The elecron curium (96)248 On has a mean life of 1013 second ist pirmary dacay mode with a probilly of 8% and the letter with a probillty of 92% Each fission released 200MeV of energy . The masses involved in a - dacay are as follows \displaystyle_{\left({96} ight)}^{{{248}}}{C}{m}={248.072220}{u},_{{{94}_{^}{\left({244} ight)}{P}{u}={244.064100}{u}{{\quad ext{and}\quad}_{{{2}}}^{{{4}}}}{H}{e}={4}{.002603}{u}}} calculate the power output from a sample of 1020Cma→m(1u=931MeV/e2)

Question

The elecron curium (96)248​ On has a mean life of 1013 second ist pirmary dacay mode with a probilly of 8% and the letter with a probillty of 92% Each fission released 200MeV of energy . The masses involved in a - dacay are as follows \displaystyle_{\left({96}ight)}^{{{248}}}{C}{m}={248.072220}{u},_{{{94}_{^}{\left({244}ight)}{P}{u}={244.064100}{u}{{\quad	ext{and}\quad}_{{{2}}}^{{{4}}}}{H}{e}={4}{.002603}{u}}} calculate the power output from a sample of 1020Cma→m(1u=931MeV/e2)

Filo · Accepted Answer

Answer: A::B::CSolution: The reaction involed in a - decay is  \displaystyle_{\left({96}ight)}^{{{248}}}{C}{m}{ightarrow_{{{94}}}^{{{244}}}}{P}{u}+_{{{2}_{^}{\left({4}ight)}{H}{e}}} Mass defect  \displaystyle\delta{m}={m}{a}{s}{s}{o}{{f}_{{{96}}}^{{{248}}}}{C}{m}-{m}{a}{s}{s}{o}{{f}_{{{94}}}^{{{244}}}}{P}{u}-{m}{a}{s}{s}{o}{f}_{{{2}_{^}{\left({4}ight)}{H}{e}}} =(248.072220−244.064100−4.002603)u  =0.005517u  Therefore , energy released in a - decay will be  Ea​=(0.005517×931)MeV=5.136MeV ltvbrgt similarly Efassion​=200MeV(given)  mass of is given as tmean​=1013s=λ1​  ∴ Disingration constant λ=10−13s−1  rate of decay at the moment when number of nuclei are 1020 is  dtdN​=λN=(10−13)(1020)=107dps  Therefore energy released , 8% are in fission and 92% are in a - decay  =(0.08×107×200+0.92×107×5.136)MeV = 2.074 xx 10^(8) MeV\displaystyle	herefore{p}{o}{w}{e}{r}{o}{f}{o}{u}{t}{p}{u}{t}{\left(\in{w}{a}{\mathtt}ight)}={E}
e{r}{g}{y}{r}{e}\le{a}{s}{e}{d}{p}{e}{r}{\sec{{o}}}{n}{d}{\left({J}/{s}ight)}= (2.074 xx 10^(8))(1.6 xx 10^(-13))poweroutput= 3.32 xx 10^(-5) watt\displaystyle.

Question Text	The elecron curium $_{(96)}^{248}$ On has a mean life of $10^{13}$ second ist pirmary dacay mode with a probilly of $8 %$ and the letter with a probillty of $92 %$ Each fission released $200 M e V$ of energy . The masses involved in a - dacay are as follows \displaystyle_{\left({96}\right)}^{{{248}}}{C}{m}={248.072220}{u},_{{{94}_{^}{\left({244}\right)}{P}{u}={244.064100}{u}{{\quad\text{and}\quad}_{{{2}}}^{{{4}}}}{H}{e}={4}{.002603}{u}}} calculate the power output from a sample of $10^{20} C m a \to m (1 u = 931 M e V / e^{2})$
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