Use the ideas presented in the text together with your own experience and imagin

Question

Use the ideas presented in the text together with your own experience and imagination to analyze the following questions. Write neatly, and use proper grammar and spelling. Refer to the Homework Guidelines for proper format for your solutions, what you will be graded on, and tips for solving problems. Special Instructions: Use the five-step problem solving process for each prob lem this week. You will not receive full credit unless you r solution includes the following five sections, clearly labeled . U: Understand _ Understand the problem . F: Focus_ Focus on physics . P: Plan Devise a plan. . S: Solve_ Carry out the plan . E: Evaluate-Look back. 1 How big is a molecule? In 1773, Benjamin Franklin observed an interesting property of oil slicks on water: The same volume of oil always spreads out to cover the same area on the surface of a lake before breaking up into smaller droplets. Franklin reasoned (correctly) that the oil must be spreading out to form a single layer of particles before breaking up Franklin found that one teaspoon of olive oil (about 5 cm3) would cover about half an acre of a pond (about 2000 m2) Use this observation to estimate the size of a single molecule of oil. 2 The Mass of Air Ordinary air has a density of about 1 mg/cm3, while liquid air has a density of about 1.0 g/cm3. (a) Estimate the number of air molecules per cubic centimeter in ordinary air and in liquid air (b) Estimate the mass of an air molecule. 3 Exoplanet Gravity The surface gravity g of a planet is the acceleration due to gravity at the surface of a planet. Newton's universal law of gravitation gives the surface gravity as =G where G is the universal gravitational constant, M is the mass of a planet, and R is the radius of the planet. The surface gravity of earth is approximately 9.8 m/s2. In the past few years, several "super-earths" have been discovered orbiting distant stars. These are rocky planets that are larger than earth, but smaller than the gas giant planets in our solar system. One of these super-earths has a radius roughly twice that of earth. If the density of this planet is the same as that of the earth, what is its surface gravity? Bonus: X-ray diffraction studies show that NaCl crystals have a cubic lattice, with a spacing of 2.820 Å between neighboring atoms. Look up the density and atomic weight of NaCl and calculate Avogadro's number. (This is one of the most precise experimental methods for determining NA.)

Explanation / Answer

1. given, Volume V = 5 cm^3

Area OF POnd covered, A = 2000 m^2

so let diameter of oil molecules be d

then A*d = V

d = V/A = 2.5*10^-9 m

2. density of air, rho = 1 mg/cm^3

density of liquid air = rho' = 1 g/cm^3

a. 1 mole of air at STP has 22.4 litres of volume

so 1 cm^3 has 1/22.4*1000 moles

n = 6.022*10^23/22.4*1000 = 2.688*10^19 molecules

for liquid air, as density is 10 1000 times moire than normal air, n = 2.688*10^16 moleculer per cm^3

b. mass of air molecule = m

then m*n = 1*10^-6 kg

m = 3.7196*10^-26 kg

3. given, radius of new planet = 2R

here R is radius of earth

its density = rho = density of earth

then acceleration due to gravity on earth

g = GM/R^2 ( where M is mass of earth)

g = GMR/R^3 = (4/3*pi*G*R)M/(4/3*pi*R^3) = rho*4pi*GR

so g' = rho*4*pi*G*(2R) = 2g

so acceleration due to gravityy on the planet is twice the value on earths surface

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