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
Hey Noh, good to see you again. a) To complete the nuclear decay equation for beta-particle emission, the mass number (top number) and atomic number (bottom number) must be conserved. A beta-particle is represented as _-1^0. Step 1: Write the general decay equation. _81^208Tl → _Z^APb + _-1^0 Step 2: Conserve the mass number (A). 208 = A + 0 A = 208 Step 3: Conserve the atomic number (Z). 81 = Z + (-1) Z = 81 + 1 Z = 82 Step 4: Complete the equation. _81^208Tl → _82^208Pb + _-1^0 b) To determine the half-life from the graph, we must first account for the background count. Step 1: Determine the initial actual activity. The initial counter reading at t=0 is 80 counts per minute. The background count is 8 counts per minute. Initial actual activity = Counter reading - Background count Initial actual activity = 80 - 8 = 72 counts per minute Step 2: Calculate the actual activity after one half-life. After one half-life, the actual activity will be half of the initial actual activity. Activity after one half-life = (72)/(2) = 36 counts per minute Step 3: Determine the corresponding counter reading for this activity. This is the value we will find on the y-axis of the graph. Counter reading = Actual activity + Background count Counter reading = 36 + 8 = 44 counts per minute Step 4: Use the graph to find the half-life. Locate 44 counts per minute on the y-axis. Draw a horizontal line from 44 counts per minute to intersect the curve. From the intersection point on the curve, draw a vertical line down to the x-axis. Read the time value on the x-axis. This value is the half-life. From the graph, a counter reading of 44 counts per minute corresponds to a time of approximately 3.3 minutes. The half-life of thallium-208 is 3.3 minutes. Send me the next one 📸