Calculate the wavelengths of the following objects:

Question

1. a muon (a subatomic particle with a mass of 1.884 × 10^–25 g) traveling at 320.0 m/s
2. an electron (m_e = 9.10939 × 10^–28 g) moving at 3.95 × 10⁶ m/s in an electron microscope
3. an 76.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile)
4. Earth (mass = 6.20 × 10²⁷ g) moving through space at 2.90 × 10⁴ m/s

(all answers are in nm)

Answer 1

Hi Alexis,

we can use de Broglie equation (λ=h/mv) to determine the wavelength of a moving object

λ = h/mv

[In this equation, h is Planck’s constant, m is the mass of the particle in kg, and v is the velocity of the particle in m/s]

{Planks constant = 6.626 x 10-34 J.s or 6.626 x 10 -34 Kg.m2/s}

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

— convert the mass to kg— 1.884 x 10^-25 g x 1 Kg. = 1.884 x 10^-28 Kg

1000 g

λ = h/mv = 6.626 x 10^-34 Kg.m²/s. = 1.099 x 10^-8 m. OR 10.99 nm

1.884 x 10^-28 Kg x 320.0 m/s

2) an electron (me = 9.10939 × 10^–28 g) moving at 3.95 × 10⁶ m/s in an electron microscope

λ=h/mv

6.626 x 10 ^-34 Kg.m²/s.                                 =   1.84 x 10 -10 m. =  0.184 nm

9.10939 x 10^-31 Kg x 3.95 x 10⁶ m/s   

3) an 76.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile)

 λ =  6.626 x 10 -34 Kg.m²/s.      =      1.3 x 10 ^-36 m or 1.3 x 10 ^-27 nm

76.0 Kg x  6.7 m/s

4) Earth (mass = 6.20 × 10²⁷ g) moving through space at 2.90 × 10⁴ m/s

 λ  = 6.626 x 10 ^-34 Kg.m²/s.                 =   3.69 x 10 ^-63 m. = 3.69 x 10^-54 nm

           6.20 x 10 ²⁴ Kg x. 2.90 x 10 ⁴ m/s