Tritium (³H)has a half-life of 12.3 years and releases 0.0186 MeV energy per decay.What is the rate at which energy is released for a 3.0-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 = 3.01605 u) A) 3.2 W B) 1.1 W C) 9.6 W D) 0.33 W

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Quizplus · Accepted Answer

The rate of energy release is given by:$$Rate = \frac{Energy \ released \ per \ decay 	imes Number \ of \ decays \ per \ second}{Number \ of \ atoms \ in \ the \ sample}$$The number of decays per second is given by:$$Number \ of \ decays \ per \ second = \frac{ln2}{Half-life} 	imes Number \ of \ atoms \ in \ the \ sample$$The number of atoms in the sample is given by:$$Number \ of \ atoms \ in \ the \ sample = \frac{Mass \ of \ the \ sample}{Atomic \ mass \ of \ tritium}$$Substituting these expressions into the equation for the rate of energy release, we get:$$Rate = \frac{Energy \ released \ per \ decay 	imes ln2}{Half-life} 	imes \frac{Mass \ of \ the \ sample}{Atomic \ mass \ of \ tritium}$$Plugging in the given values, we get:$$Rate = \frac{0.0186 \ MeV 	imes ln2}{12.3 \ years} 	imes \frac{3.0 \ g}{3.01605 \ u} 	imes \frac{1 \ year}{3.16 	imes 10^7 \ s} 	imes \frac{1 \ MeV}{1.6 	imes 10^{-13} \ J}$$$$Rate = 3.2 \ W$$Therefore, the correct answer is A.

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

Tritium (³H)has a Half-Life of 12