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?

(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