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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4. (a) The nuclear reaction shown is: ^235_92U + ^1_0n ^139_56Ba + ^94_36Kr + 3^1_0n This reaction represents a heavy nucleus (^235U) splitting into lighter nuclei (^139Ba and ^94Kr) after absorbing a neutron, releasing energy and more neutrons. This type of nuclear reaction is nuclear fission. 4. (b) (i) Based on the provided table: Isotope | Abundance ---|--- ^238U | 0.01% ^235U | 0.72% ^234U | 99.27% The isotope with the longest half-life is ^234U. Reason: It has the highest abundance (99.27%) in the given sample, which suggests it has decayed less over geological time compared to the other isotopes listed with lower abundances. 4. (b) (ii) Step 1: Use the given abundances and mass numbers to calculate the relative atomic mass. Relative atomic mass = (isotope mass × abundance) = (238 × 0.0001) + (235 × 0.0072) + (234 × 0.9927) = 0.0238 + 1.692 + 232.3998 = 234.1156 The relative atomic mass of uranium is 234.1156. 4. (b) (iii) Step 1: Write the incomplete nuclear equation for alpha decay of ^232_92U to Thorium (Th). ^232_92U ^A_ZTh + ^4_2 Step 2: Balance the mass numbers (superscripts). 232 = A + 4 A = 232 - 4 = 228 Step 3: Balance the atomic numbers (subscripts). 92 = Z + 2 Z = 92 - 2 = 90 Step 4: Write the complete nuclear equation. ^232_92U ^228_90Th + ^4_2 4. (b) (iv) One use of radioactive isotopes in the paper industry is to measure and control the thickness of paper. 5. (a) Step 1: Write the incomplete nuclear equation for the decay of carbon-14 (^14_6C) to nitrogen (^14_7N). ^14_6C ^14_7N + ^x_yP Step 2: Balance the mass numbers (superscripts). 14 = 14 + x x = 0 Step 3: Balance the atomic numbers (subscripts). 6 = 7 + y y = -1 Step 4: Identify the emitted particle. A particle with mass number 0 and atomic number -1 is a beta particle (^0_-1e). Step 5: Write the complete nuclear equation. ^14_6C ^14_7N + ^0_-1e 5. (b) (i) Step 1: Locate 50% on the y-axis (percentage of carbon-14 left). Step 2: Draw a horizontal line from 50% to intersect the decay curve. Step 3: From the intersection point on the curve, draw a vertical line down to the x-axis (age of sample in years). Step 4: Read the value on the x-axis. The value is approximately 5.7 × 10^3 years. The half-life of carbon-14 from the graph is 5.7 × 10^3 years. That's 2 down. 3 left today — send the next one.