An electron is moving with the speed of $1780 \mathrm {~m} / \mathrm { s }$. What is its de Broglie wavelength? $\left( m _ { \text {electron } } = \right.$ $\left. 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$
A) $409 \mathrm {~nm}$
B) $502 \mathrm {~nm}$
C) $302 \mathrm {~nm}$
D) $205 \mathrm {~nm}$
E) $420 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The de Broglie wavelength $\lambda$ of a particle is given by the equation $\lambda = \frac{h}{mv}$, where $h$ is Planck's constant, $m$ is the mass of the particle, and $v$ is the velocity of the particle. Substituting the given values, $\lambda = \frac{6.626 \times 10^{-34}}{9.11 \times 10^{-31} \times 1780} \approx 4.09 \times 10^{-7}$ meters or $409 $ nm.

An Electron Is Moving with the Speed Of 1780 m/s1780 \mathrm {~m} / \mathrm { s }1780 m/s

An Electron Is Moving with the Speed Of $1780 \mathrm {~m} / \mathrm { s }$