Question

Calculate the wavelengths of the following objects in nm

a) a muon (a subatomic particle with a mass of 1.884 × 10–25 g) traveling at 310.0 m/s

b) an electron (me = 9.10939 × 10–28 g) moving at 3.80 × 106 m/s in an electron microscope

c) an 75.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile)

d) Earth (mass = 6.20 × 1027 g) moving through space at 3.00 × 104 m/s

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)*10^9 in nanometers

λ= (6.626*10^-25)/(mv)

λ= (6.626*10^-25)/((1.884 *10^-28)(310)) = 11.345nm

b)

λ= (6.626*10^-25)/(mv)

λ= (6.626*10^-25)/((9.10939 *10^-31)(3.8*10^6)) = 0.19141 nm

c)

λ= (6.626*10^-25)/(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^-25)/((75)(6.704)) = 1.3178*10^-27 nm

d)

λ= (6.626*10^-25)/(mv)

λ= (6.626*10^-25)/((6.2*10^30)(3*10^4)) = 3.562*10^-60 nm