Question

A cathode ray tube has a potential difference of V volt between the cathode and the anode. The speed of cathode rays is given by

• A. $6\times {10}^{-5}\sqrt{V}cm/s$
• B. $6\times {10}^5\sqrt{V}m/s$
• C. $6\times {10}^7\sqrt{V}cm/s$
• D. $6\times {10}^3\sqrt{V}m/s$

Answer 1

The correct option is B $6\times {10}^5\sqrt{V}m/s$

The kinetic energy of electrons is
$E=\frac{1}{2}m{v}^2$
The potential between cathode and anode is V hence,
$\frac{1}{2}m{v}^2=eV$
$v^2=\frac{2eV}{m}$
$v^2=\frac{2\times 1.6\times {10}^{-19}V}{9.1\times {10}^{-31}}$
$v^2=0.35\times {10}^{12}V$
$v=\sqrt{35\times {10}^{10}V}$
$v=5.9\times {10}^5\sqrt{V}$
$v\approx 6\times {10}^5\sqrt{V}m{s}^{-1}$