According to one simple model, the lowest energy electrons of the nanotube are deseribed by the wavefunction sinx/L, where L is the length of the nanotube Find the normalized wavefunction for a nanotube according to the simple model described above. Because the wavefunction is one dimensional, you need to find the factor A that guarantees that 0L+=1. Show your work, not just the solution. Hint on integration: sin2kxdx=21x4k1sin2kx Why the wave function needs to be normalized? Question II Using the normalized function obtained in Question 1, write an expression for the probability of finding the electron in the region of interest. Question III Imagine that we want to test the function (x)=1/x as a potential wavefunction for a free particle. Would (x)=1/x be acceptable for describing the behaviour of such a particle? Give your reasons for accepting or rejecting this function. Question N Nanotubes can be classified in zigzag, amnchair or chiral, depending on how their hexagonal carbon structure is arranged with respect to the nanotube axis. They are named following two indexes (n,m) as explain in the diagram below, as well as in the examples for (5,5),(7,5) and (7,0) nanotubes: How is the SMILE representation for a (7,5) carbon nanotube with I nm of length and caped with hydrogen atoms at the edges? You can use Avogadro and open babel to do it. Show some screenshots of the process, in addition to the final SMILE representation