Question

A single NMR scan of a dilute sample exhibits a signal-to-noise ratio (S/N) of 1.8. If each scan takes 8.0 minutes, calculate the minimum time required to generate a spectrum with a S/N ratio of 20. (2 pts).

Answer 1

Lets assume X scans are to be carried out to reach at final S/N ratio of 20.

Since each time the S/N ratio is 1.8 so after X scans,

the S/N ratio would be:

= 1.8^X

this hs to be equal to the final S/N ratio of 20

so 1.8^X = 20

or X = Log (20)/Log (1.8)

or X = 5.1

Since scans can be only in integer numbers so next number higher than 5.1 is 6

so we need atleast 6 scans to reach final S/N ratio of 20

Now :

Since each scan takes 8 minutes

so total time taken in 6 scans = 6*8 = 48 minutes.