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 1.6 % of the speed of light when they hit the target?

Express your answer in volts to two significant figures

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

Express your answer in volts to two significant figures.

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

Express your answer in meters per second to two significant figures.

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

Express your answer to two significant figures.

Explanation / Answer

A) 1.6% of the speed of light is 4.8 * 10^6 m/s.The electrons will gain a kinetic energy given by
KE = (1/2) m v^2
The mass of an electron is given as 9.11 * 10^-31 Kg. So
KE = (1/2) * 9.11 * 10^-31 * (4.8 * 10^6)^2 = 1.05 * 10^-17 J

Now 1eV = 1.6 * 10^-19 J
So, dividing the KE by eV will tell us how many volts the electron was accelerated by.
V = 1.05 * 10^-17 / 1.6 * 10^-19 = 65.63 V

B) Since the magnitude of the charge on a proton is the same as that on an electron, the same potential difference gives the same KE. So the potential is 65.63 V

C) This potential would give the protons an energy of 65.63 * 1.6 * 10^-19 = 105 * 10^-19 J
The KE of the proton would therefore be 105* 10^-19 J. So
105* 10^-19 = (1/2) m v^2
the mass of a proton is 1.67 * 10^-27 kg. So
v^2 = (2 * 105 * 10^-19) / (1.67 * 10^-27) =125.74 * 10^8
v = 11.21 * 10^4 m/s

D) 0.037%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.