Question

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 1

(a) Mass of the bullet, m=0.040kg
Speed of the bullet, v=1.0km/s=1000m/s
Planck’s constant, \(h=6.6×10^{−34}Js\)
De Broglie wavelength of the bullet is given by the relation:
\(λ=\frac{h}{mv}\)
\(=\frac{6.6×10^{-34}}{0.040×1000}=1.65×10^{-35}m\)

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(b)Mass of the ball,m=0.060kg
Speed of the ball, v=1.0m/s
De Broglie wavelength of the ball is given by the relation:
\(λ=\frac{h}{mv}\)
\(=\frac{6.6×10^{-34}}{0.060×1}=1.1×10^{-32}m\)

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(c)Mass of the dust particle, \(m=1×10^{−9}kg\)
Speed of the dust particle, v=2.2m/s
De Broglie wavelength of the dust particle is given by the relation:
\(λ=\frac{h}{mv}\)
\(=\frac{6.6×10^{-34}}{2.2×1×10^{-9}}=3.0×10^{-25}m\)