Questão 24

**Working on energy calculations** I need to solve some concise readings in Portuguese, focusing on certain energy values like 180, 7.95, 90, and 8.67. I'm trying to determine whether to use 8.0, 8.6, or 8.7 as my closest options, where 8.7 seems to be leading to the best approximation of 126. I also want to clarify the total energy factor to prevent confusion. I'll make sure the equations accurately reflect my calculations, particularly Q = Bfinal - Binitial.

**Calculating and estimating values** I need to calculate readings in Portuguese, focusing on specific values like 180 and their approximate differences. By assessing values around 8.0, 8.6, and 8.7, I can refine my estimates. For instance, using values like 7.95 and 8.65 helps determine the nearest significant measures. The goal is to clearly explain my graph's approximations while ensuring accurate energy readings, ultimately converging to a clear estimate around 110, emphasizing consistency in my approach.

**Solving energy calculations** I need to solve some energy aspects related to binding energy in nuclear fission. I’m inferring values from a graph with A=180 at about 7.95 MeV and A=90 at around 8.65 MeV. The energy release difference between the binding products and the parent nucleus factors into this. Specifically, a difference of 0.70 MeV multiplied by 180 gives me 126 MeV, which leads me to consider the closest option as 110. I'll ensure to articulate how mass decrease corresponds with increased binding energy.**Interpreting graph readings** I'm looking into the possibility of graph readings, specifically using 8.6 versus 8.0, which suggests a result around 108 to 110, likely what was intended. When examining the graph, A=90 reads around 8.67, and A=180 is roughly 7.95, which gives a difference of about 0.72. Multiplying that by 180 leads to 130, pointing me toward the nearest option of 110. I need to ensure I interpret this clearly and convey my final explanation accurately in Portuguese with the appropriate formula.

Splitting A=180 into two A=90 fragments, I read off B/A≈8.0 MeV at A=180 and about 8.6-8.7 MeV at A=90 from the graph. Using these values, the energy released works out to roughly 126 MeV (using 8.7) or close to 108 MeV (using 8.6), depending on the precise graph reading.

Reading the binding energy curve, B/A at A=180 is about 7.95-8.0 MeV, while at A=90 it's roughly 8.65 MeV. Multiplying that difference by the nucleon number gives somewhere around 110-126 MeV, which points to answer C, 110 MeV.

The problem concerns nuclear fission and binding energy. The 180-mass nucleus splits into two 90-mass nuclei. The released energy equals the increase in total binding energy, which corresponds to the mass defect. The binding energy per nucleon peaks near 8.7 MeV at A=60. For A=180 it is slightly below 8 MeV. The binding energy per nucleon at A=90 is roughly 8.6 MeV. For A=180 it is about 8.0 MeV. The graph shows a slow decline from the peak down to approximately 7.7 MeV near A=240. The total binding energy of the two 90-mass nuclei equals 180 times the binding energy per nucleon at A=90. The initial total binding energy is 180 times the value at A=180. The released energy Q is therefore 180 times the difference between these two binding energies per nucleon. The binding energy per nucleon at A=90 is roughly 8.6 MeV, and at A=180 it is about 8.0 MeV. The difference is approximately 0.6 MeV. Multiplying by the total mass of 180 gives a released energy of roughly 108 MeV. This value is closest to alternative C. The binding energy per nucleon at A=90 is closer to 8.7 MeV, and at A=180 it is slightly below 8 MeV. The released energy is therefore closer to 120 MeV, not 108 MeV. The dot at A=180 appears to sit exactly on the 8.0 MeV line. The closest answer is therefore alternative C, 110 MeV.

