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# The radionuclide $$^{56}Mn$$ has a half-life of 2.58 h and is produced in a cyclotron by bombarding a manganese target with deuterons. The target contains only the stable manganese isotope $$^{55}Mn$$, and the manganesedeuteron reaction that produces $$^{56}Mn$$ is $$^{55}Mn + d \rightarrow ^{56}Mn +p$$ If the bombardment lasts much longer than the half-life of $$^{56}Mn$$, the activity of the $$^{56}Mn$$ produced in the target reaches a final value of $$8.88 \times 10^10 Bq$$. (a) At what rate is $$^{56}Mn$$ being produced? (b) How many $$^{56}$$Mn nuclei are then in the target? (c) What is their total mass?

Solution
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#### If $$M_He$$ is the mass of an atom of helium and $$M_C$$ is the mass of an atom of carbon, then the energy released in a single fusion event is $$Q= (3M_He - Mc)c^2 = 3 [3(4.0026 u) (12.0000 u)](931.5 MeV/u)= 7.27 MeV$$. Note that $$3M_He$$ contains the mass of six electrons and so does $$M_C$$. The electron masses cancel and the mass difference calculated is the same as the mass difference of the nuclei.

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Q1
The radionuclide $$^{56}Mn$$ has a half-life of 2.58 h and is produced in a cyclotron by bombarding a manganese target with deuterons. The target contains only the stable manganese isotope $$^{55}Mn$$, and the manganesedeuteron reaction that produces $$^{56}Mn$$ is
$$^{55}Mn + d \rightarrow ^{56}Mn +p$$
If the bombardment lasts much longer than the half-life of $$^{56}Mn$$, the activity of the $$^{56}Mn$$ produced in the target reaches a final value of $$8.88 \times 10^10 Bq$$. (a) At what rate is $$^{56}Mn$$ being produced? (b) How many $$^{56}$$Mn nuclei are then in the target? (c) What is their total mass?
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Q2
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ii. half-life of the 56Mn
iii. the constant rate of production P
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At what constant rate P, 56Mn nuclei are being produced in the cyclotron during the bombardment?
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After the activity of 56Mn becomes constant, number of 56Mn nuclei present in the target is equal to
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After the activity of 56Mn becomes constant, number of 56Mn nuclei present in the target, is equal to
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