few thousand degrees, its half-life changes. What is the explanation for this?

Accepted Answer

Even if atoms are heated to a few thousand degrees, their thermal energy is still much smaller than their binding energy per nucleon. For this reason the rate of nuclear reactions is usually independent of temperature.

However, the isotope [latex] ^7 [/latex]Be transforms into [latex] ^7[/latex]Li via K-capture (the capture of an electron from the innermost K shell). At a temperature of a few thousand degrees the quantum of thermal energy [latex] kT[/latex] is comparable with the ionisation energy of the two innermost electrons of the Be atom (consider the tail of the Maxwell velocity distribution). If some fraction of the beryllium atoms becomes ionised, the probability of nuclear electron capture occurring decreases by approximately the same percentage. Thus, at such temperatures, the radioactivity, and hence the half-life, of beryllium can be affected.

Question P.189: ^7Be is a radioactive element with a half-life of 53.37 days...

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