Question

The operator of a linear accelerator tells a tour group that it is used to give protons an energy of 770 MeV .

A) This 770  must refer to the proton's total energy, kinetic energy, or rest energy?

B) What is the value for the proton's total energy?

C) What is the value for the proton's kinetic energy? D) What is the value for the proton's rest energy? E) What is the protons' speed?

Answer 1

Ans. A) This 770  must refer to the proton's kinetic energy.

Ans. B)The value for the proton's total energy = kinetic energy + rest energy

total energy = 46.97*10⁷ ev+  93.95*10⁷ ev

   total energy = 140.92 ev

Ans.C) The value for the proton's kinetic energy

E= 1/2 mc²

where

m= mass of the proton which is equal to 1.672*10^-27 kg

c= speed of light which is equal to 3 *10⁸  m/s

E= 1/2 *1.6726*10^-27 kg* (3*10⁸)²

E= 7.5267* 10^-11 joule

to convert joule intoelectron valts

1 joule = 6.2415 *10¹⁸ ev

so the kinetic energy of portons is 46.97*10⁷ ev

Ans. D) The value for the proton's rest energy

E= mc²

E =1.6726*10^-27 * (3*10⁸)²

E= 15.053 *10^-11 joule

E= 93.95*10⁷ ev

Ans. E)  protons' speed

W= 1/2mv²

where W is the kinematic energy of proton

so

46.97*10⁷ = 1/2 *1.67*10^-27 * V²

V² = 2* 46.97*10⁷/1.67*10^-2

V= [56.26*10³⁴] ^1/2

V= 7.5*10¹⁷ m/s