A proton and an electron are both accelerated to the same final speed. If $\lambda _ { p }$ is the de Broglie wavelength of the proton and $\lambda _ { \mathrm { e } }$ is the de Broglie wavelength of the electron, then A) $\lambda _ { p } \lambda _ { e }$.

Question

A proton and an electron are both accelerated to the same final speed. If $\lambda _ { p }$ is the de Broglie wavelength of the proton and $\lambda _ { \mathrm { e } }$ is the de Broglie wavelength of the electron, then
A) $\lambda _ { p } < \lambda _ { e }$.
B) $\lambda _ { p } = \lambda _ { e }$
C) $\lambda _ { p } > \lambda _ { e }$.

Quizplus · Accepted Answer

The de Broglie wavelength $\lambda$ is given by $\lambda = \frac{h}{mv}$, where $h$ is Planck's constant, $m$ is the mass of the particle, and $v$ is its velocity. Since both particles are accelerated to the same speed, $v$ is constant for both. However, the mass of a proton is much greater than the mass of an electron, resulting in a smaller wavelength for the proton compared to the electron.

A Proton and an Electron Are Both Accelerated to the Same