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The increase in temperature of a cathode in electronic tube by DeltaT= 1.0K from the valueT= 2000K results in the increase of sturation current by eta=1.4%. Find the work function of the electron for the material of the cathode. |
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Answer» Solution :From Richardson's eqaution `I= aT^(2)e^(-A//KT)` where `A` is the work function in `eV`. When `T` increases by `DELTAT, I` incereses to `(1+eta)I`. Then `1+eta=((T+DeltaT)/(T))^(2)e^(-(A)/(kT)((T)/(T+DeltaT))-1)-(1+(DeltaT)/(T))^(2)e^(+(A)/(kT).(DeltaT)/(T+DeltaT))` Expanding and neglecting higher powers of `(DeltaT)/(T)` we get `eta=2(Delta T)/(T)+(A)/(kT^(2))Delta T` THUS `A=kT((ETAT)/(DeltaT)-2)` Substituting we get `A= 4.48eV` |
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