Hyperfine splitting occurs due to the interaction between an electron's spin and the nucleus' spin. This interaction causes each electron spin state to split into 2I+1 levels, where I is the nuclear spin quantum number. As examples, the document discusses the hyperfine splitting in hydrogen, where the nuclear spin is 1/2, and deuterium, where the nuclear spin is 1. Hyperfine splitting has applications in radio astronomy, nuclear technology such as laser isotope separation, and atomic clocks.

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.