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Find the kinetic energy of a neutron emerging as a result of the decay of a stationary Sigma^(-) hyperon(Sigma^(-)rarrn+pi^(-)). |
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Answer» Solution :We have `O=vec(pn)+vec(p_(PI))`....(1) `m_(Sigma)C^(2)=E_(N)+E_(pi)` or `(m_(Sigma)c^(2)-E_(n))^(2)=E_(pi)^(2)` or `m_(Sigma)^(2)c^(4)-2m_(Sigma)c^(2)E_(n)=E_(pi)^(2)-E_(n)^(2)=c^(4)m_(pi)^(2)-c^(4)m_(n)^(2)` because (1) implies `E_(pi)^(2)-E_(n)^(2)=m_(pi)^(2)c^(4)-m_(n)^(2)-m_(n)^(2)c^(4)` Hence `E_(n)=(m_(Sigma)^(2)+m_(n)^(2)-m_(pi)^(2))/(2m_(Sigma))c^(2)` and ` T_(n)=((m_(Sigma)^(2)+m_(n)^(2)-m_(pi)^(2))/(2m_(Sigma))-m_(n))c^(2)=((M_(Sigma)-m_(n))^(2)-m_(pi)^(2))/(2m_(Sigma))c^(2)` Substitution gives `T_(n)= 19.55MeV` |
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