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 1.0-gram sample of tritium? (N_A = 6.02 x 10²³ mol^-1,1 year = 3.16 x 10⁷ s,1 MeV = 1.6 x 10^-13 J,and m_t = 3.016 05 u)

Question

Quizplus · Accepted Answer

Explanation:The rate of energy release is given by:$$Rate = \frac{Energy released per decay 	imes Number of decays per second}{Mass of sample}$$The number of decays per second is given by:$$Number of decays per second = \frac{Mass of sample 	imes N_A}{m_t 	imes t_{1/2}}$$Substituting the given values, we get:$$Number of decays per second = \frac{1.0 g 	imes 6.02 	imes 10^{23} mol^{-1}}{3.016 05 u 	imes 12.3 years 	imes 3.16 	imes 10^7 s/year}$$$$= 1.1 	imes 10^{12} s^{-1}$$The energy released per decay is given by:$$Energy released per decay = 0.018 6 MeV 	imes 1.6 	imes 10^{-13} J/MeV$$$$= 2.976 	imes 10^{-14} J$$Substituting the values of the number of decays per second and the energy released per decay, we get:$$Rate = \frac{2.976 	imes 10^{-14} J 	imes 1.1 	imes 10^{12} s^{-1}}{1.0 g}$$$$= 1.1 W$$Therefore, the rate at which energy is released for a 1.0-gram sample of tritium is 1.1 W.

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

Tritium (³H)has a Half-Life of 12