Speed difference between protons & heavy-ions in LHC?

In summary, the Large Hadron Collider (LHC) has protons traveling at 0.999999991 times the speed of light (c), which is about 3 meters per second slower than c. Heavy-ions (Pb-Pb) collisions at the LHC have a center of mass energy of 2.76 TeV per nucleon pair and are accelerated to 99.9999% of the speed of light, resulting in a velocity of 299.792.158 m/s, which is 300 m/s slower than c. Gravitational assistance has a negligible impact on the speed of heavy-ions compared to protons due to their significantly higher mass.
  • #1
Michel_vdg
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1
On the wiki-pages it says that in the LHC protons travel 3m/s slower than c.

I was curious what it would be for heavy-ions; is it maybe 15m/s because their energy is ~5 x lower (7 vs. 2.76 Tev) ?

And a small question on the side, does Gravitation assistance have a bigger impact on speeding up Heavy-ions- vs. Proton-cosmic rays since they are more massive, or is gravitation assistance something negligible for particles moving so close to the speed of light?

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protons have an energy of 7 TeV ... total collision energy of 14 TeV ... move at about 0.999999991 c, or about 3 meters per second slower than the speed of light (c)

https://en.wikipedia.org/wiki/Large_Hadron_Collider

heavy-ion (Pb-Pb) collisions at a center of mass energy of 2.76 TeV per nucleon pair ... accelerated to 99.9% of the speed of light
https://en.wikipedia.org/wiki/ALICE:_A_Large_Ion_Collider_Experiment
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  • #2
Well, the answer is in your question -
Michel_vdg said:
heavy-ion (Pb-Pb) collisions at a center of mass energy of 2.76 TeV per nucleon pair ... accelerated to 99.9% of the speed of light

0.999 *c = 2.995 * 10^8 m/s

vs

0.999999991*c = 2.99792455×10^8 m/s

So about 292455 m/s different.

ETA: Another way to do it: ##E_k = (\gamma -1 ) m c^2##. So if you know the energy, you know the velocity. But you can already see that 3 times less energy doesn't lead to "three times fewer c-v (m/s)"
 
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  • #3
e.bar.goum said:
Well, the answer is in your question -0.999 *c = 2.995 * 10^8 m/s

vs

0.999999991*c = 2.99792455×10^8 m/s

So about 292455 m/s different.

Alright, thanks.

mh, I just thought that the 99,9% for the ions was rounded off, cause on the wiki page of RHIC it says (but the write typically and p's are included in the list):

"To date the types of particle combinations explored at RHIC are p + p, d + Au, h + Au, Cu + Cu, Cu + Au, Au + Au and U + U. The projectiles typically travel at a speed of 99.995% of the speed of light."
https://en.wikipedia.org/wiki/Relativistic_Heavy_Ion_Collider

e.bar.goum said:
ETA: Another way to do it: ##E_k = (\gamma -1 ) m c^2##. So if you know the energy, you know the velocity. But you can already see that 3 times less energy doesn't lead to "three times fewer c-v (m/s)"

What does ##\gamma## production mean?
 
  • #4
Michel_vdg said:
Alright, thanks.

mh, I just thought that the 99,9% for the ions was rounded off, cause on the wiki page of RHIC it says (but the write typically and p's are included in the list):

"To date the types of particle combinations explored at RHIC are p + p, d + Au, h + Au, Cu + Cu, Cu + Au, Au + Au and U + U. The projectiles typically travel at a speed of 99.995% of the speed of light."
https://en.wikipedia.org/wiki/Relativistic_Heavy_Ion_Collider
What does ##\gamma## production mean?

##\gamma## in this context is the relativistic quantity ##\frac{1}{\sqrt{1-v^2/c^2}}##

If you're worried about rounding errors, you can do it the long way. The energy of the beam is 2.76 TeV per nucleon pair, so the kinetic energy of one lead ion will be 2.76 TeV * 208/2 = 287 TeV.

Now, if you know that ##E = (\frac{1}{\sqrt{1-v^2/c^2}} -1 )m*c^2##, and you know the Energy, ## E## and you can google the rest mass of lead, it's just a matter of solving for ##v## and substituting in ##E##, ##m## and ##c##. I'll let you do that. :wink:
 
  • #5
99.9% was a bad rounding error, fixed now.
The difference to the speed of light is more than 15 m/s, but still in the speed range of cars and trains.
 
  • #6
e.bar.goum said:
I'll let you do that. :wink:

Thanks ... but solving mfb's reply is slightly faster : )

mfb said:
99.9% was a bad rounding error, fixed now.
The difference to the speed of light is more than 15 m/s, but still in the speed range of cars and trains.

So it says now 99.9999% on the Alice wiki-page, this gives:

c = 299.792.458 m/s

Protons: 99.9999991% c = 0.999999991 c = 299.792.455
299.792.458 - 299.792.455 = 3 m/s slower

Heavy-ions: 99.9999% c = 0.999999 c = 299.792.158
299.792.458 - 299.792.158 = 300 m/s slower

btw the fastest train is a Maglev (magnetic levitation) train with 603 km/h = 167,5 m/s
 
  • #7
No, it says "more than 99.9999%". That way it is true for both 2013 and 2015. Without a calculation you can just tell that the difference is below 300 m/s.
 

FAQ: Speed difference between protons & heavy-ions in LHC?

1. What is the difference in speed between protons and heavy-ions in the Large Hadron Collider (LHC)?

The speed difference between protons and heavy-ions in the LHC depends on the energy of the particles. Generally, protons travel at higher speeds compared to heavy-ions due to their smaller mass. However, when heavy-ions are accelerated to higher energies, they can reach speeds that are comparable to protons.

2. Why are protons and heavy-ions used in the LHC instead of other particles?

Protons and heavy-ions are used in the LHC because they are the most commonly available and easily accelerated particles. They are also stable and have a high charge-to-mass ratio, making them ideal for colliding at high energies to study the fundamental particles and forces of the universe.

3. How do the speed differences between protons and heavy-ions affect the collisions in the LHC?

The speed difference between protons and heavy-ions does not significantly affect the collisions in the LHC. The particles are accelerated to near the speed of light, resulting in high energies and momentum, regardless of their individual speeds.

4. Can the speed difference between protons and heavy-ions in the LHC be measured?

Yes, the speed difference between protons and heavy-ions can be measured using various detectors in the LHC. These detectors can track the trajectories of the particles and calculate their velocities, allowing for the comparison of speeds between different particles.

5. Are there any advantages to using heavy-ions instead of protons in the LHC?

Yes, there are some advantages to using heavy-ions instead of protons in the LHC. Heavy-ions have a higher mass, which allows for the creation of higher-energy collisions and the production of heavier particles. This can provide valuable insights into the behavior of matter at extreme energies.

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