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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?

Answer :

Answer:

(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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