An electron of mass 9. 1 x 10\(^{-31}\) kg moves with a velocity of 4.2 x 10 ms\(^{-1}\) between the cathode and anode of an x-ray tube. Calculate the wavel...
Question 1 Report
An electron of mass 9. 1 x 10\(^{-31}\) kg moves with a velocity of 4.2 x 10 ms\(^{-1}\) between the cathode and anode of an x-ray tube. Calculate the wavelength. (Take Planck's constant h = 6.6 x 10\(^{-34}\) J S)
Answer Details
The wavelength associated with a moving electron is the de Broglie wavelength
\[ \lambda = \frac{h}{mv}, \]where \(h = 6.6\times10^{-34}\ \text{J s}\), \(m = 9.1\times10^{-31}\ \text{kg}\) and \(v = 4.2\times10^{7}\ \text{m s}^{-1}\) (the electron speed in an x-ray tube).
\[ mv = 9.1\times10^{-31} \times 4.2\times10^{7} = 3.82\times10^{-23}\ \text{kg m s}^{-1}. \] \[ \lambda = \frac{6.6\times10^{-34}}{3.82\times10^{-23}} = 1.73\times10^{-11}\ \text{m}. \]Wavelength \(\approx 1.7\times10^{-11}\ \text{m}\) (about \(0.017\ \text{nm}\)), which lies in the X-ray region.
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