Question

1. Report the units for the following properties using the base SI units kg, m, s.

   1. (a) stress

   2. (b) strain

Draw and label the following chiral vectors (3,2), (6,0), (4,4), and (2,4). Label each as either (i) incorrect notation, or describing one of the following tubes (ii) armchair, (iii) zig-zag, or (iv) chiral. When you draw the chiral vectors, please show BOTH the final vector and also the path traveled according to the notation. IT IS EASY TO MAKE SILLY MISTAKES – SO BE CAREFUL.

Answer 1

(a) The dimension of stress is that of pressure. It's S.I. unit is Pascal(Pa) that is, newtons per square meter.

Newtons have base units kg⋅m⋅s⁻².

So stress has base units

(b)Strain is the ratio of change in original length to change in length is due to stress. So it is a dimensionless quantity.

Now,

A nanotube is chiral if it has a type (n,m), with m > 0 and m ≠ n.

"zigzag" tubes are the (k,0) type.

"armchair" tubes are the (k,k) type.