Electrons are accelerated to a speed of 4.0 × $10^4$ m/s and are then aimed at a double-slit apparatus,where interference fringes are detected.If the electrons were replaced by neutrons,what speed must neutrons have to produce interference fringes with the same fringe spacing as that observed with the electrons? (h = 6.626 × 10^-34 J ∙ s,m_electron = 9.11 × 10^-31 kg,m_neutron = 1.675 × 10^-27 kg) A)2.2 × 10¹ m/s B)7.3 × 10⁷ m/s C)1.7 × 10⁶ m/s D)9.3 × 10² m/s

Question

Quizplus · Accepted Answer

The spacing between interference fringes is given by:

d = h/mv

where h is Planck's constant, m is the mass of the particle, v is the speed of the particle, and d is the spacing between interference fringes.

If we want the same fringe spacing for neutrons as for electrons, we need to solve for the velocity of the neutrons:

d(neutron) = d(electron)

h/m(neutron)v(neutron) = h/m(electron)v(electron)

Solving for v(neutron), we get:

v(neutron) = (m(neutron)/m(electron))v(electron)

Plugging in the given numbers, we get:

v(neutron) = (1.675 × 10^-27 kg)/(9.11 × 10^-31 kg) × 4.0 × 10^4 m/s

v(neutron) = 2.2 × 10^11 m/s

Therefore, the best choice is A.

Electrons Are Accelerated to a Speed of 4 10410^4104 M/s and Are Then Aimed at a Double-Slit Apparatus,where Interference

Electrons Are Accelerated to a Speed of 4 $10^4$ M/s and Are Then Aimed at a Double-Slit Apparatus,where Interference