We need answer question in Portuguese, with reasoning. Need solve. Let's restate. We have text about nuclear mass defect and binding energy per nucleon graph B/A vs A. Consider fission of nucleus A0=180 into two with mass numbers A1 = A0/2 =90 and A2 = A1 =90? Wait "em dois outros, cujos números de massa são A1 = A0/2 e A2 = A1." So both fragments mass number 90. Need energy associated with decrease of mass of system during reaction, closest value among options: 2 MeV, 50 MeV, 110 MeV, 220 MeV, 1540 MeV. We need use graph to find binding energy per nucleon for parent A=180 and for fragments A=90. Energy released = final binding energy - initial binding energy? Actually mass decrease corresponds to increase in total binding energy. Energy released = B_final - B_initial = A1*(B/A at 90) + A2*(B/A at 90) - A0*(B/A at 180). Since binding energy per nucleon curve: B/A around A=90 ~? From graph, at A=90 B/A maybe ~8.7? At A=180 B/A maybe ~8.0? Let's read graph carefully. Graph: B/A (MeV) y-axis 0 to 9. Data points. At A=180, y maybe ~8.0? At A=90, y maybe ~8.7? Let's inspect. At A=60, peak near 8.8? At A=90, points around maybe 8.7? At A=120 maybe 8.6? At A=150 maybe 8.4? At A=180 maybe 8.0? At A=210 maybe 7.9? At A=240 maybe 7.7. Let's read values approximate. Given options: If initial B/A ~8.0 MeV, final B/A ~8.7 MeV, difference per nucleon ~0.7 MeV. Total nucleons 180, energy ~126 MeV. Option C 110 MeV close. If difference 0.6 -> 108 MeV. If difference 0.5 -> 90. So likely C 110 MeV. But let's verify: At A=90, graph maybe 8.7? At A=180, graph maybe 8.0? Difference 0.7*180=126. Option 110, 220 maybe? 220 would difference ~1.22 per nucleon. At A=180 B/A maybe 7.5? At A=90 8.7? Difference 1.2*180=216 -> 220. Need exact from graph? Let's read more precisely. Let's zoom into graph: Points: At A=0, B/A=0. At A=2? 1.1. At A=4? 2.8? At A=8? 5.3? At A=12? 5.6? At A=20? 7.1? At A=30? 7.7? At A=40? 8.2? At A=50? 8.6? At A=60? 8.8? At A=70? 8.8? At A=80? 8.75? At A=90? 8.7? At A=100? 8.65? At A=120? 8.6? At A=150? 8.4? At A=180? 8.0? At A=210? 7.9? At A=240? 7.7? At A=270? 7.6? Let's see. Let's approximate from image. Coordinates: x-axis marks at 0,30,60,90,120,150,180,210,240,270. y-axis marks 0 to 9. At x=180, point? There is a point at x=180 exactly? It might be at 180, y maybe ~8.0? Actually horizontal line y=8, point at x=180 maybe slightly above 8? Let's inspect: At x=180, dot maybe y=8.0? At x=150, dot maybe y=8.4? At x=120, dot maybe y=8.6? At x=90, dot maybe y=8.7? At x=60, dot maybe y=8.8? At x=30, dot maybe y=7.7? Let's count points: There are 10 intervals? The data points may be at each integer? Let's not. Question: "Considere a fissão de um núcleo, de número de massa A0 = 180, em dois outros, cujos números de massa são A1 = A0/2 e A2 = A1." So fission into two equal mass 90. Need energy associated with decrease of mass. We can calculate using binding energy per nucleon values read from graph. Since they give graph approximate, likely use visual estimate. Options far apart: 110 vs 220. Need decide. Let's calculate using actual semi-empirical mass formula maybe? But graph is from data, maybe they expect reading graph. Let's compute with typical values: B/A for A=180 ~? Actual binding energy per nucleon for stable nuclei around A=180 (e.g., W-180) is about 7.9-8.0 MeV. For A=90 (e.g., Zr-90) is about 8.7 MeV. Difference ~0.8 MeV * 180 = 144 MeV. But options 110 or 220. Hmm 144 not in options, closest 110? Actually 110 and 220. 144 closer to 110? Difference to 110=34, to 220=76. So C. But if using graph maybe difference 0.6 =>108, closer to 110. So C likely. But let's verify with graph: At A=180, B/A maybe 8.0? At A=90, maybe 8.7? Difference 0.7*180=126. Still closer to 110 (16) than 220 (94). So C. But need be careful: Energy associated with decrease of mass = Δm c^2 = B_final - B_initial. Since B_final = 90*(B/A at 90) + 90*(B/A at 90) = 180*(B/A at 90). B_initial = 180*(B/A at 180). Energy = 180[(B/A)_90 - (B/A)_180] MeV. If (B/A)_90 = 8.7, (B/A)_180 = 8.0 => 180*0.7 = 126 MeV. Closest 110. If (B/A)_90 = 8.8, (B/A)_180=7.9 =>0.9*180=162, still closer 110? 162-110=52, 220-162=58, close. Hmm. If difference 0.8 =>144, closer 110? 34 vs 76 yes. So C. But let's see if any option D 220 could arise from using total binding energy difference maybe B_final - B_initial = 2*90*8.8 - 180*8.8? No. If someone incorrectly uses B/A difference times A0? 0.7*180=126. No 220. Let's read graph more precisely: At A=180, dot maybe at y=8.0? At A=90, dot maybe at y=8.7? Let's estimate from graph with grid: The peak around A=60 is y=8.8? The point at A=90 maybe y=8.7? At A=180 maybe y=8.0? The curve after A=60 slowly decreases. Let's count points: Between A=60 and A=90, there are maybe 3 points? At A=70? 8.8? A=80? 8.75? A=90? 8.7. At A=120? 8.6. At A=150? 8.4. At A=180? 8.0? Wait there is a point at A=180 maybe y=8.0? At A=210 y=7.9? Actually from 180 to 240 slope: At A=180, y=8.0; at A=210, y=7.9; at A=240, y=7.7. That seems plausible. At A=150, y=8.4. At A=120, y=8.6. At A=90, y=8.7. At A=60, y=8.8. At A=30, y=7.7. So difference = 8.7 - 8.0 = 0.7. Energy = 180*0.7 = 126 MeV. Closest 110. Option C. But let's consider if A0=180, fission into A1=90 and A2=90. Binding energy final = B(90)+B(90)=2*90*(B/A)_90. Initial = 180*(B/A)_180. Energy = 2*90*8.7 - 180*8.0 = 1566 - 1440 = 126 MeV. Yes. Option E 1540 MeV is huge, maybe if using mass difference? No. Option D 220 MeV maybe if using B/A difference 1.22. Could someone mistakenly use atomic mass unit? No. Let's ensure no other interpretation: "energia associada à diminuição da massa do sistema durante a reação" = Q value = Δm c^2 = B_final - B_initial. Yes. Let's answer C. Need provide explanation in Portuguese. End with "Resposta: C". We need include reasoning. Let's craft final: Leitura do gráfico: para A=90, B/A ≈ 8,7 MeV; para A=180, B/A ≈ 8,0 MeV. A energia liberada é ΔE = [2*90*(B/A)_90] - [180*(B/A)_180] = 180*(8,7-8,0) ≈ 180*0,7 = 126 MeV. Valor mais próximo: 110 MeV. Alternativa C.

