Electrons used in radiation therapy are commonly accelerated to a kinetic energy of 6 MeV. a....

Question

Question

Electrons used in radiation therapy are commonly accelerated to a kinetic energy of 6 MeV.

a. What is the ratio of the speed of this 6 MeV electron to the speed of light?

b. What would be the ratio of its speed to the speed of light according to classical mechanics?

science physics

Answer 1

Answer #1

KE = 0.5 m v^2 = 6 MeV = 9.613 x 10^-13 J

0.5 ( 9.1x 10^-31) v^2 = 9.613 x 10^-13

v^2 =2.112 x 10^ 18

v = 1.453 x 10^ 9 m/s

a) ratio = 1.453 x 10^ 9/ 3 x 10^8 = 4.844 apprx

]b) v ( as per classical mechnaics)= v / sqroot ( 1- v^2/c^2)

ratio= v / sqroot ( 1- v^2/c^2) / c = v/ c^2 sqroot ( c^2 - v^2) = ( 1.463 x 10^9)/ ( 9 x 10^ 19) sqroot ( 9 x 10^ 16-2.111x 10^ 18)

= 0.162 x 10^ -27 / sqroot ( 9 - 211) which is extremely low ratio

Answer 2

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