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.
ScanSolve AI Answer
To find the number of disintegrations in the first second, we need to calculate the initial activity of the radioactive material. The activity is given by A = N, where is the decay constant and N is the number of radioactive atoms. The number of disintegrations in a short time interval t is approximately A t. Step 1: Determine the initial number of atoms (N_0). The question states "1020 atoms". However, given the options are in powers of 10^18 and 10^20, it is highly probable that "1020" is a typo and should be 10^20 atoms. We will proceed with this assumption. So, N_0 = 10^20 atoms. Step 2: Calculate the decay constant (). The half-life (T_1/2) is given as 20 seconds. The relationship between half-life and decay constant is: = ((2))/(T_1/2) = (0.693)/(20 s) = 0.03465 s^-1 Step 3: Calculate the initial activity (A_0). The initial activity is the rate of disintegration at t=0. A_0 = N_0 A_0 = (0.03465 s^-1) × (10^20 atoms) A_0 = 3.465 × 10^18 disintegrations/s Step 4: Calculate the number of disintegrations in the first second. Since the time interval is very short ( t = 1 s), we can approximate the number of disintegrations as A_0 t. Number of disintegrations = A_0 × t Number of disintegrations = (3.465 × 10^18 disintegrations/s) × (1 s) Number of disintegrations = 3.465 × 10^18 Comparing this result with the given options: A. 3.47 × 10^20 B. 3.47 × 10^18 C. 6.93 × 10^20 D. 6.93 × 10^18 Our calculated value 3.465 × 10^18 is approximately 3.47 × 10^18, which matches option B. The final answer is B. What's next?