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Q21. For a 2/m pyroxene, the extinction angle between the vibration direction and crystallographic axis, X ˄ c, is 36°. Then the angle Y ˄ b in degrees will be _____________. (In integer)
In the study of crystal shapes (crystallography), a '2/m' pyroxene has a specific, orderly internal structure. In this structural class, the optical vibration direction 'Y' is perfectly parallel to the crystal's 'b' axis. Because they run exactly parallel, the angle between them is 0 degrees.
Q22. Radiogenic atoms of 40K have a half-life of 1.25 × 10^9 years. The percentage of 40K atoms left after six half-lives will be _____________. (Round off to two decimal places)
A 'half-life' is the time it takes for half of a radioactive substance to decay away. After 1 half-life, 50% is left. If you keep halving the amount 6 times (100 -> 50 -> 25 -> 12.5 -> 6.25 -> 3.125 -> 1.5625), you are left with about 1.56% of the original atoms.
Q23. A grain has a size of 36 mm when observed under a magnification of 125 times. The actual size of the grain in µm is __________. (In integer)
Magnification makes tiny things look bigger. To find the actual size, divide the viewed size by the magnification power: 36 millimeters / 125 = 0.288 millimeters. Since there are 1000 micrometers in a millimeter, the actual size is 288 micrometers.
Q24. The mineral formula of orthopyroxene calculated on 6 Oxygen atom basis is (Mg1.2Fe0.8)Si2O6. The weight percentage of MgO in the chemical composition of orthopyroxene is __________. (Round off to one decimal place)
A mineral's formula tells us its atomic ingredients. By taking the atomic weight of Magnesium Oxide (MgO) in the formula and dividing it by the total weight of the entire orthopyroxene molecule, we find that MgO makes up roughly 21.6% of the mineral's total weight.
Q25. A metapelite is composed of muscovite + quartz + K-feldspar + kyanite mineral assemblage. If the muscovite and K-feldspar show solid solution between ‘Na’ and ‘K’ end-members, the minimum number of components that defines this metapelitic assemblage is ____________. (In integer)
To describe a rock's chemistry, scientists count the minimum number of basic chemical building blocks (components) needed to make all its minerals. For this mix, you need 5 basic components: Silica, Alumina, Potassium, Sodium, and Water.
Q26. An orebody contains pyrite and chalcopyrite in the same molar proportions. The percentage concentration of Cu in the ore will be _______. (Round off to the nearest integer)
Pyrite (FeS2) and Chalcopyrite (CuFeS2) are both metallic sulfide minerals. If we have exactly one molecule of each, the total mix contains 1 Copper atom, 2 Iron atoms, and 4 Sulfur atoms. Using their atomic weights, the total weight of this mix is roughly 303.8 grams. The Copper part weighs 63.55 grams. Dividing Copper's weight by the total weight (63.55 / 303.8) gives about 0.209, or 21% copper.
Q27. For an anisotropic crystal of thickness 0.04 mm and refractive indices of 1.636 and 1.486 along the slow and fast directions, respectively, the retardation produced is _______ nm. (In integer)
When light shines through certain crystals, it splits into a fast ray and a slow ray. The 'retardation' is how far behind the slow ray gets. It is calculated by taking the difference between the two speeds (1.636 minus 1.486 = 0.150) and multiplying it by the physical thickness of the crystal. We convert the 0.04 mm thickness into 40,000 nanometers. 40,000 multiplied by 0.150 equals a retardation of exactly 6000 nanometers.
Q28. A rock element during deformation, experienced a pressure change of 5×104 N/m2, due to which its volume changed from 4 cm3 to 3.9 cm3. The bulk modulus of the rock is _______ ×106 N/m2. (In integer)
'Bulk modulus' measures how much a rock resists getting squeezed or compressed. It is calculated by dividing the change in pressure by the percentage change in volume. The volume shrank from 4 to 3.9, which is a change of 0.1 out of 4 (a 2.5% or 0.025 fractional change). When we divide the pressure (50,000) by this fraction (0.025), we get 2,000,000 N/m2, which is 2 × 10^6. So the integer is 2.
Q29. A partially saturated soil sample has a volume of 1200 cc. The volume of water present in the sample is 300 cc. The mass of solid in the sample is 1908 g and the particle density is 2.65 g/cc. The porosity (n) of the soil sample is _____ %. (In integer)
Porosity is the percentage of empty space (voids) inside a chunk of soil. First, we find the volume of the solid dirt grains by dividing their weight (1908 grams) by their density (2.65). This gives 720 cc of solid dirt. The whole sample is 1200 cc, so subtracting the solid 720 cc means there are 480 cc of empty void space (which currently holds some water and air). 480 divided by the total 1200 is 0.40, which means the soil is 40% empty space.
Q30. The mole fraction of forsterite in olivine with MgO = 29.17 weight %, FeO = 34.65 weight % and SiO2 = 36.18 weight % is _______. (Round off to two decimal places) (Use molecular weight, in g/mol, of MgO = 40.31, FeO = 71.85 and SiO2 = 60.00)
Olivine is a mineral made of a mixture of Magnesium (Forsterite part) and Iron (Fayalite part). To find out what fraction is Magnesium, we first convert the weight percentages into 'moles' (a chemical count of molecules) by dividing the weights by their molecular masses. MgO is 29.17 / 40.31 = 0.723 moles. FeO is 34.65 / 71.85 = 0.482 moles. The total is 1.205 moles. The fraction of Forsterite is the Magnesium part divided by the total: 0.723 / 1.205, which is roughly 0.60.