An x-ray tube is an evacuated glass tube that produces electrons at one end and

Question

An x-ray tube is an evacuated glass tube that produces electrons at one end and then accelerates them to very high speeds by the time they reach the other end. The acceleration is accomplished using an electric field. The high-speed electrons hit a metal target at the other end, and the violence of the collision converts their kinetic energy into high-energy light rays, commonly known as x-rays.

A. through what potential difference should electrons be accelerated so that their speed is 2.1 % of the speed of light when they hit the target?

B. What potential difference would be needed to give protons the same kinetic energy as the electrons?

C. What speed would this potential difference give to protons?

D. Express the speed calculated in Part C as a percentage of the speed of light.

Explanation / Answer

A)

W = 0.5*m*v^2

v = 0.021c = 0.021*3*10^8

W = V*q

V*q = 0.5*m*v^2

V*1.6*10^-19 = 0.5*9.11*10^-31*(0.021*3*10^8)^2

v = 113 V

(B)

Ke = Kp

0.5*me*ve^2 = 0.5*mp*vp^2

W = Kp = Ke

V*1.6*10^-19 = 0.5*9.11*10^-31*(0.021*3*10^8)^2

v = 113 v

(C)

0.5*me*ve^2 = 0.5*mp*vp^2

vp = ve*sqrt(me/mp)

vp = 0.021*3*10^8*sqrt((9.11*10^-31)/(1.67*10^-27))

vp = 1.47*10^5 m/s

D)

vp = vp/c *100 =((1.47*10^5)/(3*10^8))*100 = 0.049 %

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