Question

Wave-particle duality of matter

17. Calculate the de Broglie wavelength associated with each of the following:
a) A bullet of mass 25g moving at a velocity of 280 ms¹¹.
b) A sprinter of mass 90kg moving at a velocity of 11 ms¹.
c) An electron of mass 9.11 x 10-31 kg moving at a velocity of 2.0 x 107 ms ¹.

Answer 1

a) For the bullet, we have:

p = mv = 0.025 kg × 280 m/s = 7.0 kg m/s

λ = h/p = 6.626 × 10^-34 J s / 7.0 kg m/s = 9.47 × 10^-36 m

b) For the sprinter, we have:

p = mv = 90 kg × 11 m/s = 990 kg m/s

λ = h/p = 6.626 × 10^-34 J s / 990 kg m/s = 6.70 × 10^-37 m

c) For the electron, we have:

p = mv = 9.11 × 10^-31 kg × 2.0 × 10^7 m/s = 1.82 × 10^-23 kg m/s

λ = h/p = 6.626 × 10^-34 J s / 1.82 × 10^-23 kg m/s = 3.64 × 10^-11 m