Radioactive decay is characterized by the equation ln (N_t/N_0) = -kt where N_0

Question

Radioactive decay is characterized by the equation ln (N_t/N_0) = -kt where N_0 is the initial amount, N_t is the amount remaining at time t, and k is the rate constant. The half-life (t_1/2) is the time required for the number of radioactive nuclei in a sample to drop to half of its initial value. It is defined as Phosphorus-32 () decays by beta emission to form sulfur-32 (). How many half-lives have passed in the reaction shown here? (Figure 1) Express your answer as an integer. The half-life of phosphorus-32 is 14.26 days. Calculate its decay constant. Express the decay constant numerically in inverse days. k = days^-1

Explanation / Answer

part A

initial atoms of P = 24

final atoms of P = 3

we know after half life period , half of reactants are used up.

there fore After FIRST HALF LIFE PERIOD 24 P ATOPM WILL BE REDUCED TO 12.

After SECOND HALF LIFE PERIOD 12 P ATOMS WILL BE REDUCED TO 6.

After THIRD HALF LIFE PERIOD 6 P ATOMS WILL BE REDUCED TO 3.

ANSWER 3 HALF LIFE PERIODS.

PART B

we know t1/2 = .693/k

here so k = .693 /  t1/2 = .693 / 14.26 = . 0485 days -1.

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