Question

A question of long-standing interest has been the motion and reactions of atomic oxygen along the surface of aluminum crystals. Assume that a typical speed for the O atom is 8 ⋅ 10^5 cm/s and the typical distance traveled along the surface is 40 Å. 1 amu = 1.661 ⋅ 10^-27 kg h = 6.626 ⋅ 10^-34 Js

Part A Determine the de Broglie wavelength of the O atom.

Express your answer to one significant figure and include the appropriate units. λdB =

Part B

Is quantum mechanics critical to the analysis?

yes or no

Answer 1

de Broglie wavelength  λ = h/mv

h =  6.626 ⋅ 10^-34 Js

m = mass of Oxygen atom = 16 amu = 16 x 1.661 ⋅ 10^-27 kg

v = speed of Oxygen atom = 8 ⋅ 10^5 cm/s = 8 ⋅ 10^3 m/s

Then, de Broglie wavelength of the O atom

λ = h/mv

= [6.626 ⋅ 10^-34 Js] / [ 16 x 1.661 ⋅ 10^-27 kg x 8 ⋅ 10^3 m/s ]

= 0.03 x 10^-10 m

   λ = 0.03 x 10^-10 m

Therefore,  de Broglie wavelength of the O atom = 0.03 x 10^-10 m

Is quantum mechanics critical to the analysis?

No