This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Here is the solution to question 4: a) The possible radiations that could be emitted by radioactive nuclei are: • Alpha () radiation • Beta () radiation (which can be ^- or ^+) • Gamma () radiation b) Step 1: Determine the number of half-lives (n) that have passed. Given: Half-life (T_1/2) = 24 days Total time (t) = 96 days n = (t)/(T_1/2) n = 96 days24 days n = 4 Step 2: Calculate the number of nuclei remaining (N) after 96 days. Given: Initial number of atoms (N_0) = 6.4 × 10^8 Number of half-lives (n) = 4 N = N_0 ((1)/(2))^n N = (6.4 × 10^8) ((1)/(2))^4 N = (6.4 × 10^8) ((1)/(16)) N = 6.4 × 10^816 N = 0.4 × 10^8 N = 4.0 × 10^7 nuclei Step 3: Determine the number of nuclei that would have decayed. Number of decayed nuclei = Initial number of nuclei - Number of remaining nuclei N_decayed = N_0 - N N_decayed = (6.4 × 10^8) - (4.0 × 10^7) N_decayed = (64 × 10^7) - (4.0 × 10^7) N_decayed = (64 - 4) × 10^7 N_decayed = 60 × 10^7 N_decayed = 6.0 × 10^8 nuclei The number of nuclei that would have decayed after 96 days is 6.0 × 10^8 nuclei.