Lecture 1: Introduction and Basic Concepts

Question 1

Describe how a nucleus’ magnetic moment is related to its spin quantum number and gyromagnetic ratio.

Answer 1

The spin quantum number is directly proportional to the spin angular momentum (P) ; so,

P = h × sqrt(I(I+I))
ų = Pý
ų = hý × sqrt(I(I+))

Question 2

Identify the NMR behavior (inactive/active) and spin quantum number of a nucleus based on its atomic number and spin quantum number:

Answer 2

Mass # Atomic # I NMR behavior

even even 0 inactive
even odd 1,2,3… active
odd even/odd 1/2,3/2,5/2… active

Question 3

Describe how a nucleus’ Lamor frequency is related is related to its gyromagnetic ratio and magnetic field:

Answer 3

w = ýBo

Nuclei with spin induce a magnetic moment of their own which (once placed in an external magnetic field) will experience an angular torque
, causing the magnetic moments axis of rotation to precess around this external magnetic field. This is known as Larmor precession which precesses around the applied magnetic field.

Question 4

Describe the Zeeman effect. Know how to relate the energy difference between two states of a spin 1/2 with its Larmor Frequency or gyromagnetic ratio:

Answer 4

E = -mýhBo = -mhw

-The Zeeman effect describes the splitting of energy levels between spin states in the presence of the magnetic field.

Question 5

The resonance frequency of which the nucleus is the magnetic field strength of an NMR Spectrometer referred to?

Answer 5

In NMR, the frequency of the photon is in the radio frequency range. In NMR, v is between 60 and 600 MHz for hydrogen nuclei.

Question 6

Describe the limiting factors for the sensitivity of NMR method.

Answer 6

The signal in NMR results from the difference between energy absorbed (making a transition from the lower energy state to higher energy state) and the energy emitted ( making a transition from the higher energy state to the lower energy state). NMR is sensitive because it is able to pick up these small differences in populations between energy levels. It is the exchange of energy at a specific frequency that give NMR its sensitivity.

Question 7

Describe the factors that affect the macroscopic (net) magnetization.

Answer 7

The magnitude of Mo depends on:

• Bo : the magnitude of the static magnetic field.
• I and ý^2 : the identity of the nucleus
• T : temperature
• N : the number of nuclei