Question

Both parts of this one please. Answers are a) 1.5x10-17 kg

(b) 0.999980

a) A carbon nanotube is like graphene rolled into a tube. The C-C distance is 1.41 A. Estimate the mass of a nanotube of diameter 6.3 A and length 1 cm. [5 marks] b) Nuclear magnetic resonance in hydrogen atoms arises because in a magnetic field the energy for up- and down-spin protons is different by 0.176 ueVT. Calculate the ratio of up-spin (parallel to the B-field) to down-spin hydrogen nuclei in thermal equilibrium at 37 C and a field of 3 T [5 marks]

Answer 1

a) Structure of graphene is Hexagonal with 6 carbon atom situated at each vertex Now, distance between e-e atom is a = 1.41 A degrees = 1.41 times 10^-10 m therefore Area of the hexagon = squareroot 3/4 times 6 times a^2 Now, each atom is shared by 3 cell so effectively each Hexgon contains 6/3 = 2 atom therefore area per atom = squareroot 3/4 times 6 times a^2 times 1/2 = 3 squareroot 3/4 a^2 Now, Length of the tube is l = 1 cm = 1 times 10^-2 m Diameter of the tube is D = 6.3 A degrees = 6.3 times 10^-10 m therefore surface area of the tube is = 2 pi times D/2 times l \r\n therefore No. of atom contained by this tube is n = surface area of the tube/area per atom = pi Dl/3 squareroot 3/4 a^2 mass of one carbon atom is m_c = 1.99 times 10^-26 kg