Inside a vessel, there are 4 10²³ tritium atoms. The half-life for the decay of tritium nuclei is 12.3 y . Evaluate the number of decays that will occur over the next 6.15 y .

Step-by-step solution

The number of remaining atoms after time t is given by the radioactive decay law: N = N₀ ( 1 2 )^ t T_ 1/2 Given N₀ = 4 10²³ , T_ 1/2 = 12.3 y , and t = 6.15 y . The number of half-lives elapsed is n = 6.15 12.3 = 1 2 . Substituting the values: N = 4 10²³ ( 1 2 )^ 1 2 = 4 10²³ 2 The number of decays that occur is the difference between the initial number of atoms and the remaining atoms: N = N₀ - N = 4 10²³ - 4 10²³ 2 N = 4 10²³ (1 - 1 2 ) Using 2 1.414 : N = 4 10²³ (1 - 1 1.414 ) 4 10²³ (1 - 0.707) N = 4 10²³ 0.29