Protons are being accelerated in a particle accelerator. When the speed of the protons is doubled, their de Broglie wavelength will
A) decrease by a factor of $\sqrt { 2 }$.
B) increase by a factor of 4 .
C) decrease by a factor of 2 .
D) increase by a factor of $\sqrt { 2 }$.
E) increase by a factor of 2 .

Question

Quizplus · Accepted Answer

The de Broglie wavelength $\lambda$ of a particle is given by $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is the momentum of the particle. For a proton, the momentum $p$ is given by $p = mv$, where $m$ is the mass of the proton and $v$ is its velocity. When the speed of the protons is doubled, the momentum doubles ($p' = 2mv$), leading to a halving of the de Broglie wavelength ($\lambda' = \frac{h}{2mv} = \frac{\lambda}{2}$). Therefore, the de Broglie wavelength decreases by a factor of 2.

Protons Are Being Accelerated in a Particle Accelerator 2\sqrt { 2 }2​

Protons Are Being Accelerated in a Particle Accelerator $\sqrt { 2 }$