A nucleus with mass number 220 initially at rest emits an α-particle. lf the Q value of the reaction is 5.5MeV, calculate the kinetic energy of the α-particle.
4.4MeV
5.4MeV
5.6MeV
6.5MeV
A
4.4MeV
B
5.4MeV
C
6.5MeV
D
5.6MeV
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Solution
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Let the velocity of alpha particle be v.
Mass of the alpha nucleus is 4amu.
From conservation of momentum,
216(vatom)=4v
⟹vatom=v54
Total energy =Q=5.5MeV=12(4)v2+12(216)(v54)2 Solving gives KE of alpha particle =12(4)v2=5.4MeV
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