InterviewSolution
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InterviewSolution
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An electron (mass m) with an initial velocity `v=v_(0)hat(i)(v_(0)gt0)` is in an electric field `E=-E_(0)hat(l)(E_(0)="constant"gt0)`. Its de-Broglie wavelength at time t is given byA. `(lamda_(0))/((1+(eE_(o))/(m)(t)/(v_(0))))`B. `lamda_(0)(1+(eE_(0)t)/(mv_(0)))`C. `lamda_(0)`D. `lamda_(0)t` |
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Answer» Initial de-Broglie wavelength of electron, `" "lamda_(0)=(h)/(mv_(0))` Force on electron in electric field, `" "F=-eE=-e[-E_(0)hati]=eE_(0)hati` Acceleration of electron `" "a=F/m=(eE_(0)hati)/(m)` Vfelocity of electron after time t, `" "v=v_(0)hati+((eE_(0)hati)/(m))t=(v_(0)+(eE_(0))/(m)t)hati` `" "v_(0)(1+(eE_(0))/(mv_(0)))hati` de-Broglie wavelength associated with electron at time t is `" "lamda =(h)/(mv)` `implies" "=(h)/(m[v_(0)(1+(eE_(0))/(mv_(0))t)])=(lamda_(0))/([1+(eE_(0))/(mv_(0))])" "[thereforelamda_(0)=(h)/(mv_(0))]` |
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