MPSC State Service 2019 · CSAT · Question 12 of 72

Passage: DENSITY A property of any substance is its density ρ (Greek letter rho), defined as the amount of mass contained in a unit volume, which we usually express as mass per unit volume: ρ = m V For example, aluminum has a density of 2.70 g/cm3, and lead has a density of 11.3 g/cm3, Therefore, a piece of aluminum of volume 10.0 cm3 has a mass of 27.0 g, whereas an equivalent volume of lead has a mass of 113 g. The difference in density between aluminum and lead is due, in part, to their different atomic masses. The atomic mass of an element is the average mass of one atom in a sample of the element that contains all the element՚s isotopes, where the relative amounts of isotopes are the same as the relative amounts found in nature. The unit for atomic mass is the atomic mass unit (u), where 1 u = 1.6605402 × 10-27 kg. The atomic mass of lead is 207 u, and that of aluminum is 27.0 u. However, the ratio of atomic masses, 207 u/27.0 u = 7.67, does not correspond to the ratio of densities, (11.3 g/cm3) ⟋ (2.70 g/cm3) = 4.19. The discrepancy is due to the difference in atomic separations and atomic arrangements in the crystal structure of these two substances. The mass of a nucleus is measured relative to the mass of the nucleus of the carbon-12 isotope, often written as 12 C . (This isotope of carbon has six protons and six neutrons. Other carbon isotopes have six protons but different numbers of neutrons.) Practically all of the mass of an atom is contained within the nucleus. Because the atomic mass of , C -12 is defined to be exactly 12 u, the proton and neutron each have a mass of about 1 u. One mole (mol) of a substance is that amount of the substance that contains as many particles (atoms, molecules, or other particles) as there are atoms in 12 g of the carbon-12 isotope. One mole of substance A contains the same number of particles as there are in 1 mol of any other substance B. Experiments have shown that this number, known as Avogadro՚s number, NA, is NA = 6.022137 × 1023 particles/mol. Avogadro՚s number is defined so that 1 mol of carbon-12 atoms has a mass of exactly 12 g. In general, the mass in 1 mol of any element is the element՚s atomic mass expressed in grams. For example, 1 mol of iron (atomic mass = 55.85 u) has a mass of 55.85 g (we say its molar mass is 55.85 g/mol), and 1 mol of lead (atomic mass = 207 u) has a mass of 207 g (its molar mass is 207 g/mol). Because there are 6.02 × 1023 particles in 1 mol of any element, the mass per atom for a given element is matom = molar mass/NA For example the mass of an Iron atom is, 55.85 g M Fe = m ol 6.02 × 10 23 atoms m ol 10 − 23 g = 9.28 × at o m Substance Density = (103 kg/m3) Gold 19.30 Uranium 18.70 Lead 11.30 Copper 8.92 Iron 7.86 Aluminum 2.70 Magnesium 1.75 Water 1.00 Air 0.0012 Table Supporting: MPSC Rajyaseva Prelims 2019 CSAT Paper II Official Paper Part 1 According to densities given in the table, if we prepare two spheres out of Gold and Copper each of a similar weight of 0.50 kg, then

Reading Comprehension

1. AThe Golden sphere will be bigger than copper
2. BThe Golden sphere will be smaller than copperCorrect
3. CBoth the spheres will be of same size 19.30
4. DGolden sphere will be exactly 8.96 times than copper.