Protons are being accelerated in a particle accelerator. When the energy 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 of a particle is given by $\lambda = h/p$, where $h$ is Planck's constant and $p$ is the momentum of the particle. Since momentum is directly proportional to the square root of energy, doubling the energy of the protons will increase their momentum by a factor of $\sqrt{2}$. Therefore, their de Broglie wavelength will decrease by a factor of $\sqrt{2}$.

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

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