Question #285977

Find the minimum kinetic energy (in MeV) in the lab system needed by an alpha particle to cause


the reaction:


7𝑁


14 + 𝛼 → 8𝑂


17 + 1𝐻


1


Given that: m(


14N) = 14.00307 u; m(α) 4.003879 u; m(


1H) = 1.00783 u; m(


17O) = 17.0013 u;


1 𝑢 = 931.5 𝑀𝑒𝑉/𝑐


2

1
Expert's answer
2022-01-10T09:16:36-0500

Solution:

N14+αO17+pN^{14}+ \alpha \to O^{17}+p


Energy=E=Δmc2Energy=E= \Delta mc^2


Δm=14.00307+4.0038791.0078317.0013=0.002181\Delta m=14.00307+4.003879-1.00783-17.0013=-0.002181


E=Δmc2=0.002182×931.5𝑀𝑒𝑉=2.0316015  MeVE= \Delta mc^2=0.002182 \times931.5 𝑀𝑒𝑉=-2.0316015\;MeV


So, -2.0316015 MeV is needed by an alpha particle to cause the reaction.



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