Spectroscopy-1hnmr

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Electron Spin

Nuclear Magnetic
Resonance
(NMR)
Spectroscopy
Organic Chemistry BCH3015

• Electron spin is quantized.
• The spin quantum number ms
has only two allowed values:
ms = +½ or –½

• The two directions of
spin create oppositely
spin create oppositely
directed magnetic
fields.
fields.
61

Proton Spin

Organic Chemistry BCH3015

62

Nuclear Spin States

• A proton (the nucleus of a 1H atom) also possesses spin.

For each nucleus having the spin quantum number I,
there are (2I + 1) allowed spin states.

• The spin of a proton is also quantized.

mI   I , ( I  1), ..., ( I  1),  I
• The spin quantum number of a proton is:

I

1
2

Example: For the nucleus of
For the nucleus of

35
35Cl,

I

3
2

• There are two allowed spin states mI:
There are 4 allowed spin states:
are allowed spin states:

1
1
 or 
2
2
Organic Chemistry BCH3015

63

311
3
 ,  ,  , or 
222
2

Organic Chemistry BCH3015

64

Some Common Nuclei

We
We Will Only Discuss
Proton Nuclear Magnetic Resonance

• Any atomic nucleus that has a odd mass number
and/or odd atomic number has a quantized spin
angular momentum.
El
Element

1
1

H

2
1

H

12
6

C

13
6

C

14
7

1H

NMR
1
I
2

N

Nuclear spin quantum
spin quantum
number

1
2

1

0

1
2

1

Number of spin states
of spin states

2

3

0

2

3

17
8

19
9

31
15

Element

16
8

O

O

F

P

35
17

Cl

Nuclear spin quantum
spin quantum
number

0

5
2

1
2

1
2

3
2

Number of spin states
of spin states

0

6

2

2

4

Organic Chemistry BCH3015

65

Nuclear Spin

Allowed
Allowed Spin States
1
1

and

2
2
Organic Chemistry BCH3015

66

Effects of an Applied Magnetic Field B0

• The spinning nucleus generates a magnetic field.
spinning nucleus generates magnetic field

Ealigned < Eagainst
• B0 applies a force to
the small bar magnet,
so that it is twisted to
align with B0.
Organic Chemistry BCH3015

67

• The bar magnet that
aligns with B0 has a
lower energy than
that aligns against B0.

Organic Chemistry BCH3015

68

Proton Magnetic Moments

- and -Spin States
• Similarly, the nucleus that aligns with B0 (-spin state) has a lower energy than that aligns against B0 (-spin state). lower energy than that aligns against
state).

B0

• -Spin



1
2

• -Spin

• Aligned with B0
• Lower in energy



• Against B0
• Higher in energy
Organic Chemistry BCH3015

69

Organic Chemistry BCH3015

EI  

hmI
B0
2

:
h:
B0 :

the allowed quantum states
magnetogyric
magnetogyric ratio of a given nucleus
of given nucleus
Planck’s constant
the applied magnetic field

E1/ 2
No
field

E
E1/ 2  

h
B0
4

Organic Chemistry BCH3015

• A nucleus is in resonance when it is irradiated with photons having energy equal to the energy difference between the spin states. • A proton in the -spin state can absorb a photon and flip to the spin state.

E1/ 2

For the proton, I = 1/2 and mI = +1/2 or –1/2
the proton
1/2 and
or 1/2

h
B0

4

m

1
2

1
2

E

E1/ 2

B0

m

70

Absorption of Energy

Energy Levels of Nucleus in B0
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