# Finding the velocity of an electron accelerated

Question: For an accelerating voltage of 900 V calculate the time taken for an electron to reach the anode after being accelerated from rest (u=0) at the cathode of a CRT. Anode-cathode separation is 1cm.

I am looking for the working's out for this problem and the answer.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Let m = mass of an electron

e = charge on an electron

V = potential difference between cathode and anode of discharge tube

v = velocity of the electron as it comes out of anode

As the electron is accelerated from cathode to anode, its potential energy gets

converted into kinetic energy.

Thus

P.E. of an electron at the cathode = Gain in its K.E. at the anode

eV = (1/2) mv<sup>2</sup>

from this,

velocity = sqrt[2eV/m]

= sqrt[2*1.6 *10^-19 *900/9.11 * 10^-31 kg ]

= 1.7780 *10^7 m/s

since the separation between the plates is only 1cm = 0.01 meter,

the time of travel is given by

time = distance/velocity = 0.01/1.7780 *10^7 = 5.6242 * 10^-10sec

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