Question 15

What is the de Broglie wavelength of

(a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s,

(b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and

(c) a dust particle of mass 1.0 × 10^{−9} kg drifting with a speed of 2.2 m/s?

Answer

**(a)** Mass of the bullet, m = 0.040 kg

Speed of the bullet, v = 1.0 km/s = 1000 m/s

Planck’s constant, h = 6.6 × 10^{−34} Js

De Broglie wavelength of the bullet is given by the relation: *λ = h/mv*

= 6.6 x 10^{-34} / 0.040 x 1000 = 1.65 x 10^{-35} m

**(b)** Mass of the ball, m = 0.060 kg

Speed of the ball, v = 1.0 m/s

De Broglie wavelength of the ball is given by the relation: *λ = h/mv*

= 6.6 x 10^{-34} / 0.060 x 1 = 1.1 x 10^{-32} m

**(c)** Mass of the dust particle, m = 1 × 10^{−}9 kg

Speed of the dust particle, v = 2.2 m/s

De Broglie wavelength of the dust particle is given by the relation:* λ = h/mv*

= 6.6 x 10^{-34} / 2.2 x 1 x 10^{-9} = 3.0 x 10^{-25} m

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