Scales of chemical shifts:
Usually, the δ scale ranges from 0 to 12 ppm. A higher value of δ denotes the signal to be more downfield from the reference while a high field signal will correspond to a lower δ value.
This makes the shift dimensionless, other than a problem still keep. The value of the ratio is very small because the shift in field or frequency is nearly 106 times smaller than the measuring field or frequency. Thus, we multiply this dimensionless quantity by 106 and express it in terms of parts per million (ppm). Thus, the chemical shift, δ, is mathematically defined as follows:
δ = ((vTest - vTMS )/vop )×106
In sequence to circumvent this problem another scale called τ scale has been proposed. It is described as
τ = 10 - δ
Here the TMS is arbitrarily assigned a value of 10 τ. The unit is still in ppm with only difference in scale. The two scales are related as shown in Figure.
![1894_Scales of chemical shifts.png](https://www.expertsmind.com/CMSImages/1894_Scales%20of%20chemical%20shifts.png)
Figure: Schematic representation of δ the relationship between the δ and τ scales of chemical shifts
The classic chemical shift positions of some generally encountered function groups are given in Figure.
![47_Scales of chemical shifts1.png](https://www.expertsmind.com/CMSImages/47_Scales%20of%20chemical%20shifts1.png)
Figure: Range of chemical shift values for different types of protons