The Stanford Linear Accelerator Center (SLAC)can accelerate electrons to an energy of 50 GeV.The wavelength of these electrons is of the order
A)0.2 fm
B)0.02 fm
C)0.002 fm
D)0.006 fm
E)0.008 fm

Question

Quizplus · Accepted Answer

According to de Broglie's wavelength equation, the wavelength of the electrons is given by λ = h/p, where h is Planck's constant and p is the momentum. The momentum of the electrons can be calculated using the relativistic momentum equation, p = γ*m*v, where γ is the Lorentz factor, m is the rest mass of the electrons and v is their velocity. At a relativistic factor of 1.057 (corresponding to an energy of 50 GeV), the velocity of the electrons is approximately 0.99998*c, where c is the speed of light. Therefore, the momentum is p = γ*m*v = 50 GeV/c^2 * 0.99998*c = 49.998 GeV/c. Substituting this value into the wavelength equation gives λ = h/p = 0.02 fm. Therefore, the correct answer is B.

The Stanford Linear Accelerator Center (SLAC)can Accelerate Electrons to an Energy