Tritium (³H)has a half-life of 12.3 years and releases 0.018 6 MeV energy per decay.What is the rate at which energy is released for a 1.5-gram sample of tritium? (N_A = 6.02 × 10²³ mol^-1,1 year = 3.16 × 10⁷ s,1 MeV = 1.6 × 10^-13 J,and m_t = 3.016 05 u) A)1.6 W B)2.3 W C)9.9E+12 W D)5.0E+7 W E)85.4 W

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The rate of energy release for a 1.5-gram sample of tritium can be calculated by first determining the number of tritium atoms in the sample, then using the half-life to find the decay rate, and finally multiplying by the energy released per decay. 1. Calculate the number of moles of tritium in 1.5 grams:$$ \text{Moles of tritium} = \frac{\text{mass}}{\text{molar mass}} = \frac{1.5 \, \text{g}}{3.01605 \, \text{g/mol}} $$$$ \text{Moles of tritium} = 0.497 \, \text{mol} $$2. Calculate the number of tritium atoms:$$ \text{Number of atoms} = \text{moles} \times \text{Avogadro's number} = 0.497 \times 6.02 \times 10^{23} $$$$ \text{Number of atoms} = 2.99 \times 10^{23} $$3. Calculate the decay rate using the half-life formula:$$ \text{Decay rate} = \frac{\ln(2)}{\text{half-life}} \times \text{number of atoms} $$$$ \text{Decay rate} = \frac{0.693}{12.3 \times 3.16 \times 10^7 \, \text{s}} \times 2.99 \times 10^{23} $$$$ \text{Decay rate} = 5.0 \times 10^{14} \, \text{decays/s} $$4. Calculate the energy released per second:$$ \text{Energy released per second} = \text{Decay rate} \times \text{energy per decay} $$$$ \text{Energy released per second} = 5.0 \times 10^{14} \times 0.0186 \times 1.6 \times 10^{-13} \, \text{J} $$$$ \text{Energy released per second} \approx 1.6 \, \text{W} $$Therefore, the rate at which energy is released for a 1.5-gram sample of tritium is approximately 1.6 W.

Tritium (3H)has a Half-Life of 12

Tritium (³H)has a Half-Life of 12