Question
You are given four different radioactive samples. Rank the samples in order of what fraction of...
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 × 106 s
(ii) A sample of fluorine-18 (18F), with a half-life of 6.586 × 103 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
Answers
Theory o time t, Let at a of annelei At the no. of radioactive nuclei = N time dt, the no. disintegrate is dn. Rate of disintegration dN dt o's So, dN α Ν dt IN at or AN [A is disintegration Constant - ve sign indicate the decrease of atom with increase of time. radio active = 1 FAN dt 2312 f ddt ar 0 No in N No anat 2 - DE =e For, half life N = No = No t= ty -ath e -10 : xty In 2 = 0.693 693 2 Y0 Given information. Half life ty 11235x10ls Sample of phosphorus -32 (320) Answes : From equation 2 0.683 2 ער tyr 0.693 1:2354106 0.6 x 10-6 s-l re endt N No z e fraction of sample maining [from equation 07 -0.6010- 3600 [nt=im 0.998 : fraction of sample remaining for phosphorus +32 (32p) is = 0.998 236005 11 No3 1.65 x 10-9 ii) Given information of Half life, ty = 6.586x10²5 Time Z 1 h = 3600s from equation 0.693 0.693 6.586410 Answer: ty 3 a fraction of sample remaining -at 1.05X10-9 x3600 Mo е. 0.685 Given information 8 For the sample of nobe lium-259 (259 No) which 0.490 of the nuclei original remains after 1.00h, 0.490 Noiv) X yw 63 year Given information : For titaninum, = (63x3 658 24x3600) 19.86 x 10 S 8 xy time, t = 1 h it = 3600s Answer:- 0.693 d [from equation o ty 0.693 19.868108 sz - 10 s-2 2 3.489 x 10 i fraction of sample remaining -at zl e 3.489 x10-10 3600 e (1 o.ggg No Fraction of (44€ Ti) Sample remaining =o.ggg " Rank of the sample from the sample from largest fraction Smallest fraction is 44 Ti) 32p) 18 F) 259 No
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