The document discusses the Zeeman effect, which is the splitting of a spectral line into multiple components when exposed to a magnetic field, first discovered by Pieter Zeeman in 1896. It outlines the types of Zeeman effects, namely the normal and anomalous effects, and provides both classical and quantum mechanical explanations for the normal Zeeman effect. The document also includes historical context, definitions, and mathematical descriptions related to the phenomenon.

1. ZEEMAN EFFECT
PRESENTED BY : ABHIJIT PUHAN
ROLL NO : 16122P001
DEPARTMENT OF PHYSICS
F.M. AUTONOMOUS COLLEGE , BALASORE
UNDER THE GUIDANCE OF
DR. PURNACHANDRA PATRA
ASSISTANT PROFESSOR
DEPARTMENT OF PHYSICS,FMAC,BALASORE

2. OUTLINES
INTRODUCTION TO ZEEMAN EFFECT
HISTORY OF ZEEMAN EFFECT
TYPES OF ZEEMAN EFFECT : NORMAL AND ANOMOLOUS ZEEMAN
EFFECT
CLASSICAL EXPLANATION OF NORMAL ZEEMAN EFFECT
VECTOR MODEL OF NORMAL ZEEMAN EFFECT
QUANTUM MECHANICAL EXPLANATION OF NORMAL ZEEMAN
EFFECT

3. Introduction
ZEEMAN EFFECT, IN PHYSICS IS THE SPLITTING OF A SPECTRAL LINE INTO TWO
OR MORE COMPONENTS OF SLIGHTLY DIFFERENT FREQUENCY WHEN THE LIGHT
SOURCE IS PLACED IN A MAGNETIC FIELD.
HENDRIK LORENTZ PIETER ZEEMAN

4. HISTORY OF ZEEMAN EFFECT
• DUTCH PHYSICIST PIETER ZEEMAN DISCOVERED THE ‘ZEEMAN EFFECT’ IN
1896.
• ZEEMAN CONDUCTED HIS GROUND BREAKING EXPERIMENT WHILE WORKING
IN THE LABORATORY OF HENDRIK LORENTZ AT THE UNIVERSITY OF LEIDEN.
• HE OBSERVED THAT WHEN A SOURCE OF LIGHT IS SUBJECTED TO A
MAGNETIC FIELD, THE RESULTING SPECTRUM IS NOT A SINGLE LINE BUT
RATHER A GROUP OF CLOSELY SPACED LINES.
• ZEEMAN INITIALLY INVESTIGATED THIS PHENOMENON USING SODIUM
FLAME, WHERE HE OBSERVED THE SPLITTING OF THE D-LINE DOUBLET.
• HE OBSERVED THAT THE SPECTRAL LINES SPLIT INTO MORE THAN THREE
COMPONENTS WHEN A MAGNETIC FIELD WAS APPLIED PERPENDICULAR TO
THE DIRECTION OF LIGHT PROPAGATION. THIS SPLITTING WAS FOUND TO BE
PROPORTIONAL TO THE STRENGTH OF THE MAGNETIC FIELD.
• THEREFORE ,PIETER ZEEMAN WON NOBEL PRIZE IN PHYSICS WITH HIS
TEACHER HENDRIK LORENTZ IN THE YEAR 1902.

5. DEFINITION
• THE ZEEMAN EFFECT IS THE NAME FOR THE SPLITTING OF
ATOMIC ENERGY LEVELS OR SPECTRAL LINES DUE TO ACTION OF
AN EXTERNAL MAGNETIC FIELD.
• THAT SHOWS AN ATOM HAS ADDITIONAL ENERGY LEVELS.

6. TYPES OF ZEEMAN EFFECT
THE ZEEMAN EFFECT IS BROADLY DIVIDED INTO TWO PARTS DEPENDING
UPON THE MAGNITUDE OF EXTERNAL MAGNETIC FIELD PROVIDED,THESE ARE
SUCH AS
I. NORMAL ZEEMAN EFFECT:
WHEN THE ATOM (OR THE SOURCE OF SPECTRAL LINE) IS PLACED IN A
STRONG MAGNETIC FIELD THE SPECTRAL LINE SPILTS INTO FEWER
(THREE)COMPONETS.
. SPIN QUANTUM NUMBER IS ZERO.
II. ANOMALOUS ZEEMAN EFFECT:
WHEN THE ATOM (OR THE SOURCE OF SPECTRAL LINE ) IS SUBJECTED TO
WEAK OR ORDINARY MAGNETIC FIELDS, THE SPECTRAL LINE SPILTS INTO
MORE THAN THREE COMPONENTS.
. SPIN QUANTUM NUMBER IS NOT ZERO.

