Question

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

Answer 1

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 Y

0 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 No

3 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 No

iv) 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