Question

Estimate the speed with which electrons emitted from a heated cathode of an evacuated tube impinge on the anode maintained at a potential difference of $500 \,V$ with respect to the cathode. Ignore the small initial speeds of the electrons. The specific charge of the electron i.e., its e/m is given to be $1.76 \times 10^{11}\, C\, kg^{-1}$

• A. $1.33\times 10^{6}\,ms^{-1}$
• B. $2.66\times 10^{7}\,ms^{-1}$
• C. $1.33\times 10^{7}\,ms^{-1}$
• D. $2.66\times 10^{6}\,ms^{-1}$

Answer 1

Answer: (C)

Energy of accelerated electron $E=500\,eV$
Specific charge, e/m $=1.76\times10^{11}C kg^{-1}$,
Kinetic energy $E = \frac{1}{2}mv^{2}=eV$
$\therefore v=\sqrt{2V \left(e m\right)}=\sqrt{2\times1.76\times10^{11}\times500}$
$=1.33\times10^{7}\,m\,s^{-1}$