RADIOACTIVITY - THEORY, NUMERICALS, NOTES, VIDEOS

MAHARASHTRA BOARD SOLUTIONS - CHAPTER 15 - CLASS 12 PHYSICS - STRUCTURE OF ATOMS AND NUCLEI

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16. Sample of carbon obtained from any living organism has a decay rate of 15.3 decays per gram per minute. A sample of carbon obtained from very old charcoal shows a disintegration rate of 12.3 disintegrations per gram per minute. Determine the age of the old sample given the decay constant of carbon to be 3.839 x 10^-12 per second. [Ans: 1803 yrs]

17. The half-life of Sr is 28 years. Determine the disintegration rate of its 5 mg sample.
[Ans: 2.626 x10 '° s-9

18. What is the amount of Co necessary to provide a radioactive source of strength 10.0 mCi, its half-life being 5.3 years? [Ans: 8.88x 10-6g]

19. Disintegration rate of a sample is 10^10 per hour at 20 hrs from the start. It reduces to 6.3 x 109 per hour after 30 hours. Calculate its half life and the initial number of radioactive atoms in the sample.
[Ans: 15 hrs, 5.45x101

20. The isotope 57Co decays by electron capture to 57Fe with a half-life of 272 d. The 57Fe nucleus is produced in an excited state, and it almost instantaneously emits gamma rays.

(a) Find the mean lifetime and decay constant for "Co.

(b) If the activity of a radiation source "Co is 2.0 pCi now, how many "Co nuclei does the source contain?

21. A source contains two species of phosphorous nuclei, 32 P (T1/2 = 14.3 d) and 33 P (T 1/2= 25.3 d). At time t = 0, 90% of the decays are from 32P.

How much time has to elapse for only 15% of the decays to be from 32P ? [Ans: 186.6 d]

22. Before the year 1900 the activity per unit mass of atmospheric carbon due to the presence of "C averaged about 0.255 Bq per gram of carbon.

(a) What fraction of carbon atoms were 14C?

(b) An archaeological specimen containing 500 mg of carbon, shows 174 decays in one hour. What is the age of the specimen, assuming that its activity per unit mass of carbon when the specimen died was equal to the average value of the air?

Half-life of 14C is 5730 years?

[Ans: Four atoms in every 3x1012 carbon atoms were '4C, 8020 years]

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12. Determine the amount of 210 Po necessary to provide a source of a particles of 5 mCi strength. The halflife of polonium is 138 days.

Example 29. In an experiment, the activity of 1.2 milligrams of radioactive potassium chloride (chloride of isotope K-40) was found to be 170 s-1. Taking molar mass of to be 0.075 kg mole ', find the number of K-40 atoms in the same and hence find the half-life of K-40. Avogadros' number =6.0 1023 mole- 1.

Example 22. The half-life of radium is 1500 years. After how many years will one gram of the pure radium

(i) reduce to one centigram ?
(ii) lose one milligram ?

Example 24. The half life of 238 U against a-decay is 1.5 x 1017 s. What is the activity of a sample of 238 U having 25 x 1020 atoms ?

Example 25. The half life of 299 U against a-decay is 4.5 x 10° years. Calculate the activity of 1 g sample of 238 U. 92