7. DEFINITION OF NORMAL ZEEMAN EFFECT
• FOR A SINGLET STATE( NO UNPAIRED ELECTRON ), THE SPIN IS ZERO.
• THE TOTAL ANGULAR MOMENTUM 𝐽 IS EQUAL TO ORBITAL ANGULAR
MOMENTUM 𝐿.
• FOR EXAMPLE : 𝐻𝑔, 𝐻ⅇ, 𝐶𝑑 etc

8. CLASSICAL EXPLANATION OF NORMAL ZEEMAN
EFFECT
• THE NORMAL ZEEMAN EFECT WILL BE EXPLAINED BY THE CLASSICAL THEORY
ON THE BASIS OF
BOHR’S ATOMIC MODEL.
WHEN THERE IS NO EXTERNAL FIELD; THE CENTRIPETAL FORCE OF THE
ELECTRON IS GIVEN BY
𝐹𝐶 =
𝑀ⅇ𝑣2
𝑟
=
• IN PRESENCE OF MAGNETIC FIELD ( PERPENDICULAR TO V )
• LORENZ FORCE FL = Bⅇ v = 𝐵ⅇ𝑟𝜔
• CHANGE IN FORCE ⅆ𝐹 = ±𝐵ⅇ𝑟𝑤 ⇒ ⅆ𝐹 = 2𝑀𝑒𝑟𝜔 ⅆ𝑤,
ⅆ𝑤 = ±
𝐵𝑒
2𝑀𝑒
⇒ 𝑑𝜈𝑜 = ±
𝐵ⅇ
4𝛱𝑚𝑒
𝑀𝑒𝑟𝑤2

9. VECTOR MODEL OF NORMAL ZEEMAN
EFFECT
• WHEN AN ATOM PLACED IN AN EXTERNAL MAGNETIC FIELD , THE ENERGY OF AN ATOM
CHANGES BECAUSE OF THE ENERGY OF ITS MAGNETIC MOMENT IN THE FIELD WHICH IS GIVEN
BY
∆𝐸 = 𝜇𝑙. 𝐵 =-𝜇𝑙𝑧𝐵 (MAGNETIC FIELD ALONG Z-AXIS)
𝜇𝑙𝑧 = −𝑚𝑙𝜇𝐵 =
𝑀𝑙ⅇℎ
2𝑚ⅇ
∆𝐸 = 𝑚𝑙
𝑒ℏ𝐵
2𝑚𝑒
= 𝑚𝑙𝜇𝐵B
⇒ ∆𝐸 ∝ 𝑀𝑙 (WHERE 𝑚𝑙 = (2𝑙 + 1) VALUES FOR ‘𝑙′
SINCE EACH ENERGY LEVEL SPLITS INTO (2𝑙 + 1) LEVELS
• THE SELECTION RULE FOR TRANSITION , Δ𝑚𝑙 = 0, ±1
• BECAUSE OF UNIFORM SPLITTING OF THE LEVELS THERE ARE ONLY THREE DIFFERENT
TRANSITION ENERGIES , 𝐸0 +
ⅇ𝐵ℏ
2𝑚𝑒
, 𝐸0, 𝐸0 −
ⅇ𝐵ℏ
2𝑚𝑒
CORRESPONDING TO THE TRANSITION WITH
Δ𝑚𝑙 = +1,0, −1
• THE CHANGE IN FREQUENCY OF THE EMITTED SPECTRAL LINE IS ENERGY CHANGE DIVIDED BY ℎ
• THE FREQUENCY CHANGE ARE THEREFORE ±
ⅇ𝐵
4𝛱𝑚𝑒
OR ‘0’.

10. QUANTUM MECHANICAL EXPLANATION OF
NORMAL ZEEMAN EFFECT
• THE MAGNETIC MOMENT OF AN ELECTRON MOVING IN ITS ORBIT IS GIVEN BY
𝝁𝒍 =
−ⅇ
𝟐𝒎𝒆
𝑳
THIS MAGNETIC MOMENT INTERACT WITH EXTERNAL MAGNETIC FIELD AND GIVES THE PERTURBING
HAMILTONIAN AS
H’=−𝝁𝒍 ⋅ 𝑩 =
ⅇ
2𝑚𝑒
𝐿 ⋅ 𝐵
TO CALCULATE THE SPLITTING OF SPECTRUM LINES, THE OPERATOR FORMS OF H’ IS USED IN THE PERTURBATION
THEORY. THE FIRST ORDER INTERACTION ENERGY IS GIVEN BY
Δ𝐸 = 𝛹∗𝐻′𝛹 𝑑𝜏 = 𝛹∗𝐿𝐵𝛹 𝑑𝜏 =
𝑒𝐵𝑍
2𝑚𝑒
𝜓∗𝐿𝛹 𝑑𝜏=
ⅇℎ
2𝑚𝑒
𝐵𝑧𝑚𝑙
THEREFORE, THE ENERGY OF THE HAVING ORBITAL QUANTUM NUMBER 𝑚𝐿1 IS
𝐸1 = 𝐸 1
+
ⅇℎ
2𝑚𝑒
𝐵𝑚𝐿1
AND 𝐸2 = 𝐸 2 +
𝑒ℎ
2𝑚𝑒
𝐵𝑚𝐿2
𝐸2 − 𝐸1 = 𝐸2 − 𝐸1 +
ⅇℎ
2𝑚𝑒
𝐵Δ𝑀𝐿
ℎ𝜈 = ℎ𝜈0 +
𝑒ℎ
2𝑚𝑒
𝐵Δ𝑀𝐿 ⇒ 𝑣 = 𝑣0+
𝑒𝐵
4𝛱𝑚𝑒
∆𝑀𝐿
• THE EXPRESSION WHEN SUBJECTED TO SELECTION RULE Δ𝑀𝐿 = 0, ±1 GIVES RISE TO ZEEMAN NORMAL
TRIPLET.Δ𝑀𝐿 = 0 CORRESPONDS TO 𝜋 COMPONENTS AND Δ𝑀𝐿 = ±1 GIVES COMPONENTS