# Chapter 6

## Instructions

Answer the following questions and then press 'Submit' to get your score.

### Question 1

What is the strength (B1) of a 13C 90° pulse of duration 1 μs?

### Question 2

The equilibrium populations of the 1H energy levels of a molecule are nα = nαeq and nβ = nβeq. What are the populations after a 5.0 μs pulse when B1 = 4.697 mT?

### Question 3

During a delay, spins with an offset frequency Ω = 250 rad s-1 precess through an angle of 60°. How long is the delay?

### Question 4

The amplitude of a free induction decay drops to 25% of its initial intensity after 1.0 s. Assuming exponential relaxation and Ω = 0, determine the value of T2.

### Question 5

The NMR spectrum obtained by Fourier transforming a free induction decay of the form cos(Ω0t)exp(-t/T2) comprises a single line at offset frequency Ω = Ω0 . Determine the appearance of the spectrum obtained by Fourier transforming the free induction decay, cos3Jt) cos(Ω0t)exp(-t/T2).
[cos3x = ¼cos3x + ¾cos x; cos x cos y = ½cos(x + y) + ½cos(x - y).]

### Question 6

In an NMR experiment on a sample with the equilibrium polarization peq, it takes 0.30 s to record a single pulse-acquire free induction decay. The signal-to-noise ratio (SNR) of the corresponding spectrum is 0.1. Using signal averaging, how long would it take to obtain a spectrum with SNR = 100 when the polarization immediately before each repeat of the pulse-acquire sequence is (i) peq and (ii) 100peq?

### Question 7

In an inversion recovery experiment, the signals at τ = 0.0 and at τ = 1.60 s have relative intensities -A and +A/3 respectively. Assuming exponential relaxation, calculate the value of T1.

### Question 8

Fig. 6.13 shows the operation of a 90°x - τ - 180°y - τ spin echo sequence. What is the result of the sequence 90°x - τ - 180°x - τ in which the 180° pulse has phase x instead of y?

### Question 9

The spectrum of a molecule containing an isolated proton is recorded using the pulse sequence: 90°x - τ - 90°-x. In the first experiment, Ω = 0. In a separate experiment, Ωτ = ½π. Which of the following statements is true?

### Question 10

What is the enhancement factor obtainable in a 1H-103Rh INEPT experiment?
[|ɣ(103Rh)| = 8.468 x 106 T-1 s-1]