**Analyzing Physics Query** I am currently analyzing the user's request, which involves solving a physics problem from the ITA exam. My immediate focus is on understanding the initial portion of the provided text, which hints at a non-intuitive concept regarding nuclide mass. **Deconstructing Nuclei Concepts** I'm currently working through the initial physics problem, focusing on the fundamental concept that a nuclide's mass is less than the sum of its constituent nucleons. This mass defect, directly linked to binding energy, is the key I need to grasp before proceeding. **Interpreting Graph Data** I'm now interpreting the binding energy per nucleon graph. I'm focusing on pinpointing the precise values for nuclei around mass number 90 and the initial nucleus's mass, ensuring accuracy for the subsequent energy release calculation. **Estimating Energy Values** I'm refining my estimates for binding energy per nucleon from the graph. I'm focusing on the values around mass numbers 90 and 180, carefully observing the curve's position relative to the horizontal axis, and noticing a lack of distinct horizontal grid lines to aid precise readings. **Clarifying Graph Grid** I've re-examined the graph and confirmed the absence of internal horizontal grid lines. However, I've noted distinct tick marks on the y-axis at unit intervals from 0 to 9, which I'm now using to refine my binding energy estimations. **Calculating Pixel to Energy** I've precisely calibrated the y-axis pixel measurements to energy units, establishing a clear relationship between pixel position and MeV. This allows me to accurately extract binding energy values from the graph for my subsequent calculations. **Refining Nuclei Calculations** I'm now refining my binding energy per nucleon calculations. I've identified specific points on the graph for nuclei around mass numbers 90 and 180, and I'm actively calculating the energy difference to proceed. **Verifying Energy Calculations** I've performed the final energy calculation using my refined binding energy values. The result strongly aligns with option C, and I've rigorously checked alternative energy values (50 and 220 MeV) against the graph, confirming their significant discrepancies with the plotted data. **Confirming Reaction Energy** I have confirmed the energy calculation for the nuclear reaction. The energy released is approximately 108 MeV, which aligns closely with 110 MeV. I am now verifying the precise interpretation of "energia associada à diminuição da massa do sistema durante a reação" to ensure no subtleties were missed.