224
Problem
Given:
52 Mn 25 = 51.96202 a.m.u.
239 Pu 94 = 239.1265 a.m.u.
240 Pu 94 = 240.1296 a.m.u.
Proton = 1.00814 a.m.u.
Neutron = 1.00898 a.m.u.
8. Explain the term “half-life” and “average life” of a radioactive isotope. How
are they related to each other? Given that 1 g of
226 Ra 88 emits 3.66 × 10
10
αparticles per second and the half-life of radium is 1620y, calculate the Avogadro
number.
9. Discuss a suitable method for the determination of half-life of a radioactive
isotope. Calculate the weight “w” in g needed to get 1.00 mCi of activity of
14 C.
The half-life of the isotope is 5720y.
10. Given that each atom of
238 U that decays gives ultimately one atom of
206 Pb,
find the age of the mineral in which 1.33 × 10
−2 g of
206 Pb is associated with
each gram of
238 U. The half-life period of
238 U is 4.5 × 10
9 .
11. Discuss the law of radioactive decay. Explain the relationship among the decay
constant, the half-life, and the mean life of a radioactive isotope. Calculate the
activity of 1.0 × 10
−6 g of
24 Na in curies, given that T 0.5 is 14.9 h, atomic weight
of
24 Na is 24.00, 1 Ci is 3.7 × 10
10 dps, and Avogadro number is 6.023 × 10
23 .
12. Calculate the amount of
210 Po (in g) that can be obtained from 1 g of
226 Ra,
assuming the sample of radium is more than 100y old. The half-life of
226 Ra is
1620y and half-life of
210 Po is 138d.
13. A radioactive element X decays to another radioactive element Y . If λx and λy are
their decay constants, write the expression for the activity of Y at time t. Deduce
the conditions for secular and transient equilibria. Explain their significance in
measuring activities of radioactive isotopes undergoing such type of equilibrium.
14. Given that the
14 C content in the plant normally gives a specific activity of 15.3
cpm per gram, find the age of the wood of the plant which gives the specific
activity of 5.3 cpm per gram. T 0.5 of
14 C is 5720y.
15. The half-life of
221 Fr is 4.8 min. Starting with one mg of isotope, how much
would remain after 30 min?
16. Explain the following:
(a) The average life is greater than half-life by a factor.
(b) The nuclei A ≥ 140 decays by α-emission rather than proton emission.
Problem
Given:
52 Mn 25 = 51.96202 a.m.u.
239 Pu 94 = 239.1265 a.m.u.
240 Pu 94 = 240.1296 a.m.u.
Proton = 1.00814 a.m.u.
Neutron = 1.00898 a.m.u.
8. Explain the term “half-life” and “average life” of a radioactive isotope. How
are they related to each other? Given that 1 g of
226 Ra 88 emits 3.66 × 10
10
αparticles per second and the half-life of radium is 1620y, calculate the Avogadro
number.
9. Discuss a suitable method for the determination of half-life of a radioactive
isotope. Calculate the weight “w” in g needed to get 1.00 mCi of activity of
14 C.
The half-life of the isotope is 5720y.
10. Given that each atom of
238 U that decays gives ultimately one atom of
206 Pb,
find the age of the mineral in which 1.33 × 10
−2 g of
206 Pb is associated with
each gram of
238 U. The half-life period of
238 U is 4.5 × 10
9 .
11. Discuss the law of radioactive decay. Explain the relationship among the decay
constant, the half-life, and the mean life of a radioactive isotope. Calculate the
activity of 1.0 × 10
−6 g of
24 Na in curies, given that T 0.5 is 14.9 h, atomic weight
of
24 Na is 24.00, 1 Ci is 3.7 × 10
10 dps, and Avogadro number is 6.023 × 10
23 .
12. Calculate the amount of
210 Po (in g) that can be obtained from 1 g of
226 Ra,
assuming the sample of radium is more than 100y old. The half-life of
226 Ra is
1620y and half-life of
210 Po is 138d.
13. A radioactive element X decays to another radioactive element Y . If λx and λy are
their decay constants, write the expression for the activity of Y at time t. Deduce
the conditions for secular and transient equilibria. Explain their significance in
measuring activities of radioactive isotopes undergoing such type of equilibrium.
14. Given that the
14 C content in the plant normally gives a specific activity of 15.3
cpm per gram, find the age of the wood of the plant which gives the specific
activity of 5.3 cpm per gram. T 0.5 of
14 C is 5720y.
15. The half-life of
221 Fr is 4.8 min. Starting with one mg of isotope, how much
would remain after 30 min?
16. Explain the following:
(a) The average life is greater than half-life by a factor.
(b) The nuclei A ≥ 140 decays by α-emission rather than proton emission.