Question

Protons are being accelerated in a particle accelerator. When the energy of the protons is doubled, their de Broglie wavelength will ________

Answer 1

Doubling the energy of protons in a particle accelerator leads to an increase in their momentum and a corresponding decrease in their de Broglie wavelength.

Step-by-step explanation:

When the energy of the protons is doubled in a particle accelerator, their de Broglie wavelength will decrease. The de Broglie wavelength, λ, can be calculated using the equation λ = h/p, where 'h' is the Planck constant and 'p' is the momentum of the particle. If the energy, and hence the kinetic energy (assuming non-relativistic speeds), of the protons is doubled, their momentum will increase since momentum p is related to kinetic energy KE by p = √(2︅KE/m), where 'm' is the mass of the particle. A larger momentum implies a smaller de Broglie wavelength, as they are inversely proportional.