Question

The electron beam in a television tube consists of electrons accelerated from rest through a potential difference of about 20 000V. What is the speed of the electrons? (Ignore relativistic effects). Electron rest mass is
9:11×10−31
kg and electronic charge is
1:6×10−19

Answer 1

Answer on Question #45701 – Physics – Electromagnetism

Question: the electron beam in a television tube consists of electrons accelerated from rest through a potential difference of about $20\,000\,\mathrm{V}$. What is the speed of the electrons? (Ignore relativistic effects). Electron rest mass is $9,11\cdot 10^{-31}\,\mathrm{kg}$ and electronic charge is $1,6\cdot 10^{-19}\,\mathrm{C}$.

Solution: we can use the law of conservation of energy: the work done by electric field accelerating every electron in the beam is equal to the final kinetic energy of each electron. Thus, we get the equation

$$\frac{m v^2}{2} = e U,$$

where $U$ is the potential difference between the ends of a television tube. Therefore the speed of each electron is

$$v = \sqrt{\frac{2 e U}{m}} = \sqrt{\frac{2 \cdot 1,6 \cdot 10^{-19} \cdot 20000}{9,11 \cdot 10^{-31}}} \simeq 8,4 \cdot 10^7\,\frac{\mathrm{m}}{\mathrm{s}}.$$

Answer:

$$v = \sqrt{\frac{2 e U}{m}} \simeq 8,4 \cdot 10^7\,\frac{\mathrm{m}}{\mathrm{s}}.$$