When would they accelerate protons and neutrons at the speed of the light at CERN?

Question

CERN(the world's largest particle physics laboratory)

Answer 1

Not gonna happen.  It has been known for some time now, that no accelerator will ever be able to accelerate baryonic particles to the speed of light.  This is not due to technological limitations.  It's a kind of cosmic absolute.

It went something like this.  With X megavolts they were able to accelerate a particle to 0.9 light speed.  With X gigavolts they were able to accelerate it to 0.9999 light speed.  For each factor of ten that the power is increased, the speed increases only by adding another 9 to the decimal.  (Or thereabouts.)  It's asymptotic.  You can't ever reach light speed.

Answer 2

The latest and greatest accelerator is called the Large Hadron Collider (or LHC for short), and according to wikipedia, "The collider is currently undergoing commissioning while being cooled down to its final operating temperature of approximately 1.9 K (−271.25 °C). The first particle beams are due for injection in August 2008, with the first collisions planned to take place about two months later."

The particles will not be accelerated to the speed of light though, but very very close to it. It is in fact impossible to accelerate a particle to the speed of light, as it would require infinite energy.