A nucleus at rest undergoes a decay emitting an α−particle of de-Broglie wavelength λ=5.76×10−15m. If the mass of the daughter nucleus is 223.610 amu and that of the α−particle is 4.002amu, determine the mass of the parent nucleus inamu. (1amu=931.470MeV/c2].

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Filo · Accepted Answer

[a] By conservation of momentum, we have 0=P⃗ α+P⃗ d⇒P⃗ α=−P⃗ d  or  Pα=Pd=P The kinetic energy released in the process K=Kα+Kp=P22mα+P22md =P22mα(1+mαmd)=(h/λ)22mα(1+mαmd) After substituting the given values, we get K=6.25MeV If mP is the mass of the parent nucleus, then                         K+(mα+md)c2=mpc2 or  6.25+(223.61+4.002)c2=mpc2 After simplifying, we get   mp=227.62 amu.

Question Text	A nucleus at rest undergoes a decay emitting an α−particle of de-Broglie wavelength λ=5.76×10−15m. If the mass of the daughter nucleus is 223.610 amu and that of the α−particle is 4.002amu, determine the mass of the parent nucleus inamu. (1amu=931.470MeV/c2].
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A nucleus at rest undergoes a decay emitting an α−particle of de-Broglie wavelength λ=5.76×10−15m. If the mass of the daughter nucleus is 223.610 amu and that of the α−particle is 4.002amu, determine the mass of the parent nucleus inamu. (1amu=931.470MeV/c2].

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