In a color television tube, electrons are accelerated through a potential differ
ID: 2304477 • Letter: I
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?
Explanation / Answer
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.