Soal IChO Ke-26

THEORETICAL PROBLEM No 8

(9 blue points, 7 red points)

Avogadro’s Number: 6.022E23

a) An atom of ²³⁸U disintegrates by a series of [[alpha]]-decays and ß^--decays until it becomes ²⁰⁶Pb, which is stable.

i) How many a-decays and how many ß^--decays does an atom starting as

²³⁸U undergo before it becomes stable ?

ii) One of the following ten nuclides is formed from a series of

disintegrations starting at ²³⁸U. Which one ?

²³⁵U, ²³⁴U, ²²⁸Ac, ²²⁴Ra, ²²⁴Rn, ²²⁰Rn, ²¹⁵Po, ²¹²Po, ²¹²Pb, ²¹¹Pb.

b) In a thermal neutron-induced fission process, ²³⁵U reacts with a neutron and breaks up into energetic fragments and (normally) 2-3 new neutrons.

We consider one single fission event:

²³⁵U + n -> ¹³⁷Te + X + 2n

Identify the fragment X.

c) The half-life of ²³⁸U is 4.5 .E09 years, the half-life of ²³⁵U is 7.0 .E08 years

Natural uranium consists of 99.28 % ²³⁸U and 0.72 % ²³⁵U

i) Calculate the ratio in natural U betweeen the disintegration rates of these

two uranium isotopes.

ii) A mineral contains 50 weight percent uranium. Calculate the disintegration rate of ²³⁸U in 1.0 kg of this mineral.

d) We have the following radioactive sequence:

⁹⁷Ru -> ⁹⁷Tc -> ⁹⁷Mo (stable)

Halflives: ⁹⁷Ru: 2.7 days ; ⁹⁷Tc: 2.6^.10⁶ years

At t= 0, a radioactive source containing only ⁹⁷ Ru has a disintegration rate of 1.0^.10⁹ Bq.

i) What is the total disintegration rate of the source at t = 6.0 days ?

ii) What is the total disintegration rate of the source at t = 6000 years

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