1). Consider one hexagon unit in a graphene sheet. Given the carbon-carbon bond length as acc=1.42Å (1Å=10^-10m), calculate the total surface area (both top and bottom surfaces) of one hexagon unit. (Hint: the area of a hexagon with edge of r is: A = (3√3 / 2)r²).
2). How many carbon atoms are there in one hexagon unit? (Hint: Each carbon atom is shared by 3 hexagons).
3). Calculate the mass/area density of graphene sheet. (e.g. the mass of carbon atoms per unit graphene surface area). (Hint: The mass of 1 mole (1mole=6.02×10²³) carbon atoms is 12g).
4). Based on above calculation, if we have 1kg of graphene sheet, what is the total surface area (both top and bottom surfaces)?