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

Question

Quizplus · Accepted Answer

The de Broglie wavelength $\lambda$ is inversely proportional to the momentum $p$ of a particle, given by $\lambda = \frac{h}{p}$, where $h$ is Planck's constant. Since the momentum of a particle is the product of its mass and velocity ($p = mv$), doubling the speed of the protons doubles their momentum. Therefore, their de Broglie wavelength will decrease by a factor of 2, as the relationship between wavelength and momentum is inversely proportional.

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

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