What is electron spin and intrinsic spin of elementary particles?

In summary: This equation has a few terms, one of which is the angular momentum operator. The angular momentum operator has an intrinsic component (spin) and an extrinsic component (the linear momentum). The intrinsic component is always quantized, just like the electric and magnetic fields.The linear momentum is always quantized, but the intrinsic component can only have certain specific values. These values are determined by the value of l, which is an integer.The equation for quantizing the angular momentum operator is similar to the equation for quantizing the electric and magnetic fields:| \vec L | = L = \sqrt{l(l+1)} \hbarThe difference is that the electric and magnetic fields have a magnitude that can take on any value
  • #1
anantchowdhary
372
0
What exactly is electron spin and intrinsic spin of elementary particles.Any link teaching these concepts from scratch would also be appreciated .

Thnx
 
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  • #3
Sorry still haven't understood at all!

What is the quantum number?
 
  • #4
All of the quantum mechanics of spin originates with the operator for angular momentum (remember the components of angular momentum come from a cross product p x r).
 
  • #5
anantchowdhary said:
Sorry still haven't understood at all!

OK, let's go backwards a bit. How much do you know about angular momentum in classical mechanics? Do you know about how to represent angular momentum as a vector?
 
  • #6
I just about know that L=r X p

where p is linear momentum and r is the displacement position vector
 
  • #7
OK, that's what we use for orbital angular momentum, like the Earth going around the sun. The cross product gives you a vector that's perpendicular to the plane of the orbit. In QM, the vector [itex]\vec L[/itex] is quantized, both in magnitude and in direction. The magnitude is quantized according to

[tex]| \vec L | = L = \sqrt{l(l+1)} \hbar[/tex]

where [itex]l[/itex] is an integer 0, 1, 2, 3... Furthermore, the component of [itex]\vec L[/itex] along any direction is quantized. Usually we talk about the z-direction but it can actually be any direction. After you've chosen the value of [itex]l[/itex], then

[tex]L_z = m_l \hbar[/tex]

where [itex]m_l[/itex] can have values ranging from [itex]-l[/itex] to [itex]+l[/itex] in steps of 1. For example, if [itex]l = 2[/itex], then the possible values of [itex]m_l[/itex] are -2, -1, 0, +1, +2.

Something like the Earth also has spin angular momentum, from spinning around its own axis. We can describe this with a vector [itex]\vec S[/itex] that points along the axis of rotation. Even though particles like electrons actually aren't little tiny spinning balls, they still have intrinsic angular momentum which we often call "spin," and we use the vector [itex]\vec S[/itex] for it.

The rules for quantizing [itex]\vec S[/itex] are similar to the rules for quantizing [itex]\vec L[/itex]:

[tex]| \vec S | = S = \sqrt{s(s+1)} \hbar[/tex]

[tex]S_z = m_s \hbar[/tex]

where [itex]m_s[/itex] can have values ranging from [itex]-s[/itex] to [itex]+s[/itex] in steps of 1. The differences from orbital angular momentum are:

1. [itex]l[/itex] must be an integer, but [itex]s[/itex] can be either integer or half-integer.

2. For a particular particle (e.g. electron) [itex]l[/itex] and/or [itex]m_l[/itex] can change when its "orbit" changes, but [itex]s[/itex] is always the same for a particular kind of particle. For example, all electrons have [itex]s = 1/2[/itex], and so they must have [itex]m_s = -1/2[/itex] ("spin down") or [itex]m_s = +1/2[/itex] ("spin up").

However, [itex]m_s[/itex] can change. With the right circumstances, we can "flip" an electron's spin from [itex]m_s = -1/2[/itex] to [itex]m_s = +1/2[/itex] or vice versa.
 
  • #8
sry I am not clear with the equation [tex]| \vec L | = L = \sqrt{l(l+1)} \hbar[/tex]

What do you mean by quantizing [itex]\vec L[/itex] ?

The help was much appreciated.Thnx
 
  • #9
The magnitude of [itex]\vec L[/itex] (which we usually write as just [itex]L[/itex]) can have only certain specific values, corresponding to the allowed values of [itex]l[/itex]. For example, [itex]l = 0[/itex] gives [itex]L = 0[/itex]; [itex]l = 1[/itex] gives [itex]L = \sqrt{2} \hbar[/itex]; [itex]l = 2[/itex] gives [itex]L = \sqrt{6} \hbar[/itex]; etc.
 
  • #10
That seems fairly easy to follow, what is the difference with anti matter particles like a positron, do they spin in the opposite direction ie they go towards the other half of the circle? Or do they just spin in an opposite direction, starting at an opposite position, sorry if this is a stupid question.
 
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  • #11
No, spin is not one of the things that's "opposite" for an antiparticle. For example, an electron can already have its spin either "up" or "down" along a given axis, and likewise for a positron.
 
  • #12
I just would like to know how the equation: [tex]| \vec L | = L = \sqrt{l(l+1)} \hbar[/tex] came into being.

and why is the spin defined in such a way?
 
  • #13
jtbell said:
No, spin is not one of the things that's "opposite" for an antiparticle. For example, an electron can already have its spin either "up" or "down" along a given axis, and likewise for a positron.

I see, so it's just the charge that is reversed? e+ e- the spin is the same or can be the same according to an axis, thanks.
 
  • #14
Why is the spin defined in such a way?How do we get the equation?
 
  • #15
anantchowdhary said:
Why is the spin defined in such a way?How do we get the equation?
Orbital angular momentum falls out when the Schrödinger Wave Equation is solved for a Hydrogen atom.
 

1. What is electron spin?

Electron spin is a fundamental characteristic of an electron, which is a subatomic particle with a negative charge. It is a type of angular momentum that is intrinsic to the electron and does not arise from its motion around the nucleus. Electron spin is one of the quantum numbers that describes an electron's state in an atom.

2. What is intrinsic spin of elementary particles?

Intrinsic spin is a fundamental property of elementary particles, which are the building blocks of matter. It refers to the spin that is inherent to a particle and cannot be explained in terms of its motion or composition. Intrinsic spin is quantized, meaning it can only have certain discrete values, and it is a crucial factor in determining the behavior and interactions of particles.

3. How is electron spin different from orbital angular momentum?

Electron spin and orbital angular momentum are both types of angular momentum, but they describe different aspects of an electron's motion. Orbital angular momentum is associated with the motion of an electron around the nucleus, while electron spin is an intrinsic property of the electron itself. Additionally, electron spin can only have two possible values (up or down), while orbital angular momentum can have multiple values.

4. Why is electron spin important in chemistry?

Electron spin is important in chemistry because it influences the way electrons behave and interact with each other. The spin of an electron affects its energy level and the bonding between atoms. It also plays a role in determining the magnetic properties of materials. Understanding electron spin is crucial for predicting and explaining chemical reactions and properties of substances.

5. Can the spin of an electron change?

Yes, the spin of an electron can change, but only under specific circumstances. According to the laws of quantum mechanics, the spin of an electron can flip from "up" to "down" or vice versa when it interacts with other particles or an external magnetic field. However, the spin of an electron is a conserved quantity, meaning that the total spin of a closed system remains constant, so any change in the spin of one electron must be balanced by an opposite change in another particle's spin.

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