Taking a closer look at LHC

Electronvolt, unit for energy denoted by eV, is used for small energies.

 1 electron-Volt

eV is defined as the amount of energy equivalent to that gained by a single unbound electron (or proton) when it is accelerated through an electrostatic potential difference of one volt, in vacuo

So, a 1,5 V battery provides to each electron an energy of 1.5 eV. Or the CRT of a TV set provides ~ 20 keV.


1 eV = 1.602·10-19 Joule

1 MeV = 106 eV

1 GeV = 109 eV

1 TeV = 1012 eV


Energies at CERN .....


Linac   50 MeV

(Linac4  160 MeV)


PSB    1.4  GeV


PS      25  GeV


SPS   450 GeV


LHC   7 TeV



So, each proton reaches 7 TeV energy while moving in LHC accelerator.

They would be needed 350 millions "connected" TV sets (~20 keV) to reach that energy.

Taking a 12 cm accelerator section in the TRC, we have a very special complex accelerator:

0.12 x 350·10 ~ 40·10m (40000 km !).

"Our accelerator" should be placed on the Equator line.

So, is the CERN's accelerator complex so big?


We can also consider a common 1,5 V battery.

ELHC / EBattery = 4.7×1012.

Taking the its 5 cm size:

4.7×1012×0,05  ~  2.3·1011 m (230 million km!).

The average distance between the Sun and the Earth is 149 million kilometers.

We can calculate the necessary orbit to cover that length:

2.3·1011 /2π

orbital radius =3.7·1010 m

So, about 100 times de Moon's orbital radius.

Definitely, LHC is not too big !!!


Mass Unit

From the equivalence between mass and energy the unit used is eV/c2 and their multiples MeV/c2 or GeV/c2 .

(1 atomic mass unit - 1 u = 0,9315 GeV/c2)

For instance:

electron mass= 0,5110 MeV/c2

proton mass= 0,9383 GeV/c2

neutron mass= 0,9396 GeV/c2

But for shortness, using the so-called "natural units" (c = 1), it is wrtitten eV ( or MeV or GeV) only, giving for sure that who reads knows how the equivalence works.


Xabier Cid Vidal, PhD in experimental Particle Physics for Santiago University (USC). Research Fellow in experimental Particle Physics at CERN from January 2013 to Decembre 2015. Currently, he is in USC Particle Physics Department (Spanish Postdoctoral Junior Grants Programme).

Ramon Cid Manzano, secondary school Physics Teacher at IES de SAR (Santiago - Spain), and part-time Lecturer (Profesor Asociado) in Faculty of Education at the University of Santiago (Spain). He has a Degree in Physics and in Chemistry, and is PhD for Santiago University (USC).



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