An electron is travelling at 0.7c.What is the deBroglie wavelength of this electron?
A)2.47 pm
B)3.48 pm
C)2.74 nm
D)1.85 µm
E)3.26 mm

Question

Quizplus · Accepted Answer

The de Broglie wavelength ($\lambda$) of a particle is given by the equation $\lambda = \frac{h}{p}$, where $h$ is Planck's constant ($6.626 \times 10^{-34} m^2 kg / s$) and $p$ is the momentum of the particle. For a relativistic particle like an electron moving at a significant fraction of the speed of light (in this case, 0.7c), its momentum is given by $p = \frac{mv}{\sqrt{1 - v^2/c^2}}$, where $m$ is the rest mass of the electron ($9.109 \times 10^{-31} kg$), $v$ is the velocity of the electron, and $c$ is the speed of light ($3.00 \times 10^8 m/s$). Substituting the given values and solving for $\lambda$ yields a wavelength in the picometer range, with the correct calculation aligning with option A, 2.47 pm.

An Electron Is Travelling at 0