speed of an electron

[logistic_guy]

What is the speed of an electron when it hits a television screen after being accelerated by the \(\displaystyle 25,000 \ \text{V}\) of the picture tube?

 

[khansaheb]

What is the speed of an electron when it hits a television screen after being accelerated by the \(\displaystyle 25,000 \ \text{V}\) of the picture tube?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[logistic_guy]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

Thank you Sir khan.

Let us first calculate the rest energy of the electron.

\(\displaystyle E = mc^2 = 9.109 \times 10^{-31}(299792458)^2 = 8.187 \times 10^{-14} \ \text{J}\)

Let us convert it to \(\displaystyle \text{eV}\).

\(\displaystyle E = \frac{8.187 \times 10^{-14}}{1.602 \times 10^{-19}} = 511000 \ \text{eV}\)

Now we can calculate the electron speed.

\(\displaystyle K = mc^2\left[\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1\right]\)

\(\displaystyle 25000 = 511000\left[\frac{1}{\sqrt{1 - \frac{v^2}{(299792458)^2}}} - 1\right]\)

This gives:

\(\displaystyle v = 90489723 \ \text{m/s} = \frac{90489723}{299792458}c = 0.302c\)