An X-ray tube operates at a potential of 2500 V. If the power of the tube is 750 W, calculate the speed of the electron striking the target. [e = 1.6 x 10\(...
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An X-ray tube operates at a potential of 2500 V. If the power of the tube is 750 W, calculate the speed of the electron striking the target. [e = 1.6 x 10\(^{-19}\) C; mass of electron = 9.1 x 10\(^{-3}\) kg]
Answer Details
Given: accelerating p.d. \(V = 2500\ \text{V}\), \(e = 1.6\times10^{-19}\ \text{C}\), electron mass \(m = 9.1\times10^{-31}\ \text{kg}\). (The mass is taken as \(9.1\times10^{-31}\ \text{kg}\), the standard electron mass; the exponent printed as \(10^{-3}\) is a typographical slip.)
The work done by the accelerating field is converted to kinetic energy of the electron:
\[ eV = \tfrac{1}{2}mv^{2} \] \[ v = \sqrt{\frac{2eV}{m}} = \sqrt{\frac{2(1.6\times10^{-19})(2500)}{9.1\times10^{-31}}} \] \[ v = \sqrt{\frac{8.0\times10^{-16}}{9.1\times10^{-31}}} = \sqrt{8.79\times10^{14}} \] \[ v \approx 2.97\times10^{7}\ \text{m s}^{-1} \]The electron strikes the target at about \(3.0\times10^{7}\ \text{m s}^{-1}\). (The power rating of 750 W is not needed for the speed; it would fix the tube current.)
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