| Quantum Mechanics for Engineers | | © Leon van Dommelen |
5.4 Spin
At this stage, it becomes necessary to look somewhat closer at thevarious particles involved in quantum mechanics themselves. Theanalysis so far already used the fact that particles have a propertycalled mass, a quantity that special relativity has identified asbeing an internal amount of energy. It turns out that in additionparticles have a fixed amount of build-in
angularmomentum, called spin.
Spin reflects itself, forexample, in how a charged particle such as an electron interacts witha magnetic field.
To keep it apart from spin, from now on the angular momentum of aparticle due to its motion will on be referred to asorbital
angular momentum. As was discussed in chapter4.2, the square orbital angular momentum of a particle isgiven by
where the azimuthal quantum number
is a nonnegative integer.
The square spin angular momentum of a particle is given by a similarexpression:
| (5.14) |
but the “
spin
” is a fixed number for a given type of particle. Andwhile
can only be an integer, the spin
can be any multiple ofone half.
Particles with half integer spin are called “fermions.” For example, electrons, protons, and neutrons allthree have spin and are fermions.
Particles with integer spin are called “bosons.” For example, photons have spin 1. The-mesons have spin 0 and gravitons, unobserved atthe time of writing, should have spin 2.
The spin angular momentum in an arbitrarily chosen -direction is
| (5.15) |
the same formula as for orbital angular momentum, and the values of
range again from
to
in integer steps. For example,photons can have spin in a given direction that is
, 0,or
. (The photon, a relativistic particle with zerorest mass, has only two spin states along the direction ofpropagation; the zero value does not occur in this case. But photonsradiated by atoms can still come off with zero angular momentum in adirection normal to the direction of propagation. A derivation is inaddendum {
A.21.6} and {
A.21.7}.)
The common particles, (electrons, protons, neutrons), can only havespin angular momentum or in any givendirection. The positive sign state is called “spin up”, the negative one “spin down”.
It may be noted that the proton and neutron are not elementaryparticles, but are baryons, consisting of three quarks. Similarly,mesons consist of a quark and an anti-quark. Quarks have spin, which allows baryons to have spin or. (It is not self-evident, but spin values can beadditive or subtractive within the confines of their discreteallowable values; see chapter 12.) The same way, mesonscan have spin 1 or 0.
Spin states are commonly shown in “ket notation” as . For example, the spin-upstate for an electron is indicated by and the spin-down stateas . More informally, and are often used.
Key Points
- Most particles have internal angular momentum called spin.
- The square spin angular momentum and its quantum number are always the same for a given particle.
- Electrons, protons and neutrons all have spin . Their spin angular momentum in a given direction is either or .
- Photons have spin one. Possible values for their angular momentum in a given direction are , zero, or , though zero does not occur in the direction of propagation.
- Particles with integer spin, like photons, are called bosons. Particles with half-integer spin, like electrons, protons, and neutrons, are called fermions.
- The spin-up state of a spin one-half particle like an electron is usually indicated by or . Similarly, the spin-down state is indicated by or .
5.4 Review Questions
- 1.
Delta particles have spin . What values can their spin angular momentum in a given direction have?
Solution spin-a
- 2.
Delta particles have spin . What is their square spin angular momentum?
Solution spin-b
FAQs
The second generation 5.4L, produced from 2004 to 2014, has three valves per cylinder. This one has several problems, some of which are related to inadequate oiling. Upon tearing apart failing engines, mechanics discovered the buildup of sludge and debris clogging the oil passages, particularly in the cylinder heads.
How much HP can a 5.4 Triton make? ›
The 4-valve Ford 5.4 Triton engine was designed to be used in some of Ford's high-performance cars and some iterations are made as high as 550 HP. Unsurprisingly, this engine didn't share much with the 2-valve and 3-valve given the intended use.
What is the most common problem with the 5.4 Triton? ›
The most popular issue but easiest to fix, is the ignition system. The 3 valve 5.4L Triton contains a coil-on-plug design. Each cylinder has a separate coil that fits onto the spark plug. The design is very efficient but can lead to excessive heat.
