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 .
E) decrease by a factor of .

Question

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 . 
E) decrease by a factor of .

Quizplus · Accepted Answer

The de Broglie wavelength is (h/mv)^1/2 where h is Planck's constant, m is the mass of the particle, and v is the velocity. Since the mass of the proton and Planck's constant are constants, doubling the energy of the proton means doubling its velocity. Therefore, the de Broglie wavelength will be given by (h/m(2v))^1/2 = (1/2)^1/2(h/mv)^1/2, which means the wavelength will decrease by a factor of (1/2)^1/2 = 0.707, or approximately 11ea6ebb_731a_3b45_9d78_d5ecff8e4542_TB6213_11. Therefore, the correct answer is E.

Protons Are Being Accelerated in a Particle Accelerator