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
1.6×10−19C

Answer 1

Answer on Question #47194-Physics-Atomic Physics

The electron beam in a television tube consists of electrons accelerated from rest through a potential difference of about 20000V. 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

Kinetic energy of electron accelerated from rest is equal to its potential energy change.

$$\frac{m_e v^2}{2} = eU,$$

where $m_e = 9.11 \cdot 10^{-31} \mathrm{~kg}$ is electron's rest mass, $e = 1.6 \cdot 10^{-19} \mathrm{C}$ is electron's charge, $U = 20000V$ is potential difference, $v$ is the speed of the electrons.

Find the electron's speed:

$$v = \sqrt{\frac{2eU}{m_e}} = \sqrt{\frac{2 \cdot 1.6 \cdot 10^{-19} \cdot 20000}{9.11 \cdot 10^{-31}}} = 8.4 \cdot 10^7 \frac{m}{s}.$$

Answer: $8.4 \cdot 10^7 \frac{m}{s}$.

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