The phosphorus isotope ³²P is used in biochemical studies to determine the pathways of phosphorus atoms in living organisms. Its presence is detected through its emission of β^– particles. 

(a) What is the decay constant for ³²P, expressed in the unit s^–1? 

(b) What is the activity of a 1.00 mg sample of ³²P (that is, how many atoms disintegrate per second)? 

(c) Approximately what mass of ³²P will remain in the original 1.00 mg sample after 57 days? (See Table 25.1.) 

(d) What will be the rate of radioactive decay after 57 days?

Table 25.1

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TABLE 25.1 Some Representative Nuclide Half-Life Nuclide H 12.33 a 14C 5715 a 8.7 x 10-³ s 130 19 Mg 21 h P 14.3 d 87.9 d 10K Br gSr 1331 13 Cs Half-Lives Half-Lifea 1.26 × 10⁰ a 17.6 min 29.1 a 8.021 d 30.2 a Nuclide 214 Po 222Rn 86 88 23 Th 23 U Half-Lifea 1.64 x 10-4 s 3.823 d 1.599 × 10³ a 24.10 d 4.47 × 10 a