Wednesday, December 23, 2009

What is the de Broglie wavelength of a 300g object moving @ velocity of 50m/second (about 100mph)?

The de Broglie wavelength W of an object with momentum p is





W = h / p,





where h is Planck's constant ( http://en.wikipedia.org/wiki/Planck%27s_鈥?/a> ). So, we need the momentum, which for a particle with mass m and velocity v is





p = m * v





non-relativistically, and





p = gamma * m * v = m * v / sqrt[ 1 - (v / c)^2 ]





relativistically, where





gamma = 1 / sqrt[ 1 - (v / c)^2 ]





is the Lorentz factor ( http://en.wikipedia.org/wiki/Lorentz_fac鈥?/a> ) and c is the speed of light ( http://en.wikipedia.org/wiki/Speed_of_li鈥?/a> ).





Since the speed you're given is very small compared to c, it won't matter much if you use the non-relativistic formula for p. The larger v is, though, the larger the error in this approximation becomes.
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