Question

Activity 27-6. Nuclear decays I [Accompanies Section 27-6] You are given four different radioactive samples. Rank the samples in order of what fraction of the original nuclei remains after 1 hour (1 h = 3600 s), from largest fraction to smallest fraction. If any two samples have the same fraction remaining, state this. Explain how you made your ranking (i) A sample of phosphorus-32 (32P), with a half-life of 1.235 100s (ii) A sample of fluorine-18 (18F), with a half-life of 6.586 x 10's (iii) A sample of nobelium-259 (259No), for which 0.490 of the original nuclei remains after 1.00 h (iv) A sample of titanium-44 (44Ti), with a half-life of 63 years

Answer 1

N=ne-dt No anos e Су half life tya 0.693 for phosphory & tia = 1.235xloo SEL to Decay constant 1,700693 Xya da 0.693 = 0.561t10 sect 1.23 sx 106 No. of atoms at time t -dt Nano e N=e-ht No se U ett 0.561 4 106 x 3600 e - 1.002 2 (i) tya ? 1 6.586X100 sec tq=0.693 = 0 lost lor sect 6.586x106 0.10 Sx 10+ 3600 = 1.0003 . 1.000327 etat ران е N=0.49 No at t= 1 hour a 3600 sec No = ett take en both side ² en no att to Jen No = t I en to 3600 0.49 0.000198 0.000198+3600 ران) ng= 2.040 to 0.693 1.98+109 0.643 tva [ tyg263 year = 1:48+169 sec ta 0.35+ loa hu= No = 0.35+10-9x3600 N n₂>n, ang=na