What is the wavelength of the matter wave associated with an electron moving with a speed of $2.5$ $\times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$ ? (melectron $\left. = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$
A) $35 \mathrm { pm }$
B) $29 \mathrm { pm }$
C) $53 \mathrm { pm }$
D) $47 \mathrm { pm }$

Question

Quizplus · Accepted Answer

The wavelength of a matter wave is given by the de Broglie equation $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is the momentum of the particle. The momentum $p$ can be calculated as $mv$, where $m$ is the mass of the electron and $v$ is its velocity. Substituting the given values, $p = 9.11 \times 10^{-31} \mathrm{kg} \times 2.5 \times 10^7 \mathrm{m/s}$, and then calculating $\lambda = \frac{6.626 \times 10^{-34} \mathrm{Js}}{p}$, results in a wavelength of approximately $29 \mathrm{pm}$.

What Is the Wavelength of the Matter Wave Associated with an Electron