Q19 of 94 Page 442

: The decay constant of (electron capture to ) is 1.8 × 10–4 s–1.

(a) What is the half-life?


(b) What is the average-life?


(c) How much time will it take to convert 25% of this isotope of mercury into gold?


a) Half-life





b) Average-life





c) We know,



where A= Activity of the substance


A0 = Initial activity


N = number of half lives


According to the problem,


Present activity = (1-0.25) A0


= 0.75A0


So,






More from this chapter

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17

228Th emits an alpha particle to reduce to 224Ra. Calculate the kinetic energy of the alpha particle emitted in the following decay:

228Th → 224Ra* + α


224Ra* → 224Ra + γ (217 keV).


Atomic mass of 228Th is 228.028726u, that of 224Ra is 224.020196 u and that of is 4.00260 u.


 18

Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:

12N → 12C* + e+ + v


12C* → 12C + γ (4.43 MeV).


The atomic mass of 12N is 12.018613 u.


 20

The half-life of 198Au is 2.7 days.

(a) Find the activity of a sample containing 1.00 μg of 198Au.


(b) What will be the activity after 7 days? Take the atomic weight of 198Au to 198 g mol-1.


 21

Radioactive 131I has a half-life of 8.0 days. A sample containing 131I has activity 20 μ Ci at t = 0.

(a) What is its activity at t = 4.0 days?


(b) What is its decay constant at t = 4.0 days?