Question

Calculate the wavelengths of the following objects:

a muon (a subatomic particle with a mass of 1.884 × 10–25 g) traveling at 320.0 m/s

an electron (me = 9.10939 × 10–28 g) moving at 4.20 × 106 m/s in an electron microscope

a 77.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile)

Earth (mass = 5.80 × 1027 g) moving through space at 2.90 × 104 m/s

Answer 1

a muon (a subatomic particle with a mass of 1.884 × 10–25 g) traveling at 320.0 m/s

m = 1.884 × 10^-25 g   = 1.884 × 10^-28Kg

v = 320m/s

h = 6.625*10^-34J-s

    = h/mv

         = 6.625*10^-34/(1.884*10^-28*320)

          = 1.01*10^-8 m

            = 101A⁰                                   [1A⁰    = 10^-10m]

an electron (me = 9.10939 × 10–28 g) moving at 4.20 × 106 m/s in an electron microscope

m = 9.10939 × 10^-28 g    = 9.10939 × 10^-31 g

v = 4.20*10^6 m/s

h = 6.625*10^-34J-s

    = h/mv

         = 6.625*10^-34/(9.10939*10^-31*4.2*10^6)

          = 1.73*10^-10 m

           = 1.73A⁰

a 77.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile)

m = 77Kg

m = 4min/mile    = 4*26.8224m/s   = 107.2896m/s

h = 6.625*10^-34J-s

    = h/mv

         = 6.625*10^-34/(77*107.2896)

          = 8.02*10^-38m

            = 8.02*10^-28A⁰

Earth (mass = 5.80 × 1027 g) moving through space at 2.90 × 104 m/s

m = 5.8*10^27 g   = 5.8*10^24Kg

v   = 2.9*10^4 m/s

h = 6.625*10^-34J-s

    = h/mv

         = 6.625*10^-34/(5.8*10^24 *2.9*10^4)

         = 4*10^-63 m

         = 4*10^-53A⁰