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.

a. 8.4×107 m/s

b. 3.8×106 m/s

c. 6×106 m/s

d. 4.7×107 m/s

Answer 1

Question #31252, Physics, Other

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 $9.11 \times 10^{\wedge} - 31 \mathrm{~kg}$ and electronic charge is $1.6 \times 10^{\wedge} - 19 \mathrm{C}$.

a. $8.4 \times 107 \mathrm{~m} / \mathrm{s}$

b. $3.8 \times 106 \mathrm{~m} / \mathrm{s}$

c. $6 \times 106 \mathrm{~m} / \mathrm{s}$

d. $4.7 \times 107 \mathrm{~m} / \mathrm{s}$

Solution.

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

$$\frac {m _ {e} \cdot v _ {e} ^ {2}}{2} = q _ {e} \cdot V;$$

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

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

$V = 20\,000$, V(J/C) – potential difference;

$v_{e}$, m/s – is the speed of the electrons;

Find the electron speed:

$$v _ {e} = \sqrt {\frac {2 \cdot q _ {e} \cdot V}{m _ {e}}} = \sqrt {\frac {2 \cdot 1 . 6 \cdot 1 0 ^ {- 1 9} \cdot 2 0 0 0 0}{9 . 1 1 \cdot 1 0 ^ {- 3 1}}} = \sqrt {\frac {2 \cdot 1 . 6 \cdot 1 0 ^ {- 1 9} \cdot 2 0 0 0 0}{9 . 1 1 \cdot 1 0 ^ {- 3 1}}} = 0. 8 4 \cdot 1 0 ^ {8} = 8. 4 \cdot 1 0 ^ {7} \mathrm{~m / s}.$$

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