(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 to of the electron, i.e., its `e//m` is given to `1.76xx10^(11)Ckg^(-1)`.
(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?

Explanation

(a) Here, `V=500V , e//m=1.76xx10^(11)Ckg^(-1) , v=?`
As `eV=1/2mv^(2) or v=[(2eV)/m]^(1//2) =[2xx(1.76xx10^(11))xx500]^(1//2)=1.326xx10^(7)ms^(-1)`
(b) For `V=10MV=10^(7)V, v=[2xx1.76xx10^(11)xx10^(7)]^(1//2)=1.8762xx10^(9)ms^(-1)`
As this speed is greater than the speed of light, so this speed is not possible, because as v approaches c, mass of electron becomes infinite`[ :' m=(m_(0))/(sqrt(1-v^(2)//c^(2)))]`, so the formula has to be modified.