Question

7. Phosphorus 32 ( 32), a radioactive isotope of phosphorus, has a half-life of 14.2 days. a. If the amount of radioactivity of phosphorus 32 decays continuously at a constant rate, what is the decay constant? Round your answer to 4 decimal places. (10 marks) If 100 grams of this substance are present initially, determine the exponential decay function by using the decay constant found in part (a). (4 marks) c. What amount of radioactivity will be left after 6 days? Round your answer to 2 decimal places. (4 marks)

Answer 1

Explanation:

(a) Given that:

Half life = 14.2 days

$t_{1/2}=\frac {ln\ 2}{k}$

Where, k is rate constant

So,  

$k=\frac {ln\ 2}{t_{1/2}}$

$k=\frac {ln\ 2}{14.2}\ days^{-1}$

The rate constant, k = 0.0488 days⁻¹

(b)Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

$[A_0]$ is the initial concentration  = 100 g

So,  

$[A_t]=100\times e^{-0.0488\times t}\ g$

(c) Given t = 6 days

So,

$[A_t]=100\times e^{-0.0488\times 6}\ g$

Amount left = 74.6171 g