Question

What is the de Broglie wavelength (in m) of the wave associated with an electron that has been accelerated through a potential difference of 50.0 V?

• A. $2.7\times {10}^{-10}$
• B. $1.74\times {10}^{-10}$
• C. $3.6\times {10}^{-9}$
• D. $4.9\times {10}^{-11}$

Answer 1

The correct option is B $1.74\times {10}^{-10}$

The kinetic energy of an electron accelerated through a potential difference of V volts is given by the equation:
$\frac{1}{2}m{v}^2=eV$ where $e$ is the electron charge (1.6x10^-19 C)

$v=\sqrt{\frac{2eV}{m}}$

$v=\sqrt{\frac{2\times 1.6\times {10}^{-19}\times 50}{9.1\times {10}^{-31}}}=4.193\times {10}^{6}m/s$

$\therefore$ wavelength= $\frac{h}{mv}=1.74\times {10}^{10}\because h=6.625\times {10}^{34}$