Question

an eiectron beam in television tube consists of electrons accelerated from rest through a potentialdifference of about 20, 000v. what is the speed of the electron? ignore realistic effects.

Answer 1

Question.

An electron beam in television tube consists of electrons accelerated from rest through a potential difference of about 20, 000v. What is the speed of the electron? Ignore realistic effects.

Solution

The electric field accelerates the electron beam. Acquired kinetic energy $E_K$ equals work A done by field: $E_K = A$;

Energy and work are given by the formulas: $E_K = \frac{m \cdot v^2}{2}; A = e \cdot U$;

Equate these values: $\frac{mv^2}{2} = eU$;

Hence we obtain: $v = \sqrt{\frac{2eU}{m}} = \sqrt{\frac{2 \cdot 1.6 \cdot 10^{-19} \cdot 20000}{9.1 \cdot 10^{-31}}} = 83900 \, (m/s)$

Answer: 83900 m/s.