Protons in an accelerator at the fermi national laboratory near chicago are accelerated to a total energy that is 400 times their rest energy.
(a) what is the speed of these protons in terms of c?
(b) what is their kinetic energy in mev?

(a) 0.99999687c

The relationship between total energy (E) and rest energy () is

where is the relativistic factor. In this problem, we know that the total energy is 400 times the rest energy: this means that

The formula for the relativistic factor is

where v is the speed of the proton and c is the speed of light. By isolating the term v/c, we find the speed of the protons in terms of c:

(b)

Given the rest mass of a proton:

its rest energy is the energy equivalent to this mass:

The protons in the Fermi Laboratory have energy that is 400 times their rest energy, so their total energy is

The total energy is also sum of rest energy and kinetic energy:

So the kinetic energy is

And since the conversion factor is

This kinetic energy converted into MeV () is

32: from largest to smallest, this hierarchy includes eons, eras, periods, epochs, and ages.

33: answer is c

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answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.