De Broglie wavelength and diffraction

[josephcollins]

Hi ppl I have a short question concerning the de Broglie hypothesis. I worked out the de Broglie wavelength of an electron in a TV picture tube accelerated by 20,000 V, using the fact that mv^2/2 = QV and then that lambda=h/mv. Now I need to answer whether this is relativistic or not, how do I do this? and then the neck of the tube is 5cm and I'm asked whether we have to worry about diffracttion blurring the picture on the screen. The wavelength is obviously much smaller than the neck of the tube, so diffraction will occur, will this then affect the picture? Thanks for any help, Joe

 

[masudr]

To check whether or not your calculations take relativity into account, first check to see if v is close to c. If it is then the energy is not given by 1/2*mv^2.

Secondly the neck of the tube has to be of the same order as the wavelength for diffraction to occur.