Question

Choose the correct answer from the alternatives given.
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 elm is given to be $1.76\times {10}^{11}Ck{g}^{-1}$.

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

Answer 1

The correct option is C $1.33\times {10}^{7}m{s}^{-1}$

Energy of accelerated electron E = 500 eV Specific charge,$e/m=1.76\times {10}^{1}1Ckg$
Kinetic energy $E=\frac{1}{2}m{v}^2=eV$
$\therefore v=\sqrt{2V\left(e/m\right)}=\sqrt{2\times 1.76\times {10}^{1}1\times 5}$
$v=1.33\times {10}^{7}m{s}^{-1}$