atomic and molecular science

1. HYPERFINE SPLITTING Its role in Atomic transition
Roll no: 15251510-002

2. DEFINITION
Interaction between electron spin and nuclear spin is known as hyperfine interaction and
splitting occur due to this interaction is called hyperfine splitting.
When the electron spin interacts with nuclear spin then each electron spin state split into 2I+1
level this is known as hyperfine splitting.

3. RULES TO DETERMINE NUCLEAR SPIN:
 A nucleus with an even number of proton and even no of neutron has zero spin I= 0
for example 𝑐12,𝑂16, 𝐻𝑒4, 𝑆32, 𝐼 = 0
 A Nucleus with an odd number of proton and odd no of neutron has an integral spin.
for example 𝐻1, 𝑁14, 𝐼 = 1, 𝐵10, I = 3
 A nucleus with an odd mass has half integral spin
for example 𝐻1
, 𝐶13
, 𝑃31
, 𝐼 =
1
2
, 𝐶𝑈65
, 𝐼 =
3
2

4. CONT….
I= nuclear spin quantum no
The nuclear spin can have several orientations
for example;
I=1 , may have 𝑚𝑖=+1,0,-1
I=1/2 may have 𝑚𝑖 = +
1
2
, −
1
2
I=7/2 may have 𝑚𝑖 = +
7
2
, +
5
2
, +
3
2
, +
1
2
, −
7
2
, −
5
2
, −
3
2
, −
1
2
that is total of 2l+1

5. EXAMPLE: HYDROGEN
One unpaired electron (𝑚 𝑠 =
1
2
) of hydrogen interacts with its nuclear spin.
I value of H is ½, therefore 𝑚𝑖 = +
1
2
, −
1
2
.
Each 𝑚 𝑠state will interact with 𝑚𝑖value and split into 2I+1.
The energy of particular 𝑚 𝑠 𝑠tate will be affected by nuclear spin –electron spin
interaction energy.
This energy varies the product of 𝑚 𝑠 𝑎𝑛𝑑 𝑚𝑖, 𝑔𝑖𝑣𝑒𝑛 𝑏𝑦 𝐴𝑚 𝑠 𝑚𝑖. A is the hyperfine
splitting constant.
The energy of different levels are given by
𝐸 = 𝑔𝛽𝑚 𝑠 + 𝐴𝑚 𝑠 𝑚𝑖

6. CONT…

7. DEUTERIUM:
It has one unpaired electron(𝑚 𝑠 =
1
2
) interacts with nuclear spin.
I value of 𝐻2 𝑖𝑠 1, therefore 𝑚𝑖 = +1,0 𝑎𝑛𝑑 − 1.
2𝐼 + 1 = 2 × 1 + 1 = 3

8. APPLICATIONS:
Astrophysics:
In radio astronomy, heterodyne receivers are widely used in detection of the electromagnetic
signals from celestial objects. The separations among various components of a hyperfine
structure are usually small enough to fit into the receiver's IF band.
Nuclear technology:
The atomic vapor laser isotope separation (AVLIS) process uses the hyperfine splitting
between optical transitions in uranium-235 and uranium-238 to selectively photo-ionize only
the uranium-235 atoms and then separate the ionized particles from the non-ionized ones.
The hyperfine structure transition can be used to make a microwave notch filter with very
high stability, repeatability and Q factor, which can thus be used as a basis for very
precise atomic clocks.