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(a) Estimate the speed with which electr...

(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?

Text Solution

Verified by Experts

Given , V = 500 V. `e/m = 1.76 xx10^(11) `C/kg , KE `= 1/2 mv^(2) = eV`
` v = sqrt(e/mxx2V) = sqrt(1.76 xx10^(11) xx 2xx 500 ) :. v = 1.326 xx10^(7) ` m/s
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Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong ? In what way is the formula to be modified ?

(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be 1.76 xx 10^(11) C kg^(-1) . (b) Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong ? In what way is the formula to be modified?

Knowledge Check

  • When the speed of electron increases, its specific charge

    A
    Increases
    B
    Decreases
    C
    Remains unchanged
    D
    Increases and then decreases
  • The drift speed of an electron in a metal is of the order of

    A
    `10^(-13)m//s`
    B
    `10^(-3)mm//s`
    C
    `10^(-4)m//s`
    D
    `10^(-30)m//s`
  • The value of e/m for an electron is

    A
    `1.78xx10^(8)c//g`
    B
    `1.6724xx10^(-24)c//g`
    C
    `0.005486c//g`
    D
    `1.00866c//g`
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