Question

Radioactive materials are often used in biological studies. A radiation biologist studies the rate of decomposition of a certain substance and obtains the following data:

Time (days)	0	4.0	8.0	12.0	16.0
Mass (μg)	23.80	17.56	12.96	9.56	7.05

Determine the rate constant in units of days^-1.

How many micrograms will remain after 22 days?

Answer 1

Solution:- clecam All natural and artificial radioactive of unstable nuclei take place by first order kinetics. TR ] In this question, we are going to use formula, First ordf& rate equation :- ok = 2.303 dog [R] - (i) (te-fo) e Where, K= rate constant t = time [R] = initial amount of Radioactive material present. or amount of Radio active material - present at time (t.) a ti ER] = amount of Radioactive materiaal present at time (t) = tz ci rate constant : From the given data ERJo= 23.80 lg ER] = 17.56 lg (Az-t,) = time ct) ? u days Foom equation (i) - te=0 days Az = 4days sate constant (K) = 2.303 log (23.80 Mg 1 udays 17.56 Mg , frate constant (K) = 0.07603 days

llid How many micrograms will remains ofter 22 days From the given data. time [R]. = 23. 80 ug [R] = ? at t t = 0 days eat time t = 22 days. days! rate constant = 0.07603 tz-to = 22 days so, From equation in 0.07603 days' as log|23.80 MB) 0.0 7603 2.303 22 days 23.80 lug CR) 7. log (23.80 Mg [R] = 0.07603 dayst x 22 days 2.303 | 35 10g (23.60 4g) - 0.263 [R ] 0.7263 =) 23.80 Mg = [R] 10 - 5.325 [ R] = 23.80 Mg - 5.325 TER]= 4. 47 lg 1 4.47 micrograms will remain after 22 days