Question

In a color television tube, electrons are accelerated through a potential difference of  15500 V. With what speed do the electrons strike the screen? Give this speed in terms of the speed of light. Hint: The kinetic energy of an electron which has been accelerated through a potential difference of 1 V has a kinetic energy equal to 1 eV. The Range of answers is between  0.230 and 0.310c

I tried to use the conservation principle (1/2 mv²=qv), but that didn't get me the right answer. Any other suggestions?

Answer 1

You might have assumed some wrong values. Below is the correct way.

Let the speed of electron be V m/s

Mass of electron =9.1*10^-31 kg

Charge on electron= - 1.6*10^-19 C

So we have kinetic energy of electron =1/2 mv²

Put values

1/2*9.1*10^-31 v²..............1

Energy is also equal to qv when q charge is accelerated through V potential

Put values, we get qv=

1.6*10^-19 *15500.............2

As both the energies are same thing so we have 1 =2

1/2*9.1*10^-31*v² =1.6*10^-19*15500

V²=1.6*10^-19 *15500*2/9.1*10^-31

V²=1.6*15500*2*10^12/9.1

V²=49600*10^12/9.1

V²=5450.55*10^12

V= 73.82*10^6 m/s

Divide and multiply by c we get

V=0.73*10^8 *c/c

Put value of c in denominator ie c=3*10^8 we get

V=0.73*10^8*c/3*10^8

V=0.246c m/s. ie speed of electron in terms of speed of light.