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Q131. The radii of A+2 and B- ions are 1.12Å and 1.31Å, respectively. The coordination number of A+2 in mineral AB2 is_____________.
The correct answer is 8. In crystal chemistry, the 'coordination number' determines how many large negative atoms (anions) can physically pack around a smaller positive atom (cation). This geometric limit is found using the radius ratio rule. We divide the radius of the cation A (1.12) by the radius of the anion B (1.31), which equals approximately 0.855. According to Pauling's geometric rules, any ratio falling strictly between 0.732 and 1.0 mandates a cubic coordination, meaning exactly 8 atoms will tightly pack around the center.
Q132. Assume: (i) geothermal gradient = 25 °C/km in the crust, (ii) density of the crustal rocks = 3000 kg/m3, and (iii) acceleration due to gravity = 10 m/s2. Based on these values, the lithostatic pressure at a point where temperature is 400 °C will be __________ MPa.
The correct answer is 480. First, we must find how deep into the Earth this hot point is. Assuming the surface is at 0°C, the temperature increases by 25°C every kilometer. Dividing 400°C by 25°C/km gives a depth of exactly 16 kilometers (16,000 meters). Lithostatic pressure is calculated by multiplying Depth × Density × Gravity. So, 16,000 m × 3000 kg/m3 × 10 m/s2 equals 480,000,000 Pascals. Because 1 Megapascal (MPa) is one million Pascals, we divide by one million to get exactly 480 MPa.
Q133. The intensity of an earthquake of magnitude 8 on the Richter scale is greater than the intensity of an earthquake of magnitude 5 on the same scale by ___________ times.
The correct answer is 1000. The Richter magnitude scale is strictly logarithmic base-10. This means every time you go up one single whole number on the scale, the physical shaking amplitude (intensity) increases by exactly 10 times. To calculate the difference between a magnitude 5 and a magnitude 8 earthquake, subtract 5 from 8 to get a difference of 3 steps. Multiplying 10 × 10 × 10 (or 10 to the power of 3) equals exactly 1000 times more intense shaking.
Q134. A confined sandstone aquifer with a uniform cross-sectional area of 7 m2 and a hydraulic conductivity of 2 m/s, transmits water across a hydraulic gradient of 3.2. Assuming steady state Darcian flow, the volumetric flow rate through the aquifer is _____ m3/s (answer in one decimal place).
The correct answer is 44.8. We use Darcy's Law for groundwater flow, which states: Total Volumetric Flow = Hydraulic Conductivity × Cross-Sectional Area × Hydraulic Gradient. We simply plug the given numbers into the formula: 2 m/s (conductivity) × 7 m2 (area) × 3.2 (gradient). 2 × 7 = 14. Then, 14 × 3.2 equals exactly 44.8 cubic meters per second.
Q135. When a dunite comprising pure forsterite undergoes melting, the weight % of MgO in the melt is _____ (answer in one decimal place; given molecular weights of SiO2 = 60.08; MgO = 40.30).
The correct answer is 57.3. Pure forsterite is a magnesium-rich olivine with the chemical formula Mg2SiO4. When it melts entirely, the liquid has the exact same chemistry. We must calculate the weight percentage of the MgO part. The formula contains two MgO molecules (2 * 40.30 = 80.60) and one SiO2 molecule (60.08). The total molecular weight is 140.68. Dividing the MgO part (80.60) by the total (140.68) and multiplying by 100 gives approximately 57.3%.
Q136. The mass of a fully dried rock sample of volume 100 cm3 is 300 g. The mass of the sample, when fully saturated with water of density 1.00 g/cm3, is 325 g. Assuming no volume change, the computed porosity of the rock is _____ % (answer in one decimal place).
The correct answer is 25.0. Porosity is the percentage of empty space inside a rock. The dry rock weighs 300g. When soaked, it weighs 325g. The difference is 25g, which is the weight of the water that soaked into the empty spaces. Because water has a density of 1 g/cm3, 25g of water perfectly equals a volume of 25 cm3. The whole rock's volume is 100 cm3. Dividing the empty space (25) by the total volume (100) shows the rock is exactly 25.0% empty space (porosity).
Q137. 600 tons of low grade iron ore (40% Fe) are blended with 400 tons of high grade iron ore (65% Fe). The grade of the blended ore is _____ % Fe (answer in one decimal place).
The correct answer is 50.0. This is a mass balance calculation. First, find the total tons of pure iron. The low-grade ore has 600 tons * 40% (0.40) = 240 tons of pure iron. The high-grade ore has 400 tons * 65% (0.65) = 260 tons of pure iron. Adding them together gives 500 tons of pure iron in the mix. The total weight of the blended pile is 600 + 400 = 1000 tons. 500 tons of iron divided by 1000 tons total equals 50.0%.
Q138. Based on 8 oxygen atoms, the number of silicon atoms in a plagioclase of composition Ab20An80 is _____ (answer in one decimal place).
The correct answer is 2.2. Plagioclase is a mixture of Albite (NaAlSi3O8) and Anorthite (CaAl2Si2O8). Albite has 3 Silicon atoms, and Anorthite has 2 Silicon atoms. The rock composition is 20% Albite (Ab20) and 80% Anorthite (An80). To find the average number of Silicon atoms, multiply the fraction of each mineral by its Silicon count: (0.20 * 3) + (0.80 * 2). This equals 0.6 + 1.6, giving an exact average of 2.2 Silicon atoms.
Q139. Assuming the Earth to be an ideal sphere, the volume % of the core relative to the total volume of the Earth is _____ (answer in one decimal place).
The correct answer is 16.2. The volume of a sphere is proportional to the cube of its radius. The Earth's core has a radius of about 3480 km, while the whole Earth has a radius of about 6371 km. To find the percentage of volume the core takes up, we divide the core's radius by the Earth's radius, cube that fraction, and multiply by 100. (3480 / 6371)^3 * 100 mathematically calculates to roughly 16.2%.
Q140. In the garnet formula (Fe2.5Mg0.3Cax)Al2Si3O12, x represents the number of atoms of Ca. The mole % of grossular in the garnet is _____ (answer in one decimal place).
The correct answer is 6.7. A standard garnet formula is written based on 12 Oxygen atoms, and the front 'cation' slot (where Fe, Mg, and Ca sit) must always total exactly 3.0 atoms. The formula given is Fe(2.5) + Mg(0.3) + Ca(x). Adding 2.5 and 0.3 equals 2.8. To reach the required total of 3.0, the Calcium (x) must be exactly 0.2. 'Grossular' is the calcium-rich version of garnet. To find its percentage, divide the calcium amount (0.2) by the total in that slot (3.0) and multiply by 100, which equals roughly 6.66% (rounds to 6.7%).