Electrons emerge from an electron gun with a speed of 2.0 × 10⁶ m/s.They are made to pass through a double-slit apparatus.Interference fringes with spacing of 2.7 mm are detected on a screen far from the double slit.What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? A)1.5 μm B)4.9 m C)0.93 nm D)1.2 km

Question

Quizplus · Accepted Answer

The de Broglie wavelength is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. The momentum of an electron is given by p = mv, where m is the mass of the electron and v is its speed. The momentum of a neutron is given by p = mv, where m is the mass of the neutron and v is its speed. Since the electrons and neutrons have the same speed, their momenta are the same. Therefore, their de Broglie wavelengths are also the same. The fringe spacing is given by d = λL/D, where L is the distance between the double slits and D is the distance between the double slits and the screen. Since the electrons and neutrons have the same de Broglie wavelength, the fringe spacing will be the same for both particles.

Electrons Emerge from an Electron Gun with a Speed of 2.0