A radioisotope with a half-life of 5.0 days is used as a medical tracer. How man

Question

A radioisotope with a half-life of 5.0 days is used as a medical tracer. How many atoms of the radioisotope must be in the patient's body to give a total activity 4.0 times 10^5 Bq? A G-M tube placed close to a radium source gives an initial average corrected count rate of 334 s^-1. a) The tube detects 10% of the radiation. What is the initial activity of the source? b) Initially there were 1.5 times 10^9 radium nuclei in the sample. What is the decay constant for radium? c) What is the half-life of the radium in days? The initial activity of a sample of a radio nuclide is 800 Bq. The half-life of the nuclide is 5.0 min. Draw a sketch graph to show how the activity of the sample changes over a time interval of 20 min.

Explanation / Answer

(a) Since, the tube detects 10% or (0.1) of the radiation, thus, the activity is dN/dt = 334 x 0.1 = 3340 s-1  

(b) The rate of disintegration of any nuclide at any time is directly proportional to the number of atoms,

dN/dt - N, here the minus sign indicates that N decreases as time increases.

   dN/dt = - N,

here is constant of proportionality called the radioactive decay constant has the units s-1

here, N = 1.5 x 109 (given)

from (a)

dN/dt = 3340 s-1  

-3340 = - x 1.5 x 109

radioactive decay constant = 2.23 x 10-6 s-1  

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