What is the life expectancy of a Ford 5.4 engine? ›
You should be able to get 250,000 miles out of it, assuming that you do the proper maintenance and dont abuse it all the time. My dad had a 99 F250 5.4, 5spd, 4x2. Drove it to 200,000miles. Alot of highway but also a decent bit of pulling.
What year 5.4 are bad? ›
what years should I avoid? The only one to really avoid is the 5.4 3v Triton which was in the F150 from 04-10. The smaller 4.6 Triton doesn't share any of those issues and, while not as fast, is very reliable.
What is the problem with the 5.4 L V8? ›
Problem: The Ford 5.4-liter engine has a record of problematic timing chain guides that wear out prematurely. Repair and Cost: Although the plastic guides are relatively inexpensive, the process of getting to them isn't.
Can a 5.4 Triton be rebuilt? ›
Rebuilt 5.4L Ford 3 valve Triton engines will only correct the issue with the "core" engine used as raw material, but will typically not include any other machining or remanufacturing on the rest of the engine or have any updates performed.
How much HP does a supercharger add to a 5.4 Triton? ›
Edelbrock E-Force Supercharger Kits: 5.0 Coyote & 5.4 Triton
For owners of the 5.4 Triton engine from 2004-2010, these kits elevate power outputs to 478 HP and 504 lb-ft of torque. This boost is partially achieved thanks to Eaton TVS rotors, renowned for their superior airflow capabilities.
Is the 5.4 a 351? ›
The 5.4 Triton engine is considered a modular engine style. It comes in at around 330 CID, which is smaller than the 351 that is typical of 5.7-L vehicles.
What years did the 5.4 have spark plug problems? ›
One of the common issues of the modular platform was its tendency to blow out spark plugs. This issue happened the most on the 5.4 Triton from 1997 to 2003. During this era, the motor commonly powered the F-Series pickups, E-Series vans, and the Expeditions/Navigators.
The last f150 with the 5.4 triton was built in 2010. Good riddance, it had a lot of oil related issues.
What does Triton mean Ford? ›
Triton was just Ford's branded term for the Modular V8 installed in their trucks and vans. This was opposed to their earlier pushrod V8's, their V6es, or their Powerstroke series of Diesel engines (Diesel was not offered in the F150, but was in larger trucks and vans).
What Ford engines last the longest? ›
Diesel engines.
Ford trucks and SUVs with diesel engines will last much longer than their gasoline counterparts. Diesel engines are known for their longevity, frequently surpassing 400,000 miles. There are even reports of a Ford diesel engine making it to 1 million miles.
What year did Ford stop using the Triton engine? ›
Modular engines used in Ford trucks were marketed under the Triton name from 1997–2010 while the InTech name was used for a time at Lincoln and Mercury for vehicles equipped with DOHC versions of the engines.
How many miles will a 2010 F150 5.4 last? ›
A Ford F-150 is expected to last around 200,000 miles when properly cared for. Since the average driver clocks in about 12,000 miles per year, this comes out to roughly 17 years.
Which 5.4 have spark plug problems? ›
One of the common issues of the modular platform was its tendency to blow out spark plugs. This issue happened the most on the 5.4 Triton from 1997 to 2003. During this era, the motor commonly powered the F-Series pickups, E-Series vans, and the Expeditions/Navigators.
Which Ford diesels to stay away from? ›
The 6.4-liter Powerstroke engine was very short-lived. It was put in Ford trucks beginning in 2007 for the 2008 model year and the last production year was 2011 for the 2010 model year. The 6.4 Powerstroke came after the 6.0 Powerstroke, which was widely panned for its problems and poor performance.
What years to stay away from f150? ›
If you want a F-150, but also want to avoid engine problems, then steer away from getting model years 2004-2008, 2010, and 2015-2017.
What Ford truck motors to avoid? ›
If you're considering a used truck with the 5.4 liter Triton V8, especially the 3-valve per cylinder version, it's probably best to assume the worst and set some funds aside for repair or replacement.
”
-
-
,
,
.
.
