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An external magnetic field along vertical z-axis is shown. Several spectral lines are shown originating from the same point on the z-axis which represents orbital angular momentum.
Only certain angles are allowed between the orbital angular momentum and an external magnetic field. This is implied by the fact that the Zeeman effect splits spectral lines into several discrete lines. Each line is associated with an angle between the external magnetic field and magnetic fields due to electrons and their orbits.

We already know that the magnitude of angular momentum is quantized for electron orbits in atoms. The new insight is that the direction of the orbital angular momentum is also quantized . The fact that the orbital angular momentum can have only certain directions is called space quantization    . Like many aspects of quantum mechanics, this quantization of direction is totally unexpected. On the macroscopic scale, orbital angular momentum, such as that of the moon around the earth, can have any magnitude and be in any direction.

Detailed treatment of space quantization began to explain some complexities of atomic spectra, but certain patterns seemed to be caused by something else. As mentioned, spectral lines are actually closely spaced doublets, a characteristic called fine structure    , as shown in [link] . The doublet changes when a magnetic field is applied, implying that whatever causes the doublet interacts with a magnetic field. In 1925, Sem Goudsmit and George Uhlenbeck, two Dutch physicists, successfully argued that electrons have properties analogous to a macroscopic charge spinning on its axis. Electrons, in fact, have an internal or intrinsic angular momentum called intrinsic spin     S size 12{S} {} . Since electrons are charged, their intrinsic spin creates an intrinsic magnetic field     B int size 12{B rSub { size 8{"int"} } } {} , which interacts with their orbital magnetic field B orb size 12{B rSub { size 8{"orb"} } } {} . Furthermore, electron intrinsic spin is quantized in magnitude and direction , analogous to the situation for orbital angular momentum. The spin of the electron can have only one magnitude, and its direction can be at only one of two angles relative to a magnetic field, as seen in [link] . We refer to this as spin up or spin down for the electron. Each spin direction has a different energy; hence, spectroscopic lines are split into two. Spectral doublets are now understood as being due to electron spin.

Image a shows a magnified view of two spectral lines. The magnified view shows that these spectral lines are doublets, which means two parallel lines being placed together. In image b a structure in which concentric waves are expanding out is shown.
Fine structure. Upon close examination, spectral lines are doublets, even in the absence of an external magnetic field. The electron has an intrinsic magnetic field that interacts with its orbital magnetic field.
The image shows two cases of intrinsic magnetic field of an electron due to its spin. In the first case, circular orbit is shown with external magnetic field in the vertical direction and the direction of the intrinsic magnetic field of electron due to its spin is upwards at an angle of fifty four point seven degrees with the vertical axis. In the second case, circular orbit is shown with external magnetic field in the vertical direction and the direction of the intrinsic magnetic field of electron due to its spin is downwards at an angle of fifty four point seven degrees with the vertical axis.
The intrinsic magnetic field B int size 12{B rSub { size 8{"int"} } } {} of an electron is attributed to its spin, S size 12{S} {} , roughly pictured to be due to its charge spinning on its axis. This is only a crude model, since electrons seem to have no size. The spin and intrinsic magnetic field of the electron can make only one of two angles with another magnetic field, such as that created by the electron’s orbital motion. Space is quantized for spin as well as for orbital angular momentum.

These two new insights—that the direction of angular momentum, whether orbital or spin, is quantized, and that electrons have intrinsic spin—help to explain many of the complexities of atomic and molecular spectra. In magnetic resonance imaging, it is the way that the intrinsic magnetic field of hydrogen and biological atoms interact with an external field that underlies the diagnostic fundamentals.

Section summary

  • The Zeeman effect—the splitting of lines when a magnetic field is applied—is caused by other quantized entities in atoms.
  • Both the magnitude and direction of orbital angular momentum are quantized.
  • The same is true for the magnitude and direction of the intrinsic spin of electrons.

Conceptual questions

What is the Zeeman effect, and what type of quantization was discovered because of this effect?

