Electrons emerge from an electron gun with a speed of 2.0 × 10⁶ m/s and then pass through a pair of thin parallel slits.Interference fringes with a spacing of 2.7 mm are detected on a screen far from the double slit and fairly close to the center of the pattern.What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? (m_el = 9.11 × 10^-31 kg,m_neutron = 1.67 × 10^-27 kg) A)1.5 µm B)4.9 µm C)0.93 nm D)1.1 µm E)1.5 nm

Question

Quizplus · Accepted Answer

The fringe spacing is given by:$$d = \frac{\lambda L}{a}$$where:* d is the fringe spacing* λ is the wavelength of the electron* L is the distance between the slits and the screen* a is the distance between the slitsThe wavelength of the electron is given by:$$\lambda = \frac{h}{p}$$where:* h is Planck's constant* p is the momentum of the electronThe momentum of the electron is given by:$$p = mv$$where:* m is the mass of the electron* v is the speed of the electronSubstituting these equations into the equation for the fringe spacing, we get:$$d = \frac{hL}{mv}$$Since the speed of the electron is the same for both electrons and neutrons, the fringe spacing will be inversely proportional to the mass of the particle. Therefore, the fringe spacing for neutrons will be:$$d_{neutron} = d_{electron} \frac{m_{electron}}{m_{neutron}}$$Substituting the given values, we get:$$d_{neutron} = 2.7 	ext{ mm} \frac{9.11 	imes 10^{-31} 	ext{ kg}}{1.67 	imes 10^{-27} 	ext{ kg}} = 1.5 \mu 	ext{m}$$Therefore, the correct answer is A.

Electrons Emerge from an Electron Gun with a Speed of 2.0