Question

Pellets of mass 2.0 g are fired in parallel paths with speeds of 130 m/s through a hole 2.5 mm in diameter. How far from the hole must you be to detect a 1.0-cm-diameter spread in the beam of pellets?

Answer 1

1 cm diameter spread = 0.5 cm = 0.005 m in radius

Diffraction angle is given as

Tan (theta) = 0.005 / d

where d is the distance between us and hole

Wavelength = h / mv = 6.63e-34 / 0.002*130 = 2.55e-33 m

As we have a circular aperture, we can use airy disc formula

sin (theta) = 1.22*wavelength / D ( where D is diameter of hole or aperture)

sin (theta) = 1.22*2.55e-33 / 0.0025

As the angle is very small, we can write

0.005 / d = 1.22*2.55e-33 / 0.0025

solve for d, we get

d = 4.02e27 m