Page 103 - Radiochemistry and nuclear chemistry

92 Radiochemistry and Nuclear Chemistry

4.4. 16N decays through B- decay to 260 with a half-life of 7.1 s. A number of very energetic 3~'s follow after
the B-emission, the dominating one with an energy of 6.14 MeV. What is the ITS:) recoil energy?
4.5. The binding energy of a K-electron in barium is 37 441 eV. Calculate from Figure 4.1 the internal
conversion energy for 137tuBa (Fig. 4.5).
4.6. From the specific activity of potassium (1850 dpm/g K) and the fact that it all originates in the rare isotope
4~ (0.0117%), calculate the half-life of 4~
4.7. One may assume that when 23SU was formed at the genesis an equal amount of 235U was formed. Today
the amount of 238U is 138 times the amount of 23SU. How long a time ago did the genesis occur according to this
assumption?
4.8. The interior of the earth is assumed to be built up of a solid core (radius 1371 km) followed by a molten
core (radius 3471 km) and a molten mantle (radius 6354 km) covered by a 17 km thick crust. One assumes that
2 % by weight of the molten mantle and crust is potassium; the average mantle density is assumed to be 6000 kg
m -3 and that of the crust 3300 kg m -3. What energy outflow will the radioactive decay of this element cause at
the earth's surface? The decay scheme of 4~ is given in eqn. (5.5). For the EC branch Q = 1.505 MeV, for the
B- branch 1.312 MeV. Each decay by the EC branch leads to emission of a 1.46 MeV % Compare this energy
output to the solar energy influx to the earth of 3.2 x 1024 J y-l.
4.9. A hospital has a 1.5 Ci source of Z2~a in the form of a RaBr~ solution. If the ~2Rn is pumped out each
48 h, what is (a) the radon activity (in Bq) at that moment, (b) the radon gas volume at STP?
4.10. (a) Prove the correctness of eqn. (4.20) by using Newton's laws of motion. (b) Prove the correctness of
eqn. (4.34).
4.11. A recently prepared 2t2pb sample has the activity of 106 dpm. (a) What is the activity 2 h later? (b) How
many lead atoms are left in the sample at this moment? t, h 10.64 h.
4.12. A radioactive sample was measured at different time intervals:

Time (h) Activity (dpm) Time (h) Activity (dpm)
0.3 11100 30 1015
5 5870 40 888
10 3240 50 826
15 2005 100 625
20 1440

Determine the half-lives of the two nuclides (not genetically related) in the sample and their activities (in Bq) at
time t = 0. The background of the detection device was 100 376 counts per I 000 min; its counting efficiency was
17%.
4.13. The c~-activity of a mixture of astatine isotopes was measured at different times aRer their separation,
giving the following results:

t(min) A(dpm) t(min) A(dpm)
12 756 121 256
17.2 725 140 215.5
23.1 638 161 178.5
30.0 600 184 150.7
37.7 545 211 127.3
47.5 494 243 101.9
59.5 435 276 84.9
73 380 308 68.2
87 341 340 55.0
102 288

Calculate the half-lives of the isotopes and their activities at t - O.