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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?

A

`1.33xx10^(6)ms^(-1)`

B

`1.33xx10^(7)ms^(-1)`

C

`2.66xx10^(7)ms^(-1)`

D

`2.66xx10^(6)ms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
(c ) : (a) Energy of accelerated electron E=500 eV Specific charge, `e//m=1.76xx10^(11)Ckg^(-1)`,
Kinetic energy `E=(1)/(2)mv^(2)=eV`
`:.v=sqrt(2V(e//m))=sqrt(2xx1.76xx10^(11)xx500)`
`=1.33xx10^(7)"m s"^(-1)`
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Knowledge Check

  • When the speed of the electron increases, the specific charge

    A
    Decreases
    B
    Increases
    C
    Remains same
    D
    None

  • If the electronic charge e=1.6xx10^(-19)C and the specific charge e/m off electron is 1.76xx10^(11)C(kg)^(-1) then calculate the mass m of the electron.

    A
    `3.2xx10^(-31)kg`
    B
    `5.1xx10^(-31)kg`
    C
    `9.1xx10^(-31)kg`
    D
    `8.2xx10^(-31)kg`

  • When the speed of electrons increases, then the value of its specific charge

    A
    Increases
    B
    Decreases
    C
    Remails unchanged
    D
    Increases upto some velocity and then begins to decrease