Suppose the daughter nucleus in a nuclear decay is itself radioactive. If λd and λm, denote the decay constants of daughter
Suppose the daughter nucleus in a nuclear decay is itself radioactive. If λd and λm, denote the decay constants of daughter and mother nuclei and Nd and Nm, the numbers of daughter and mother nuclei present at a time, then the number of daughter nuclei becomes constant when
(a) λm Nm = λd Nd
(b) λm Nd = λd Nm
(c) Nm - Nd = λm - λd
(d) Nm + Nd = λm + λd
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The correct option is (a) λm Nm = λd Nd
Explanation:
The number of mother nuclei decaying in a short time interval dt is Nm λm dt But death of a mother nucleus implies the birth of a daughter nucleus.
The number of daughter nuclei decaying in the same time interval is Nd λd dt.
The number of daughter nuclei will remain constant when
Nm λm dt = Nd λd dt
λm Nm = λd Nd
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