1. Wavelength of particles

a. Consider a dust particle of diameter d =1 μ, mass m≈10^-15 kg, and speed ν= 1 mm/s. Calculate the de Broglie wavelength of the particle and compare with the particle's size.

b. Now consider a thermal neutron, i.e, a neutron (m=1.67 x 10^-27 kg) with a speed ν corresponding to the average thermal energy at (absolute) temperature T, give by:

1/2 mν² = p² / 2m = 3/2 k_BT,

where k_B= 1.38 x 10^-23 J/K (joule/degree) is Boltzmann's constant. Find the wavelength of such a neutron at room temperature (T=300 K).

2. Wavelength and Resolution:
The smallest separation resolvable by a microscope is of the order of the wavelength used. In an electron microscope, what energy of electrons would be needed to resolve separations of:

a. 100 Amps
b. 5 Amps