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Problem On page 217: Determine the de Broglie wavelength of an oxygen molecule moving at a speed of 50,000. cm/s.
Subject Wave-Particle duality, Fine: pages 186-191
Solution The de Broglie wavelength follows directly from the de Broglie relationship on page 187, which relates the (de Broglie) wavelength (l) to the mass and velocity (ie. the momentum) of the particle. It also uses the Planck constant (see page 168 or 171) h:
| m v = |
h
l
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, or equivalent: l = |
h
m v
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The Planck constant is h = 6.626 ×10-34 J·s (see, for example, the caption of the equation). The velocity is given as 50,000. cm/s , which is equal to 500.00 m·s-1. The mass of the oxygen molecule is twice the mass of the oxygen atom (see for example BINAS) which is 15.9994 amu (and 1 amu = 1.66×10-24 g; BINAS):
| mO2 = 2 ·15.9994 amu = 53.1180 ×10-24 g, |
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so that we get a value of
| l = |
6.626 ×10-34 J·s
500.00 m·s-1 · 53.1180 ×10-24 g
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= 2493 ·10-12 m = 0.2493 Å. |
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