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Questions & Answers

Why is there no 2nd harmonic in the classical electron orbit?
Shree Reply
how to reform magnet after been demagneted
Inuwa Reply
A petrol engine has a output of 20 kilowatts and uses 4.5 kg of fuel for each hour of running. The energy given out when 1 kg of petrol is burnt is 4.8 × 10 to the power of 7 Joules. a) What is the energy output of the engine every hour? b) What is the energy input of the engine every hour?
Morris Reply
what is the error during taking work done of a body..
Aliyu Reply
what kind of error do you think? and work is held by which force?
I am now in this group
theory,laws,principles and what-a-view are not defined. why? you
Douglas Reply
A simple pendulum is used in a physics laboratory experiment to obtain an experimental value for the gravitational acceleration, g . A student measures the length of the pendulum to be 0.510 meters, displaces it 10 o from the equilibrium position, and releases it. Using a s
Emmanuel Reply
so what question are you passing across... sir?
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed?
Emmanuel Reply
54 joule
Reduce that two body problem into one body problem. Apply potential and k. E formula to get total energy of the system
i dont think dere is any potential energy... by d virtue of no height present
there is compressed energy,dats only potential energy na?
yes.. but... how will u approach that question without The Height in the question?
Can you explain how you get 54J?
Because mine is 36J
got 36J too
OK the answer is 54J Babar is correct
Conservation of Momentum
woow i see.. can you give the formula for this
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed? Asume there is no external force.
Emmanuel Reply
Please help!
please help find dy/dx 2x-y/x+y
By using the Quotient Rule dy/dx = 3y/(x +y)²
may be by using MC^2=MC^2 and Total energy=kinetic energy +potential energy so 1st find kinetic energy and den find potential energy which is stored energy
i think i m correct
But how?
what's the big bang?
kwame Reply
yes what is it?
it is the explanation of how the universe began
it is a theory on how the universe began. to understand more I would suggest researching the topic online.
thanks guys
if a force of 12N is applied to load of 200g what us the work done
Joshua Reply
We can seek accelation first
we are given f=12 m=200g which is 0.2kg now from 2nd law of newton a= f/m=60m/s*2 work done=force applied x displacement cos (theta) w= 12x60 =720nm/s*2
this very interesting question very complicated for me, í need urgent help. 1,two buses A and B travel along the same road in the same direction from Harper city (asume They both started from the same point) to Monrovia. if bus A maintains a Speedy of 60km/h and bus B a Speedy of 75km/h, how many
hours Will it take bus B to overtake bus A assuming bus B starts One hour after bus A started. what is the distance travelled by the buses when They meet?.
pls í need help
4000 work is done
speed=distance /time distance=speed/time
now use this formula
what's the answer then
great Mudang
please Ana explain 4000 ?
hey mudang there is a product of force and acceleration not force and displacement
@Mohammed answer is 0.8hours or 48mins
its not possible
í want the working procedure
the answer is given but how Will One arrive at it. the answers are 4hours and 300m.
physics is the science that studies the non living nature
isidor Reply
ancient greek language physis = nature
what is phyacs
technical Reply
if i am going to start studying physics where should i start?
I think from kinematics
You can find physics books at the library or online. That's how I started.
And yes, kinematics is usually where you can begin.
study basic algebra and calculus and can start from classical mechanics
yes think so but dimension is the best starting point
3 formula's of equations of motion
benjamin Reply
vf=vi+at........1 s=vit+1/2(at)2 vf2=vi2+2as
solve the formula's please
those are the three .. what you wanna solve ?
For first equation simply integrate formula of acceleration in the limit v and u
For second itegrate velocity formula by ising first equation
similarly for 3 one integrate acceleration again by multiplying and dividing term ds
any methods can take to solve this eqtions
a=vf-vi/t vf-vi=at vf=vi+at......1
suppose a body starts with an initial velocity vi and travels with uniform acceleration a for a period of time t.the distance covered by a body in this time is "s" and its final velocity becomes vf
what is the question dear
average velocity=(vi+vf)/2 distance travelled=average velocity ×time therefore s=vi+vf/2×t from the first equation of motion ,we have vf =vi+at s=[vi+(vi+at)]/2×t s=(2vi+at)/2×t s=bit+1/2at2
find the distance
Two speakers are arranged so that sound waves with the same frequency are produced and radiated through a room. An interference pattern is created. Calculate the distance between the two speakers?
Hayne Reply
How can we calculate without any information?
I think the formulae used for this question is lambda=(ax)/D
Practice Key Terms 7

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