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20 May, 20:29

Electrons (each with charge qe = 1.602 x 10-19) are ejected from a hot filament at a rate of 1.9 x 1013 electrons/second and then they are accelerated through an electric potential difference of 1000 V. The beam of electrons then hits a metal collector where the charge is deposited. (a) What is the kinetic energy of an electron after it is accel - erated? (b) What electric current does the electron beam constitute? Give both the magnitude, in Ampres, and its direction. (c) How much charge is deposited in the collector in 10 seconds?

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  1. 20 May, 22:50
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    (a) Kinetic energy of electron after acceleration is 1.602 x 10⁻¹⁹ J

    (b) Electric current is 3.0438 x 10⁻⁶ A and its direction is opposite to the direction of electrons.

    (c) Charge deposited in 10 s is 3.0438 x 10⁻⁵ C

    Explanation:

    Given:

    Electron charge, q = 1.602 x 10⁻¹⁹ C

    Rate of electrons, n = 1.9 x 10¹³ electrons/second

    Potential difference, V = 1000 volts

    (a)

    Kinetic energy of electrons, K = q x V

    Substitute the values of q and V in the above equation.

    K = 1.602 x 10⁻¹⁹ x 1000 = 1.602 x 10⁻¹⁶ J

    (b)

    Electric current due to electrons, I = n x q

    Substitute the values of n and q in the above equation.

    I = 1.9 x 10¹³ x 1.602 x 10⁻¹⁹ = 3.0438 x 10⁻⁶ A

    The direction of electric current is opposite to the direction of electrons.

    (c)

    Time, t = 10 s

    Charge deposited, Q = I x t

    Substitute the values of I and t in the above equation.

    Q = 3.0438 x 10⁻⁶ x 10 = 3.0438 x 10⁻⁵ C
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