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
C.
8.4×107
m/s
3.8×106
m/s
6×106
m/s
4.7×107
m/s

Answer 1

Answer on Question #55894, Physics / Electromagnetism

Task: The electron beam in a television tube consists of electrons accelerated from rest through a potential difference of about 20 000 V. What is the speed of the electrons? (Ignore relativistic effects). Electron rest mass is $9.11 \times 10^{-31} \, \mathrm{kg}$ and electronic charge is $1.6 \times 10^{-19} \, \mathrm{C}$.

$$\begin{array}{l} 8.4 \times 10^{7} \, \mathrm{m/s} \\ 3.8 \times 10^{6} \, \mathrm{m/s} \\ 6 \times 10^{6} \, \mathrm{m/s} \\ 4.7 \times 10^{7} \, \mathrm{m/s} \\ \end{array}$$

Solution:

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

$$m_e \cdot v_e^2 / 2 = q_e \cdot V,$$

where $m_e = 9.11 \cdot 10^{-31} \, \mathrm{kg}$ – is electron rest mass;

$q_e = 1.6 \cdot 10^{-19} \, \mathrm{C}$ – is electron electronic charge;

$V = 20\,000 \, \mathrm{V}$ – potential difference;

$v_e$ – is the speed of the electrons.

Find the electron speed:

$$v_e = \sqrt{\frac{2 q_e V}{m_e}} = \sqrt{\frac{2 \cdot 1.6 \cdot 10^{-19} \cdot 20\,000}{9.11 \cdot 10^{-31}}} = 8.4 \cdot 10^{7} \, \mathrm{m/s}$$

Answer: the electron speed is $8.4 \cdot 10^{7} \, \mathrm{m/s}$.

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