question_answer 20)

(a) Estimate the speed with which electrons emitted from a heated cathode of an evacuated tube impinge on the anode maintained at a potential difference of 500 V with respect to the cathode. Ignore the small initial speeds of the electrons. The 'specific charge? of the electron i.e., its el m is given to be (b) Use the same formula you employ in (a) to obtain electron speed for an anode potential of 10 MV. Do you see what is wrong ? In what way is the formula to be modified ?  

Answer:

(a) Here, V = 500 V Using or (b) Using the same formula for . Since v is comparable to the velocity of light, the kinetic energy  is not exact relation. The relativistic expression for kinetic energy [i.e. K.E. = c2  must be used, so that = eV, where .