CERN brochures:

Information booklet for teachers

WG Leader: Antonella del Rosso

LHC and educational activity

 

The Large Hadron Collider (LHC) is a particle accelerator. This accelerator is being built in CERN. Hopefully it will work in 2006. This new accelerator will be installed into the same tunnel as the Large Electron-Positron collider operated before. The circular underground tunnel is 27 km long. Two proton beams will be accelerated to 7 TeV in the opposite directions to collide with each other. Superconducting magnets keep the proton beams on track. Four huge detectors will be built to detect the collision events. 

 

A possible activity for the theme LHC:

The aim of the activity is:

·        to practice the concept of the electronvolt (eV),

·        to determine the collision energy of two accelerated protons in the LHC,

·        to point out, that this energy is not too large,

·        to determine the velocity of some macroscopic object, whose energy is the same,

·        to determine the volume of a proton and a chosen macroscopic object,

·        to determine the energy volume density in both cases,

·        to take the ratio of the two energy densities, and discuss the obtained result,

·        to show how large number is it, using an example with linear dimension

 

To practice the concept of the electronvolt (eV):

·        If a charge Q passes through a potential difference U the work done by the field on the charge is W = Q U

·        If the charge is just an electron Q = 1.6 10- 19 C, and the potential difference is U = 1 V, then the work is W = Q U = 1.6 10-19 J.

 

To determine the collision energy of two accelerated protons in the LHC:

·        Determine the energy of the collision, if both proton is accelerated to 7 TeV, that is E = 14 TeV

·        1 keV = 103 eV

·        1 MeV = 106 eV

·        1 GeV = 109 eV

·        1 TeV = 1012 eV

·        E = 14 TeV = 14 1012 1.6 10-19 = 2.24 10-6 J

 

To point out, that this energy is not too large:

·        This energy is not too large, precisely saying it is very very small if this energy is possessed by a macroscopic object

 

To determine the velocity of some macroscopic object, whose energy is the same:

·        Consider four different macroscopic objects with masses

·        Dust m0 = 10-6 kg

·        Fly m1 = 10-3 kg

·        Small block m3 = 1 kg

·        Car m4 = 103 kg

·        So one object has the half of the energy above Ehalf = 1.12 10-6 J

·        We can apply the classical kinetic energy formula, as , and solving the equation for vi we can obtain .

·        For the different macroscopic object the velocities respectively are:

·        Dust v0 = 1.5 m/s

·        Fly v1 = 4.73 10-2 m/s

·        Small block v2 = 1.5 10-3 m/s

·        Car v3 = 4.73 10-5 m/s

 

To determine the volume of a proton and a chosen macroscopic object:

·        As we know the radius of a proton is rp ~ 0.7 10-15 m, so its volume is , that is Vp = 1.44 10-45 m3.

·        Choose the macroscopic object to be this slowly flying fat fly, whose dimensions are 3 mm x 3 mm x 5 mm, that is its volume is V1 = 4.5 10-8 m3.

 

To determine the energy volume density in both cases:

·        Now we can already determine the energy volume density in the place of the collision, in both cases:

·        In case of the proton , that is rp = 7.78 1038 J/m3.

·        In case of the slowly flying fly r1 = 2.49 101 J/m3.

·        So we have already got the answer for the question, why the LHC is being built!!!

 

To take the ratio of the two energy densities, and discuss the obtained result:

·        Take the ratio of the two energy densities as , inserted the numerical values the result: n » 3 1037.

·        This is a huge number. So we can understand that the energy produced by the Large Hadron Collider is very small, but it is concentrated into the very tiny space, where the two protons collide.

·        Some part of this energy will be materialized  ( E = m c2 ).

 

To show how large number is it, using an example with linear dimension:

·        A man could not imagine a number which is greater than 1 million that is 106.

·        To imagine such a huge number, a comparison would be helpful.

·        Consider first the size of the known universe, it is about 1026 m, and the size of an atom, is about 10-10 m, and compare them, that is take their ratio.

·        The obtained number is only 1036, one can see that it is only the tenth part of the huge number above.