Question

Calculate the wavelengths of the following objects: Part 1 a muon (a subatomic particle with a mass of 1.884 × 10–25 g) traveling at 330.0 m/s 10.66 nm Part 2 an electron (me = 9.10939 × 10–28 g) moving at 3.85 × 106 m/s in an electron microscope nm Part 3 an 75.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile) x 10 nm Part 4 Earth (mass = 6.10 × 1027 g) moving through space at 2.80 × 104 m/s nm

Answer 1

De Broglie Wavelength Equation

The Equation is given by

λ= h/(mv)

where

λ= Wavelength

h = Planck Constant = 6.626*10^-34 J s

m = mass in kg

v = velocity in m/s

Now, substitute all data

a)

λ= h/(mv)

λ= (6.626*10^-34)/(mv)

λ= (6.626*10^-34)/((1.884 *10^-28)(330)) = 1.065*10^-8 m

b)

λ= (6.626*10^-34)/(mv)

λ= (6.626*10^-34)/((9.10939 *10^-31)(3.85*10^6)) = 1.889*10^-10 m

c)

λ= (6.626*10^-34)/(mv)

V = 4 min/mi = 1/4 mi/min = 0.25/60 mi/s = 0.25/60*1609 m/s = 6.704m/s

λ= (6.626*10^-34)/((75)(6.704)) = 1.317*10^-36 m

d)

λ= (6.626*10^-34)/(mv)

λ= (6.626*10^-34)/((6.2*10^30)(2.8*10^4)) = 3.816*10^-69 nm