Question

if you take a rock the has a mass of 1 pound 10 ounces, and you throw it with a velocity of 75 mph what would the wavelength be?

Answer 1

Mass of rock = 1 pound 10 ounces = 1 pound + 10 ounces

= 0.454 Kg + 0.283 ( 1 pound = 0.454 Kg and 1 ounce = 0.0283 Kg)

Mass of rock (m) = 0.737 Kg.

Velocity of rock = V = 75 miles/hr

= 75 x 0.447 m/s (as 1 mph = 0.447 m/s)

Velocity of rock = 33.53 m/s.

Then,

Linear Momentum of rock (p) = Mass x Velocity

= mV

= 0.737 Kg x 33.53 m/s

= 24.71 Kg.m/s

By De Broglie Hypothesis,

= h/p

h = Plack's constant = 6.626 x 10^-34 J.s = 6.626 x 10^-34 Kg.m²/s

p = 24.71 Kg.m/s

Using these values in above eq.

   = (6.626x10^-34 Kg.m²/s) / (24.71 Kg.m/s)

   = 2.68 x 10^-35 m

Wavelength of rock is 2.68 x 10^-35 m.

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